What's up guys, welcome to today's video. So today what I wanted to do is walk you guys through a 100% dry haircut. So we're gonna be creating a face frame. We're gonna be creating layering. We're gonna do it all dry. One of my favorite things about this cut today is that there's a ton of movement in the layers. So it's taking something that could be kind of boring, long, just one length haircut and adding a lot of life to it. On this cut, we're gonna do a technique called slide cutting. Now that's just a half close of the scissor.  That creates a really nice texture to the hair. So that's really what this haircut's all about. It's creating texture, creating movement, creating that face frame.  So a ton of techniques packed into this video. Hope you like it. Let's get started. Here we go. All right guys, so we're gonna start off today's technique with the center parting. I wanna create some really cool textured face frame layers starting at that jawline all the way down. So what I'm gonna do is I'm gonna take diagonal forward partings. Again, we're doing this on dry hair. So what I did was I smoothed and polished it out with a paddle brush. First, I used the Ergo paddle brush, the one I love the most. And what I'm gonna do is bring that hair forward and I'm gonna slide from the top down. And what I'm doing when I do this technique is a half open, half close, just really slightly moving that scissor blade down the hair shaft. Now you wanna have really sharp scissors to do this to make sure you get a nice glide over the hair.  What that's doing is removing weight, adding texture, but also creating that face frame at the same time. So removing some length from that as well. So I'm gonna work my way all the way to the ear, now pretty much at vertical sections and again just sliding across and cutting. You can see all the movement that happens just from those three sections, guys. That's why this technique is so cool for me is because you get maximum results with the little effort as you're going in and cutting. So now the next technique that I'm doing here is still slide cutting, half open, half close. I'm just working on the details in right around that face frame. So breaking it up a little bit and taking off just the very end part of the hair. So you can see the pieciness that happens just from that technique. Look at the difference between the one side and the other. That's the goal, guys, removing that weight, creating a texture, creating a movement with this really cool technique. So sliding again across the hair shaft and just working short to long. So it's pretty much like if you would elevate it, point cut it, you're just getting a softer angle on this by doing this technique for this face frame. So again, see the half open, half close. That's a pretty good angle of it. Just sliding down the hair and you can see those shorter pieces and then it gets longer as it falls back off the face. So same thing here, body position right in front of the head. I didn't move from this whole haircut. So I stayed on the same side of the head and just worked my way through. It's a little bit awkward on this side, but not too bad and just kind of pushing that hair forward across the face. So then sliding all the way to the end, taking out that hair. Now again, I go in half open, half close, really detailing, look how it just breaks apart that face frame really creates that peaceiness, super cool look to this cut. So now once I've got that exactly where I want it, now I'm gonna check everything, make sure the balance looks good in the mirror and then I'm gonna start working on the back. Now the back's pretty simple. We're gonna work on a traveling guide, work our way all the way around to the other ear and just slide cutting again. So again, like I said at the very beginning of this video, this is a super easy technique to create a nice textured haircut. Now where this might be a little bit complicated is if you have a guest that comes in really needs a trim, they're not just looking for some extra texture in their haircut. You're gonna wanna do a nice one length haircut or something to get the ends nice and strong, maybe even go through and do a little bit of layering first before you do this dry texturizing technique. So there could be other options in this, but in this particular case, all I needed to do was the slide cutting to create the end result. So again, sliding out from short to long, creating those layers. And do the same thing on the opposite side. So biggest difference is now I'm pushing away from my body to the guideline before I was pulling towards it. A little overhead view so you can see me sliding there and just working my way around. So notice I take a little bit of the old hair, bring in some of the new hair, push the hair away from my body and then I half close the scissor and slide down. So one thing I want you guys to realize is that I stop right where the hairline meets behind the ear so that the density of this cut stays very similar. So just know that. So get to the point where the hairline starts to work its way up and that's when you're gonna stop. And those layers come together from what you cut in the front and what you cut in the back. Now I go through, I get a nice blunt line on the cut so it looks nice and healthy. I do that at the end and I'm gonna go in with the Joico body shake texturizing finisher. There's one for thicker hair and there's one for medium to fine hair. I'm gonna do the medium to fine on this particular haircut because she has medium density hair. I spray it in tons of texture. It also smells like you're at the beach. So if you're feeling like you need to get away at this moment, just spray some of this and you'll be good to go. So here's a fun technique that anybody can do really is a wand iron. So you grab the wand iron and you wrap the hair back off your face for the first section. And then the second section I'm gonna take I'm gonna wrap towards my face. I'm gonna rotate that all the way back to the ear. Now I'm not worried about the back of the head so much at this point. So I'm gonna do both sides just like that. So notice I went forward with this technique here and then I'm gonna go back with the next section. So I just keep rotating that back and forth till I get to the ear. That gives me a tousled texture. It works out really well. I also wanna try to get the ends nice and kind of straighter feeling. So it's more of a lived in look rather than a whole curl. So I leave a little bit of the ends out. I pinch those in my finger and I just work the back of the hair. You'll see me work it all the way around. And this is all the same direction because I don't care as much about the back. Can't see the back anyways, right? When you're in the mirror.  So that face frame, that texture that we created I'm gonna grab an extra piece and just give it a little extra curl off the face. You guys can see all the movement that happens in this haircut. If you like the color too, I just put out a color video. So go check that out. So how to do this kind of honey blonde, buttery blonde highlight using the new Joyco 9NNG and 10NNG. So hope you guys like it. We'll finish it off with a little bit of spray. Just take it off of her face a little bit. You can see those lived in ends, that texture, the movement, really love this. Let me know if you guys have questions in the comments below. Also make sure you subscribe to the channel. There's new videos coming out all the time and anytime you complete one of these haircuts or do one of these haircuts, hashtag free salon education on Instagram so I can see it. And the last thing I want you to do is go out and download our brand new app.


I hope they don't break them. She's sick. What's in your bag? What's in there? You take the one out of there. Cash, you want that one? Cash, go in your bag. Open your present. Open your present. What's in there? What's in there? Hello. What is that, buddy? What did you get? Oh, that's the big one. Oh, that's them. What is that? Who's in there? Can I have your pippies so I can hear you? Thank you. Push the buttons. Oh, push the buttons. Has it already got VHG? His head even moves. He goes like this. You know why you got a present? Hey. Can you look at mommy? Can you look at mommy? Do you know why you got a present? Because it's your birthday. And on your birthday, you get presents. Smile big. I'm getting it on video. Are you Buzz Lightyear? You want to play with Buzz? The vlog. Today is Cash's second birthday. So I'm doing a vlog of his birthday party. So that I can have it to look back on to remember this day and to just share it with all of you guys. So I'm going to quickly just do a quick party tour and show you guys all the decorations. We are not Pinterest people. We don't try to be Pinterest people. We just try to keep it real and keep it fun and keep it cheap. So I will show you guys everything right now. All right, so when you first walk in the house, you have all the paper products here ready to go because we are going to have pizza. And then I have gift bags ready to go. I got each kid a page of tattoos. Army guys, I got little green bags. And then we have a pinata with candy. And then we have rexie here making sure everything stays together. The theme is toy story if you guys couldn't tell. And then we have here some chips and dip. This is just fabric from Joanne's. My mom bought it to make a tablecloth. So she made these little extra bandanas. So we're using them as like a place setting. And then this is the table. And it's so cute. We're going to put Cache's cake right here. But I will eat this bringing it. So we're going to put it there once it's done. This is a slinky lamp that came from Cache's playroom. We're just going to keep it here. I don't think I'm going to have it on. Just because I don't want to waste the battery. And then we have his little first year book here for people to look through if they want. We have Buzz and Woody holding balloons. Some more army guys for decoration around the cake. And then obviously the candle. And then going on in the living room we have some streamers and some balloons. And we have our little alien friends hanging from the balloons. We're going to watch Toy Story while the party's going on. This little table we brought out for gifts. And then we moved our ottoman out so that we have more space for seating. Outside is the party zone. Hi, boogie. Look at his shirt. Can we see your shirt? Oh, you got some veggie sticks. So we put his pool out here with ice and it's totally holding all the drinks. And then we just have some snacks out here. Some popcorn. And I put it under this net because the flies because there is like the caramel corn in there. So we just have some more toys hanging out. We've got our little bar top for people if they want to sit. We've got some more balloons and the jump jump. And Savannah is already here playing with him. And then this is just the rest of the party just more space for people to sit and hang out. This jump jump so cool it has a basketball hoop. You guys, my mom had back surgery I don't know if you know this but she was broken in half for a while. You look so pretty. Your eyelashes look great. I just did my makeup for the first time in like six weeks. You did? Wow. I'm laying around recovering.  Look at her cute shirt. So that is the party you guys. That's how we decorated. Very minimal but it's good enough for a little two year old. So also I'll have to show you guys our shirts. So my mom actually made here I'm going to go into better light. My mom made these shirts. Well I made half of it. So we bought the shirts at Walmart and then she cut out the two part and then I did with my cricket and iron on vinyl the infinity and beyond. So Scott and I are all wearing them and we're just going to have a great day. So I'm going to try to pick this camera up as much as possible. Film everything from cake to presents to playing as much as possible without losing time in the moment. So Scott and I will both be picking the camera up. Mom will pick the camera up. Maybe Savannah will pick the camera up. Whoever sees the camera sitting still has to pick it up and film it. Okay, deal. Boogie How old are you? How old are you? Say I'm two. How old are you? This is pretty nice of you. How old are you? Say I'm two. Is that your juice? Is that empty Sissy? Isn't she the best? Hey How old are you? Say I'm two. Go put it in the trash. Let's put it in the trash can. No. Okay, fine.


Okay, so today I will continue using the notions we introduced last time. So essentially we had, we had introduced the metric structure we will use for the entire course in the complex, in the extended complex plane. We introduced a notion of convergence of series and we also observed that given a sequence of complex numbers, we can also consider, put it this, it's very difficult to see. Oh, is it very difficult? Okay, so if we have a sequence of complex numbers, we have the notion of convergence of the sequence and we also consider the sequence of sums up to the nth element. This is also a sequence of complex numbers, right? So we consider this sequence as well and we can also say that this sequence is convergent or not. If this is the case, we define the limit to be this. Okay, I can also put zero here so I put zero, okay? And we call it a series. So the infinite sum is, if it exists and is a complex number, not infinite. The limit is n tends to plus infinity of Sn. When this is a finite number, okay? When this series converges. We have the possibility to check if the series convergent using, for instance, the Cauchy criterion. We know that the metric space we have is complete, so we can check it. Good. I want to leave you as an exercise that if summation of Zk exists equivalently, if the limit of the partial sums is finite, then the nth element tends to zero. It cannot increase. It actually tends to zero, right? Sn tends to infinity. The sums are made with the elements which are infinitesimal. Good. So this is an exercise. Together with the notion of convergence of series, we also have the convergence of the associated real series. That is to say, we can also consider the series of the modules of Zk. And this is, since Zk is a real number, this is a series over the reals. If this exists, then we say that the series is absolutely convergent, okay? Or in absolute value. That's the reason why it's called absolutely convergence, okay? This notion is important because we can prove the following fact. Proposition. This is lesson 3, page 2. So if Zk is absolutely convergent, then it is convergent. There's nothing special in some sense. This is the same as in the real case. And the reason, say, very sketchy proof is the following. Well, we have to consider the convergence of what? Sorry. The convergence of this series, Z naught plus Zn. Of this sequence, right? On the other hand, we know that this, sorry, this is convergent by assumption. So to prove that the series is convergent, that is to say that the sequence of Sn, the partial sum, say it's convergent, suffices to prove that it satisfies this inequality for Nm greater than a certain m. But what is this? So if we prove this, we have the assertion. But what is this? Well, this is summation, say, assume that n is smaller than m k from n to m, okay, of Sn, you correct, correct. Sorry, if n is great, n is smaller than m, so we have exactly the opposite, right? m plus 1 to n, right? So we have a, sorry, Zk, okay, and this is a finite sum. And because of the triangle inequality, we can say that this is smaller or equal to this, n plus 1. Okay, I'm sorry. n is smaller than m, right? So we are summing from n plus 1 to m. n plus 1. Sorry, sorry, sorry, sorry, yes, sure. Thank you. Yes, n plus 1 to m, correct. And this is, in fact, smaller than epsilon, okay, because of the previous exercise if you want. So we have this check. So absolute convergence guarantees convergence, as in the real case, good. Okay, so now we go back to some notion which is real and is the following. Consider a sequence of real numbers. As you all know, this is not always the case that the sequence is either convergent or convergent. There are some other possibilities. If you don't add any other hypothesis, you can have that the sequence, for instance, minus 1, plus 1, minus 1, plus 1, plus 1, plus 1, has no limit on one side. On the other, it's not divergent. So there are some criteria for this. Monotonicity guarantees, for instance, that exist another limit, finite if the set is finite or infinite. So convergence or divergence of the sequence. In any case, we can define, and it has always meaning the lim soup and lim inf of this sequence. These two numbers always exist, possibly being plus infinity and minus infinity. And if the limit exists, lim soup and lim inf coincide. Good. So lim inf is, I will use lim soup actually more, also indicating this way which I don't like for obvious reasons in some books like this. And lim inf is, I don't like this because there is some, well, can be misleading with the conjugate. We prefer to use the overline only for conjugation. In any case, I think that you have the, well, this is limit of Rn. In any case, this is the lim as n times plus infinity of the soup, right? Lim soup is the limit of the soup, yes, of Rn, Rn plus 1, that's it. And here is the lim as n times the plus infinity of the inferior. That's why this is lim inf, okay, Rn. So we always have that this number exists, these two numbers exist, and this is greater or equal to this, okay? All right.  Yes, please. This is the real, okay? In real analysis, nothing. No, no, no. I'm just, I'm just recalling you some facts from real analysis, nothing special. Well, we can use, we can use, if you want to know why, and I recall, well, I don't want to, as I said, I don't want to bother you with properties of some of sequences. I want to use this lim soup for the sequences of the modules of complex numbers, okay? So, in order to apply the properties of real numbers, and you will see in a few minutes, the reason why, okay? I just want you to recall, okay, this problem, and just to have something put here. So, indeed, what I want to start from is a following. We have considered sum of complex numbers. So, starting from a sequence of numbers, we have the sums of these numbers, and this gives you another sequence of complex numbers, and we consider the converges of the second sequence of complex numbers. Now, we can also think of a sequence of functions of complex value functions, all right? And then sum them, because you can sum, okay, the complex numbers. Now, the point is, if the function depends on a complex number, is it always the case, choosing z in the complex realm, that the series of the sums is convergent? This is not always true, as we'll see. So, the next task is to define, so to describe in which set z can be taken in order to have convergence of sequence of sums of complex value functions. So, before continuing, let me just recall you another inspiring, in some sense, the fundamental examples we all know, probably. So, let me recall you that from the real, then you change a little bit. We have this sequence called ak to be z to the power k, k natural numbers. This is meaningful, because we can multiply z times zk times. So, this is nothing but z times z k times. Which means that this is the case power, okay? So, associated to this sequence of ak's, we also have sn, which is the sum of 1, which is z naught, a naught, sorry, z to the power 0, plus z, plus z squared, plus zm, correct? And we wonder if we can express this, and this is one of the few cases where you can do this, this sum, this sequence of sums in terms of z. And as you probably all remember, this is 1 minus z, the power n plus 1 over 1 minus z, right? So, that it is much easier than to consider the limit of this sum of objects to consider the limit of this, which is a fraction of complex value functions. So, notice that this is a power of a complex number, there are no coefficients in front. The generalization of this is, of course, to consider something like this, summation of, so, to consider bk to be, say, ak times z minus a to the power k, with ak being complex number, a being something different from 0. So, in the previous example, we have ak, all the ak is equal to 1, a equal to 0, but in some sense, well, the fact that we are considering z minus a instead of z is not very important. We consider, for instance, this change of variables putting w z minus a, we have, well, that bk is ak times w to the power k. So, the great difference is that we put some coefficients in front of the power, okay? And this coefficient is, in general, complex, not necessarily real, okay? So, what do we know about convergence of the series Sn written here? By the way, you probably all heard of the legend or legend of story, actually, or it's not a legend, it's a story. This formula was obtained by Gauss when he was very young, right? Okay, good, good to know, okay, this. And it can be, in fact, obtained as he did by considering that, well, if you take, well, let me make this small regression, if you consider Sn like here, so I copy this, and if you consider Sn plus 1, it's the same, right? Up to, then you multiply by z this, and you obtain everything from here to here, correct? So, then you make the subtract, and you obtain this formula here. This is the idea, because Gauss was asked to sum up to the first, sure, sure, of course, he was very young, he didn't have, well, but the same procedure works fine, but because he was bothering the teacher, right? Because he was very smart in calculations, and so the teacher said, okay, now sum up the numbers from one to five thousand, and he answered immediately, so how do you do this? Well, there's a general formula, say, good to know this, okay. Anyway, so here, in this expression, it is evident that this number can be very big or very small in modulus according to the fact that the modulus of z is greater than one or smaller than one, correct? Remember that we have, we're not, I'm not cheating you, okay? We're not abusing any formula up to now, because we have the Moir formula, okay? You can see this. Since the modulus of a number smaller than one is smaller than one, and the nth power of this number is the nth power, sorry, the nth power has a modulus, which is the nth power of the modulus, this decreases if the modulus of a starting number is smaller than one, correct? This is real analysis, and if it is greater than one in modulus, this number, okay, of course, this number, this real number increases, and so it cannot convert as a complex number as well. Remember that we have characterized the zero in the complex number as the complex number with zero modulus. It's the only number with zero modulus. So if we prove that the modulus tends to zero, it's enough. We don't care if the convergence is in some spiral or on a line, but well, this is important, correct? And on the other hand, if this converges, so this number tends to zero, as it is clear that the condition modulus of this more than one is sufficient to conclude this, well, the limit is one over one minus z, which is meaningful for any z but not for z equal to one. So in some sense, this example shows you the following. So we have found that we can take an open set, a disk, in this case, the disk has radius one, and for any z inside this disk, you have convergence, and you have an explicit expression of the limit of the series. When z as modulus greater than one, the series divergent, nothing can be said about the convergence of the series when the modulus of taking z is equal to one, okay? And in fact, for z equal to one itself, this has no meaning. Let me point out that, of course, this is nothing but, I have to put here three third lesson number four, this is nothing new for you, I guess. And in fact, this was known also for the real numbers, right? Same considerations, and you conclude in the same way. The only point is that in the real numbers, you can see that there is an abstraction to consider, all right, so let me put this way. There is an abstraction when considering complex numbers of modules one in the complex case, and there is an abstraction of taking real numbers of modules one, there are only two, minus one and one, you see this on the Gauss plane, okay? So, and when you restrict to the real case, the same series is convergent when z is real, when z is in here, which is the intersection of the real axis with the unit open disk. And it is also reasonable to say that nothing can be concluded when we take a real number of modules one, because when it is one, in fact, the limit does not exist. With some manipulation, we can also consider as limit this number here, say, assume that when z is real, right, is x instead of z, right? So, we take instead of one minus x to the denominator one plus x, and this can be written as the series where x, okay, is taken. So, take minus z and the previous expression, and you will see that the limit is one over one plus z, when this limit exists, so when modules of x is smaller than one. And, well, up to here, nothing changed. So, instead of having a singularity here, you have a singularity here. Say, well, what's the difference? Well, with another slight modification, you can consider this limit of the series, I'm not mistaken. So, I consider x squared here, so here everything is 2k as a power exponent, sorry. And here, in the real case, you don't see the reason why modules of x has to be smaller than one, because there is no, well, this number never vanishes, never vanishes in the real. Well, it vanishes, of course, in the complex case. It vanishes here and here. So, this is one of the explanations why, considering the real case, you have only a partial view of this phenomenon. Well, just to, okay, anyway, let's go back to the example. And, well, first, let us give this definition, and the definition is the following. So, let us consider the generic case. I want to write it down at least once. So, we said that the example we consider so far is just a simple example of a more general case of series we will consider. And it is the following. This is called power series, and A is called the center of the power series. So, we also say the power is centered complex numbers, okay, where all the elements which appear in this expression are complex, okay, in general. So, the task for our purposes, it would be important to have this information, is to describe when and how and under which condition this has a meaning. This is a number, okay. Given a z, you can obtain, so this is a function. And as I said last time, functions were not rules in the past, but essentially were extension of polynomials, so series, okay. So, the complex case in the complex case, in particular, function were considered as power series. Good. So, there is another interpretation of this series, and I will give it here. So, assume that we have a family of complex valued functions. Nothing is assumed about A, A is a set, okay, and K varies in the natural numbers, okay. Well, we can always consider this series, this, sorry, this, pardon, this sequence summation take an element A in A, so K varies from 0 to N, this is a sum of complex numbers, right. How can we do this? Well, we can do this because C has a structure of group, so we have a sum, you see, and we can sum it. And we consider now this infinite series. So, there are several definitions of convergence for a series of functions. Why are we considering functions? Well, because in the previous, let me go back to the previous notion. We can also interpret this, each of this addendum here, summand, as a function. It is a function, it is complex valued function, definitely, and just by chance it is also a function of a complex variable, okay. So, forget this, and this is the FK in this specific example, right. So, let me give it in the more generic way I can now. So, we have this series. What does it mean that it converges at A? Well, at A it means that the sum, sorry, the sequence Sn has a limit when the sum is evaluated at A. So, it is, okay, A is fixed, we consider FK of A is a complex number, then we consider the associated series. What do we mean when we say point-wise convergence in A? We repeat the same property for any A in A, correct. Now, what do we mean when we say that this series is absolutely convergent at the point A? Well, again, we remember that associated to this series of complex numbers, when FK is evaluated at A, the associated series of moduli is a series of real numbers, study the convergence of this series of real numbers, and then we conclude that if the series of the moduli converges, then the convergence of the series said to be absolute, okay, or in absolute value. There is another convergence which is also very important to know, notionally, the uniform convergence, right? Do you have a notion of uniform convergence? Well, I think that in, also in real analysis fundamental, you say that you probably know that if you have a sequence of continuous functions and you consider the uniform convergence set, of course, a sequence of continuous function on a set, so we have topology and so on, okay, now we are not assuming a day as a topology, but we have to want to have a notion of continuity, okay? So the uniform limit, or the uniform converges guarantees that the limit is, the limit of a sequence of continuous functions is continuous. How do we write uniform convergence in this special case? Well, we can say that the sequence is this uniformly convergent a if for any epsilon positive, and there exists a capital N such that for any N and M greater than N, we have that S N A minus S M A is smaller than epsilon for any A in A, correct? So uniformly means without any dependence from the point A chosen in A. All right. There is another notion, well maybe this terminology can be standard. This is not standard. I think that normal convergence is somehow, or normality property is, because normal comes out in several fields in mathematics. So normally, well in this special definition, it means that you can control each F N of Z as Z varies in a set B with, sorry, F K, with a constant number M K, okay? And M K is of course real number, positive real number, M K has to be positive real number. And we say that, well the sequence, sorry, that the series converges normally if the series associated of M K is convergent in the real sense. And I, well I probably will use it sometimes. And probably we don't need a special definition for this because it is just an application of other comparison theorems to be applied just to have this. In any case, in some books you find it, this is the bias stress M test. The use of letter M is not by chance because normally we call it M test or bias stress M test. So you test that the series of function is convergent using the fact that you know that you can control the moduli of the summands using a constant depending on the index and not depending on Z. When the Z varies in a subset. Last thing I had to say just at the very beginning of this, never use the index I in complex analysis for summations, okay? This is just, it's not compulsory, it's not, but it's warmly recommended, okay? Not to use I. That's why I use K. We use other letters. Of course it's up to you, but don't use I. And it's obvious why, okay? Finally, of course, if the series is not, is not convergent, well it is divergent. And so going back to what we had obtained, let me prove this first important result, okay? So first, consider a power series expansion, okay? Z minus I to the power K, okay? And then consider the number modules of ak, which is a real number, and take the kth root of this number, okay? And define, actually calculate the lim soup. That's why I had to recall you this definition. Lim soup always exists. Lim is not guaranteed, but lim soup exists and it can be plus infinity. Because this number here is non-negative, right? So we have three possibilities. Either this is plus infinity, or it is zero, or it is, or it is a number. Yes, sure. Call it l, right? In any case, we have one of these, one of these results. So the limit lim soup exists. And the first case, we say that r is zero, whatever r will mean, we'll say. Pardon me. When r, when this lim soup is zero, r is plus infinity. And when the lim soup of the case power of ak is l is a finite number, real number, we call that r is one over l, okay? In some sense, this is the definition with the extension for these two cases in the obvious way, okay? So that we can say that one over r is lim soup of ak one over k, as k tends to plus infinity, with the convention that r is zero when this is plus infinity and r is plus infinity, okay? When this limit is zero, correct? So this is an associative number to the power series considered. So the theorem goes back, this is a result due to Hadamard, it's the following. Now, assume you have the power expansion as before and define r to be one over lim soup with the convention with the convention we adopted just so far, right? So r is zero when this number is plus infinity, so the denominator diverges, then r is zero when r is plus infinity means that this number tends to zero. Then this number is in fact a measure of the ray of the of the of the circle center that a for which z has to be considered to have a convergent power expansion. This is the meaning of the symbol r. So if so if z and c is such that modules of z minus a is greater than r, then the series diverges and if z and c is such that z minus a smaller than r, then the series converges and something more is added. If you take, assume that this number here r is positive, so assume that r exists and is positive and take a positive real number between zero and r, you can always do this, then in particular, if r is smaller than capital R and the z minus a is smaller than that end, then the series converges uniformly in this disk. This is the content of Ademar theorem. As we will see, the proof is quite easy and keep in mind the example, the fundamental example and the fundamental example, all ak's, all the coefficients were real, well this is not very important because we are considering the modularity. But we somehow were considered the modules of all this part here and it had to be smaller. So if we had a power, each the base of this power had to be smaller than one to guarantee convergence. In this case, we don't have a power because this is the number times something which is some power.  When you consider the modularity, you are very close to the example given before. So in some sense, we are trying to find a balance of the way this number is increasing with this number, but not this number, this number. This is not the kth power of something, but the modularity of this is the kth power of this. This is the leading idea. Just another small remark, nothing is said about the convergence of the convergence of the series when the modulus of z minus a is equal to r. So when we are like in the case of the fundamental example, precisely on the boundary of the sequence and notice that because of the geometric property we are considering, the modulus does not depend on the argument. We always have disks, something which does not depend on the argument, depends only on the modules. So that's why this r associated to the series, the power series expansion is called radius of convergence. It can be 0, it can be infinite. So in this case, the entire plane is the disk. Otherwise, it is a disk centered at a. And for this z with the property here, this series defines a function. So we are in some sense describing the set where analytic or power, say, complex power expansion exists as functions. When the radius is 0, it means that, well, nothing can be said about convergence except one point. And there are examples. The example, the fundamental example shows you that, well, we have a series where the convergence is guaranteed only in a small radius. And we will show you also examples of functions which are defined on an entire complex plane, which with this terminology have radius of convergence infinite. So now, let us see the proof. And then I give you the examples. Now we are page 3. So first of all, for the sake of simplicity, as I said previously, we can always assume that a is 0. This is not, without loss of generality, we can do this because instead of considering, we can always transform this into akw to the power k where z minus a is w. Geometrically, we are just shifting everything from a to the origin, but the consideration for convergence is independent from shifting. We are taking this or something different, but it is not affected by any translation. So this is just for the sake of simplicity. Good. Now, assume that r is given and take modules of z smaller than r. R positive. We are considering convergence in a disk. So a is 0. So this is exactly the condition we have to prove to be sufficient for convergence of the series. Correct? Good. Since these are two real numbers, we can always take a raw real number such that modules of z is smaller than raw and smaller than r. And we observe that with this choice of r, when 1 over r is smaller than 1 over raw. Remember that 1 over r is the limb soup of the nth root of the ak's. That is to say, there exists a certain n such that for any n greater than n, we have a certain k greater than n that ak has the kth root of its modules smaller than 1 over raw. Now, what do we have? We have, as I said, keep in mind that we are balancing the growth of w, c minus a to the power k, and the growth of the modules of ak, the kth root of 1 over k. So we have a summation of ak zk. Take the modules of the summands. And this is smaller or equal of what? This is smaller or equal of 1 raw to the power n times z to the power k. From this, in fact, we have that modules of ak is smaller than 1 over raw. What do you mean? Yes, definitely. Yes, sure. Good point. Let me remark that, well, of course it's correct. When you consider a series, you are considered an infinite sum. So what is important to control is the infinite part. So call it the tail or whatever. So if you prove that something is converging from a certain n, it's enough because the other summands have a finite sum by definition, correct? So you have only some extra elements to sum, but they are finite. Their contribution can be only finite. So the difficult part to prove is that infinite. Okay, so correct. This is not true in general, let's say k greater than n, but this is enough to guarantee that entire series converges, okay? Why is it converging? We haven't proved that the series converges. Well, so from n to infinity, these numbers are controlled by these other numbers. And this number here, not by accident, on purpose, we have taken, remember, raw to be greater than modules of z. So that this number here is in fact converging, sorry, converging smaller than one, and therefore this series is converging because of the previous considerations, right? This is a real number. So if you want, in this case I can say we can use the m test and prove it. I conclude this, okay? So thank you for the remark. I sometimes abuse the notation and say, well, this is true for any n, for any k greater than n, then for convergence consideration it's enough. So this is, because this is smaller than one for this assumption, then we concluded this is convergent and then absolutely convergent and then convergent. So we have a series of implications which guarantees that the series we started from, the power expansion is in fact convergent. Well, slight modification of the argument applied so far guarantees that, well, if we have, as I said, z smaller than r and smaller than capital R, well, we repeat the same argument putting a raw in between the two r's, same considerations as before and then instead of having the inequalities before, depending on modules of z to the power k, we have modules of r over raw. So this is greater than n and as you see, this is smaller than one because raw is greater than r. So this is convergent because it's a power expansion, sorry, the power series with base smaller than one and as you see here, independently on the choice of z. In the previous consideration, well, we had converges but depending on the modules. And finally, well, the reverse, if z is larger than r, capital R, so it's bigger than the radius of convergence, you put a raw in between, then you obtain the other inequality with something which diverges from below. So you have an estimate like this, summation of a k z k, k greater than or not, is greater than summation of summation raw over r, the power k and this number here is greater than one. So this cannot converge because by comparison of theorem, somehow it's called the lift theorem, this diverges and this diverges. So it cannot be finite, say it this way. Now, this is how to, so up to now we have a criterion to say, well, we can consider power series, complex power series and say when these are functions or not, so we have a domain of definition, it can be empty, it can be one point, it can be a disc, it can be an entire complex plane, but we have something. Now, I'll make you calculate some ragi of convergence. Before continuing, let me recall you that, well, there are some other properties, can be useful, assume that, well, you start from, as we did, such a power expansion and assume that, assume that this limit exists. Yes. No, no, no. Okay. Okay. If I, okay, I have to repeat the question, you know, for some reasons. So, the question is about the consequences of taking C greater than R, right? So, probably I did it quite quickly, but what I'm saying is that if you take Z whose modulus is greater than R, you can always have such an estimate, correct? So, the moduli of the tail of the series cannot be finite because you have an inequality here. Assume that we are considering partial sums. These partial sums here diverge to infinity. What I'm saying is that, well, this implies that the infinite part of the series from certain N to infinity has a modulus which is not finite. You are correct. You are correct, but the series cannot converge. Are you with me or not? So, okay. Now, thank you for the question. Let's go back to the fundamental example, right? The fundamental example is the leading example for, no, it is what we actually use here, right? When you have the sum, remember that this is 1 minus Z, and you want to prove convergence of this function here. We are considering Z, it has to be smaller than 1. Otherwise, the modulus of this number here is divergent. Look, look, we can reduce, we can reduce the general problem to this situation. Probably, I didn't write it explicitly, so maybe it is worth repeating it. When you have this, okay, we started with this example, okay? The basic example was the following. Correct? And for this, everything is understood. Modules of Z greater than 1, no, convergence. Modules of Z is smaller than 1, convergence. Modules of Z equal to 1, nothing can be said, okay? Now, we somehow generalize this position by taking this. Well, the fact that we are already assuming that A is equal to Z, so the center is 0, is not important for our consideration, right? Because the radius doesn't depend on the center. Good. Now, call A, K, Z, okay? Now, we have to reproduce something, okay? So, the modulus over K Z power K, okay? I want it right this way, okay? A K, 1 over K, Z. Can I write it this way? So, and this is, call it the modulus of W. So, consideration given before is independent of the argument, and let's explain you why the radius of convergence is related to the limb soup of this number. If it is smaller than 1, greater than 1, okay? So, greater than this number or smaller than this number, which guarantees, okay? Maybe if you don't mind, okay? If I'm not convincing you, it's better if we have an extra talk somewhere later, okay? Okay. So, let me continue. Yeah, it was the kind of exercise I wanted to leave you. So, assume that this limit exists, okay? And, well, show that L is the radius of convergence. This is the ratio test for convergence, right? Okay? But if for you it's a nobule consequence, well, it's okay. Maybe for some, sure, that's what I, what I tried exactly, okay? Now, we have some, we have some time, okay? In 20 minutes, I want to give you an example of a series whose radius of convergence is plus infinity. We have an example of a series, a series which exists and is converging only for this smaller than certain value, finite value. And, well, the example I'm thinking about is, well, the complex exponential. How can we, well, it is a very important function in complex analysis. How can we define complex exponential? So, we have, of course, the notion of complex, sorry, of a real exponential function. We can introduce the exponential in several ways. But essentially, we can characterize the exponential in this way. So, it is the only function which has this property, x is equal to x. And, okay? So, this characterizes, well, this is a fact differential equation. And this implies that f of x is e to the power x. Now, from the, from this definition, we also know that e of x is real analytic, correct? And it has an expansion. What's the expansion of e of x? So, the exponential somehow, I also use this notation is 1 plus x plus x square over 2 factorial plus x n over n factorial plus so forth. So, when you don't know what to do in general, well, start to test what you have in mind from the real case and simply substitute the x with the z, okay? And try. So, I wonder if I'm doing a mistake considering, say, x is a capital E, okay, to distinguish the other of z to be an extension over the complex numbers in this way. I consider, well, this is, in fact, it's a power series, all right? Summations of xk over k factorial, correct? And, well, I just wonder if doing this, I'm doing something silly or not. This is power expansion, a complex power expansion, for sure. No, no problem. Center dot the origin, good. Coefficients are real. So, it's in particular, say, we have that ak is 1 over k factorial. So, what is the limb soup of modules of ak? Well, modules of ak is ak in this case, because ak is real and positive. What is the limb soup of modules of ak? Okay, what is that? Well, this is the limb soup of k of 1 over k-th root of k-th factorial. So, factorial is faster than the root, so, by a comparison argument, we can conclude that this number here, the denominator, diverges. So, that this limb soup is 0. And hence, the radius of convergence of the function x per z is plus infinity. So, it's entire, and as you can see, it is, well, it is well defined. So, for any z, you can define a function, sorry, for any z, it has a meaning to consider the function x z as defined here, correct? What you cannot do at this stage is to prove or to look for a similar condition, that a similar condition holds for the complex explanation, because we still don't have any notion of derivative. We see that, well, of course, this condition is true, which means that the first coefficient is 1, a naught is 1, okay? But nothing can be said about the second. So, they're the first, sorry, the other one, correct? So, before continuing, let me just use this notation for the sequel, okay? Let us start from a series, power series, general one, okay? And assume that it has radius of convergence r. We have examples, but this set is not empty. Now, we consider another series. From this, we obtain another one, which is called, which was called by the first researchers in this field, the derived power series, derived. So, it is derived from this one, okay? Derived power series. Given this power series with radius of convergence r, the derived power series is the following. Summation for k, and then we consider k, a k, z minus a, k minus 1, okay? Sorry. Yeah, we have k greater or equal to 0. And here, the derived series, power series as index is going from 1 to infinity. This is, well, this is historically the introduction of the right power series. What do we know about the radius of convergence of this derived power series? Is it the same? Yes, it is. Luckily, because I hope that everybody remembers that this series, this, sorry, this sequence tends to 1. Because of this, we conclude that the derived power series has radius convergence r. So, the same radius of convergence of the power series we started from, which was called the primitive power series, okay? So, this terminology, of course, went in use also in other, in other, but now we want to show that, well, it's not by chance that these are called derived and primitive. So, you expect that it is a relation with some analytic operation on functions, which mean, which are supposed to be the natural one. So, derivation and integration, right? So, you say primitive of a function, a function which is the property whose its derivative is the function, the given function, vice versa. The derived function is the derivative of another one. Now, and this is exactly the case in complex analysis, as we will see. Surprisingly enough, this is the case. So, first, let me observe that the derived power series is obtained by derivating whatever it means, the term by term. So, if you apply just what you know from the real case and say, I want to consider, this is a power and I apply the rule of derivation of a power without knowing a z is a real number, complex or whatever, modify the exponent, subtract one to the exponent, right? And multiply the coefficient by k. So, it is the, I would say the term by term derivation of a power series. I want to show you that the derived power series is in fact the derivative of this function. When it exists, it is a meaning, while it is complex differentiable in the sense that the limit of the incremental ratio exists. And the two notions coincide. So, we consider, use this notation, f of z to be the starting power series, which is a function when z is such that z minus a is smaller than r. So, assume that we have power series expansion. We can calculate the radius of convergence. Then, we take z such that z minus a is smaller, modus is smaller than r. And this defines a function for any z. And this disk, you have an output, which is a complex number. Now, we define also f1 of z to be this other series expansion, the derived series expansion, which exists as a function, complex value function, when z is in the same disk as you observed before. And then, the next task is to consider this incremental ratio of f when z minus a is smaller than r and z not minus a is smaller than r. Otherwise, it doesn't have any meaning. What does it mean? Well, it means that as soon as z is different from z not, this number can be calculated, because it is the quotient of two complex numbers. This is a complex number. This is a complex number different from zero. Well, we can calculate this and it is a function. Now, f of z can be also written this way, summation of the first nth terms and then the tail. So, I consider a0 plus a1 z minus a plus a2 z minus a square plus am z minus a to the power n. And this is polynomial of the first n terms in the power expansion. And unfortunately, well, we call it sn of z. And then we remember that, of course, this is not always the case. Well, it can be that we are considering a polynomial, but in general, we have an infinite power function. So, an infinite power series, sorry. And then we consider the rest to be denoted by rn of z. What is rn of z? rn of z is f of z minus sn of z. So, just to come back to what you pointed out before, in this case, we know that this series converges when z minus a as modules more than r. But what we have to control in case we had to is this part, the modules of this, not the modules of this, because this gives you just a finite contribution to the sum. So, I don't think we can complete the proof, but just to give you an idea, let us consider this. So, when I write f of z minus f of z0 over z minus z0, I'm actually writing sn of ze plus rn of ze with the notation so far introduced. So, the sum up to the nth term plus tail, I call it tail, because normally it's the infinite part minus sn of z minus rn of z0 over z minus z0. And I can also write it in this way sn of z, sorry, z0, right? Minus sn of z0 over z minus z0 plus rn of z minus rn of z0 over z minus z0. Nothing special. Using the notation sn and rn for f, what is the relationship with the function f1 of z that the derived function? The derived function was, sorry, the derived power series is the one obtained this way. First of all, I recall that f1 of z is summation of k a k z minus a k minus 1.  This is another polynomial. Notice the coefficients here. I precisely the first n minus 1 coefficients of f1 of z. So, that f1 of z is the limit as n tends to plus infinity, so s prime n, bless you. So, if we start from this fact, we have that fz minus fz0 over z minus z0 minus f prime of z0. Turns out to be, remember that the first part was this, the incremental ratio of sn, then the incremental ratio of rn. And I can always add and subtract the same amount obtaining the following. So, I added and subtracted this complex number. Remember that z0 is in the radius of convergence in particular of f and this is a polynomial. So, it is completely meaningful. Now, you can notice that this is very close to be similar to what we started in calculus one. And as I said, this is a polynomial. This function here is a polynomial z. So, that in some sense, the terms you have to control is not, the terms are finite. The difficult part to control is this. So, next time we will complete the proof of this. And in fact, we will use an expression for this, for this ratio here and control the modules of this expression and show that this, this modules, this series converges as soon as z and z0 are in the radius of convergence. All right? I forgot to say that of course, all these considerations are, can be repeated without losing any generality for a equal to zero. So, center of the origin. And in case I, I will forget next time, I just say now that from now on, for our consideration, we take a equal to zero. Okay, I stop here. And thank you for your attention. And sorry for the inconvenience of the, the homework, the missing homework except for one of you. This was my fault. I will send it again. Okay? Please answer me back and say I received something. Okay? And then you can read it. Can you read it? Good. All right. So, see you on Tuesday afternoon. Is it correct? Maybe 2 p.m., right? Good.


Never ever feel sorry for yourself.  I'm telling you feeling sorry for yourself is a trap.  Yeah, you can think on what you did wrong. You know, you can create a plan to not do it again, but feeling sorry for yourself is a whole different animal.  Go do your duty.  It's okay. We live in a society. Everything's about turning more emotions, and that's okay. There's two sides of that coin, but there's also a time to turn off your emotions, go fulfill what you set out to do.


Tonight's event will debate what some say is a crisis spurred by the current drug policy regime and the prospects for change. Why is that? Because almost on a daily basis we hear news reports on drug-related violence around the world and if you will the horrors of mass incarceration. We routinely confront health crisis intensified by repressive drug laws and now we see public opinion in fact turning against our current criminal justice-oriented approaches. For example last week I believe there was a poll taking United States that revealed that for the first time ever the majority of citizens support Mariana regulation which in essence means as I was told over lunch means legalization of Mariana. As many of you know Colorado has recently legalized the recreational use of Mariana which now pits actually state law and US federal law and international conventions against each other even creating stark contradictions in multi-level legal regimes and multi-level issues of governance. We now have been functioning in sort of decades of a relatively someone called prohibitionist regime when it comes to drug control. Even though we have one set of conventions if you look at how countries practice or how do they interpret those conventions it actually is somewhat different. The report that we did which was launched last year and you can get a copy on the table downloaded 75,000 times in the first three weeks I am proud to say. I looked at 21 jurisdictions across the world that had adopted some form of decriminalization. That could be decriminalization of cannabis or decriminalization of old drugs. What we wanted to do was to show that if you dot non-criminal sanctions or take a decision not to enforce the criminal law around possession that the sky does not fall in, that drug use does not skyrocket, the 10 year olds don't start shooting up heroin on the streets of our cities. And what we find overwhelmingly that there was no statistically significant increase in levels of drug use in those jurisdictions that had adopted a decriminalized approach. What is important about decriminalization is that it avoids all of those negative associations that we have when we criminalize someone for possession of drugs. So a criminal record and higher impacts on employment, education, just basic life aspirations. There was never any intention to use the criminal justice system as the line of first resistance to the drug problem. The first principle was public health. It so happened in the practice that the criminal justice system was given ascendancy in it and that was wrong. That should not have happened but it has happened. Accepting historical mistakes means that we have to start moving forward with those. So I would suggest that prohibition in itself is not really the right way to frame this debate but it is something which if it's used in shorthand I find that perfectly acceptable. But I think what we need to look at is how we are going to improve the system which undoubtedly has its limitations. I actually am somewhat depressed by the statement that the drug control treaties have been put in place under the public health banner because if that's true then men I think we fail. Because in a sense if you in fact count the current public health costs like the HIV epidemic, like the overdose and all the other issues that people are struggling with then I think we really have not done a good job. That's sort of what I walk out of here with. And another issue is that my concern is that whatever was put in place potentially is making things not only not better but worse. The biggest weaknesses of the system and we went out in public and wrote them down in our World Drug Report in 2008 was that there were unintended consequences of the way the system was implemented. It created a huge criminal black market. It stigmatized users. It treated users as criminals rather than people suffering from an illness. These are the things in the system that need to be changed. And the biggest weakness was the displacement created in policy in which a system designed to protect public health turned into a system that used punitive law enforcement approaches to reach that end. We can keep the system but change this emphasis is my argument. The unintended consequences and the question to what extent all the problems that we see with drug control and indeed the stigmatization around it, the human rights violations etc. To what extent is that just attributable to wrong implementation of the model or are there fundamentally things wrong in the system itself? I think that it is not only a question of implementation. There are embedded in the treaties. There are a number of issues that have to be repaired because they have directly caused the aberrations. The main issue where in the development of the system it got out of hand was with the obligation to use the criminal system to suppress a number of acts and especially the 88th Convention. The whole language of the 88 treaty is these have to be treated as serious crimes and that is exactly what happened after that, the whole explosion of the incarceration rates. You are talking about the multilateral system and the developments that are coming from South America, particularly Bolivia and if you think about it in the sense of is it possible to think ahead when the UN assemblies on a meeting in 2016 of thinking a framework that is not a multilateral system of consensus of how to deal with this issue but that has a very cultural differentiation of how to agree with these things. The question is, is it possible the coexistence of significantly different regimes next to each other within one continent or within the world? I think that there is too much fear for diversity. If we look at the reality for example that there are still I think 12 or so countries in the world that maintain a strict alcohol prohibition regime. So there is of course a certain and it's not easy for them because everybody around them of course freely trades in alcohol. Now that same issue becomes more complicated in the case of cocaine for example because it is the cannabis market you can still consider to organize, regulate at the national level. But it's like for a country like Guatemala at the moment and they are struggling with it really because of all the violence but they can't regulate the flow of cocaine that comes illegally from the south and goes to an illegal market in the north so what can they regulate about it? And one remark on the tobacco issue because we did do the exercise by looking at the WHO tobacco framework convention and replacing everywhere with said tobacco nicotine with cannabis just to see how that treaty would work for cannabis and remarkably I think it would give a quite good framework for cannabis control. I have a question to Sandeep. What happens if the federal government of the US decides to tolerate the regulatory systems in the states of Colorado and Washington which are clearly not in line with the spirit and letter of the conventions? Is there any further mechanisms the UN system can pressurize the US government to do something? There's very little the UN system can do because first these are decisions to be taken number one by a sovereign member state. Number two it's very clear the US government has frequently said itself that there exists a problem between federal law and what has been decided in these two states. To the extent that the United States needs to maintain its obligations under the single convention this is a matter of domestic jurisdiction which the federal government will have to work out with the state government. Whichever way it's worked out if the United States is domestic drug law has to be changed then that will imply that it comes under some form of being outside the single convention. What the government of the United States will do about that I or nobody else can speculate but the issue is one which will at some point have to be faced either in terms of whether these two states go forward with creating their regulated markets and what the federal government decides about it but it is perfectly clear that it is not consistent with the terms of the single convention to which the United States is a signatory and which by the way the International Narcotics Control Board has already told the United States federal government. And the Narcotics Control Board in the UN system is the one that carries the responsibility for overlooking implementation of the drug treaties. Yeah I would say that I do hope that the momentum that is now happening that it continues to grow it looks likely in the sense that already several other states within the US are working on proposals for the dynamic of this sequence of moments towards the UN guys in 2016. I think a big difference could be whether California already does it in the halfway elections because that would have a huge impact. The moment California would regulate the cannabis market, Mexico the next day will decide to do it as well. And then there is a snowball effect that I think within a decade at least the whole hemisphere would have changed the cannabis policy. But at least if that kind of momentum keeps building up I think then what can come out of the UN guys is not yet the new agreement but is a clear display of the necessity of changing the foundations of the regime. I would be very careful to point out that by the time 2016 happens I will be retired from the United Nations. I hope that I will not follow the trend that I observed over the last five years is that every retired public official becomes a powerful advocate for drug policy reform. Oh please do. We welcome you. I said I hope I won't follow it because I hope I'm speaking honestly as it is and combining my duties as a member of the secretariat which is a servant of member states but you can be a servant with supplication and you can be a servant with integrity and I prefer the latter. So I would argue I would like to see in 2016 and something which we have hoped for for a long time and tried to work towards at least three things. First and foremost the recognition of the point I made earlier is that an exclusively criminal justice approach will not solve the drug problem. And while that may stay in the background the principle public health approach for which the conventions were built has brought back to center stage. The second thing I would like to see is I would like to see an answer to what makes the whole drug control system extremely vulnerable and that is the problem of cannabis. Exactly what Martin said because that shakes up the whole system because the system doesn't know how to deal with cannabis as we've been saying for many, many years. And the third thing that I'd like to see is I'd like to see the stigma removed from drug users so that we can treat them the same way as we treat a diabetic or a person suffering from heart disease who has the right to go into the public health system and get treatment for it and I would like to see a recognition in the system and then in the practice of governments to be able to do this so that we can treat drug users this way. I mean it is about bringing substances all together and having a dangerous substances approach or harmful substances approach that includes alcohol, that includes tobacco, that includes pharmaceutical substances and that we can regulate them more effectively as we've done with tobacco and which is why we have the reduction in it through taxation, regulation and good public health messaging. And prevention, absolutely.


Good morning cyber traders welcome back on this Thursday. Good to see you all good to see you Brad Good to see you rain and everybody on YouTube everyone Facebook. Good to see you back. Well, everyone has a room So I'm making sure we're coming out loud and clear. Good. Good. All right. Well, anyway We've got a little bit of a correction going on right now on calling Calling a little trouble. You gotta keep knowing what it was a news on it The news is on coin for somebody don't know about it Coinbase global shares are trading lower at the company received what a Wells notice from the SEC allegation valid Invalidation of federal security lawsuits in regard to the company spot market and Steak service Whatever that means doesn't sound good because this stock took a nasty hit yesterday from 85 dollars down to 64 You know what? We had a nice little rally on it And you know what even that the stock was down if you looked here on the long-term chart You know, you are big resistance levels right there Anyway, 87 was a big resistance and if you got out just a little bit earlier Guess what you know salvage because all that hard work and all that time look how quickly you can lose it Just like that so you can never trust these stocks and Or options or crypto or anything. That's why you always got to focus on taking a profit But anyway, there were a couple of good stocks that are moving There's actually a really good one that's moving pretty nicely right now You guys see SMX that thing was a five dollar stock went down to a dollar It's on a nice little push this morning. We're gonna check that one out also So there are a couple of good stocks now. Let's talk about what happened yesterday. So what did they do? They raised the Fed rate Okay, now remember what I told you how to trade today to trade the Fed rate when we trade the Fed rate Here's the announcement right here. Let me blow up this chart right here. So here's the Fed announcement, right? Here's the big Fed announcement here at that 230 time frame. So you get that big slingshot that goes on, right? So the stock went from the market went from like a 3200 or 500 went up about 250 points and then sure enough They started thinking about the guy kept chatting away kept talking away kept talking away All of a sudden here you had that slingshot a way down remember I told you we don't really know what the direction the stock market is until about maybe about three o'clock Maybe like a half hour.  What is that literally? Was it 350? Yeah, almost about 300 points. I mean like you could have traded anything anything you could have traded, you know Tesla or you could do it. You could have traded in the video. You could have traded AMD I mean look out of them. They all traded side-by-side. You could trade an apple, you know But this is everything that we talked about You're regarding about the trend is your friend You don't buck that trend now the market is up about a whopping three points Which means that is not a good sign at all. All right But we're gonna keep an eye on it. There's a couple of good stocks that did move You know, we had we had this stock Zora had a great monster Monster rally yesterday. I mean this thing at 10 o'clock was just off the effing charts I mean this thing ran from seven dollars all the way up to 35 Effing dollars. I mean this thing was amazing great was getting halted a lot It started getting crazy and we did find it early in the morning We started seeing this thing starting to make a big move and you could see it now. Are we trading it today? I don't think so. I mean that basically was just something that a lot of us, you know Gotta beat the right place to the right time you could have came a little bit late You knew if you showed up around 12 o'clock one o'clock You still have a nice little run and then it was interesting kind of held there, too It didn't really drop down too much. Let's start again is double top and started backing off coin base We already know about it coins going back on the watch list After what happened this morning So we keep an eye on that coin nugget obviously Benefitted from the news regarding about the interest rates So that stock had a nice little run up, but you know, that was more of a ETF It's kind of hard to trade ETS on the level four because kind of hard to see those levels another stock About putting this back on here Listen, these are old metal stocks. They all did pretty well a G had a really nice push It's a little bit more on the slow side, but um, but I would keep it on and Carvana I mean my god, I don't know what happened yesterday, but look at that pop-up right there I think right at the gate in pre-market thing ran from like 850 Oh, that's about 1080 came right back down and it had a good little move here in the middle of the day But she ended up coming crashing down again, but it wasn't that bad I thought right around this 1030 it started making breaking new high when it broke 920 did pretty well I mean it was good for a good 30 40 50 cents there. All right, so anyway, that's what you missed yesterday Let's don't worry about it Even though, you know, some of you saw the ZR the Zura and you like holy crap where this thing come from But these are the things that why people like day trading, you know, just make our days pay And we kill it but that one is one of those Grand Slam home runs that we find but don't worry There's gonna be other ones that come up. Let's go hop over here and see what's going on in the market Okay, so we got a little bit of a latter effect that's going on this This SMX it I saw a big buyer show up right around this dollar 50. I'll show you right here It's a dollar 50 bit right there. Okay, so we got a little bit of a buyer. It showed up I'm not really seeing it a big big big resistance, but there was this big big seller You could see it right here for over a hundred thousand shares. Yeah, right there. He showed up about a dollar So there is some big big interest in this stock and this is basically where that order is But it looks like it's got a nice little push the stock was you know, not not too long ago It's an IPO. It got really hit pretty hard, but she's on her. She's on her uptrend. So SMX It's making the watch list. Okay Now it's the biggest percentage gain or and so on I saw ADN You know ADN Cheap little stock. I'm not really seeing that many orders out there on ADN It had a really good run up at five o'clock in the morning, which you know, we're not betraying by the morning Um, and she kind of died. So I'm gonna put this on the b-list ADN AV AVSA you can see this thing is starting to come back down 700,000 shares you could see all these pre-markets. They're just not really that much going on there They're all kind of dead. Look at this. We're already Nothing right there. Absolutely not nothing going on right there New York Stock Exchange. I mean on an Azdec on the losers list You know nothing there. That's coin basically. That's probably the warrant right there But you could see coin is going down. So that's obviously pretty nice little short right there And it's not a really good silent. I think you continue to go lower at this Late into the open, you know, so Let me tell you people probably out there are really nervous on that stock right there And and some of them like not like us we could trade in pre-market. So Probably a lot of orders they're seeing that are coming in in the pre-market that they want to get these shorts off before They start filling them now. You got the bank stocks that are moving the bank stocks move pretty decent FRC moving up It's got some good volatility, but you could see it that it's really testing some major support levels the FRC Now I had a I had a dinner reservation. I've had a couple of I met somebody last night I'm talking about the real estate market And what's happening on on wall street happening in New York City happening and maybe in your own town That the occupancy is about 50. So they're expecting to be a big crash now. I'm going to have We're going to start introducing some new classes coming up to how to trade on real estate Okay, because cash is king So whenever one thought like the market was high, there's going to be some really good opportunities out there I'm going to talk a little bit about it if you're looking to buy a multiple home or whatever But we're going to have it in next week or two. We're going to be we're going to bring that in But anyway regarding that That's going to lead into more of the bank banks now From what I heard This is just the beginning Listen, there are a lot of banks out there. Okay I'm talking with the big brand names like the cities in the bed, you know, and the Bank of america is and and and so on and the chases There are the banks out there and they're and a lot of them are getting a little bit You know, we're going to get screwed and what happens is that If a company comes out with bad news, you know what? There's no better time than do it So we're going to keep an eye on some of these bank stocks that are out there If we see in them, they're going to start popping up on our watch list So please make sure you're connected with us. Make sure you're watching what we're doing Make sure you get our alert service because you know what a lot of us miss that great opportunity If there's another opportunity with another another industry of banks that has something to do it together You know here at cyber trade university, we're going to be all over it So it'll be really really uh, want to be focused on that And then obviously pal you know raising interest rates a quarter But it's not what he just registered now. It's what they Projected and what did he say anyway Samuel? I think he said something like they overestimated it even and apparently like raising all these races still not fixing inflation, so That's not the good sign. Anyway, let's get ready for the market open up We got about a little less than 20 minutes.  I'll fill up your coffees. Maybe hit the restroom and like I said, we'll get ready for the open If you're watching here on youtube and facebook, uh, just to let you know everybody we do have I'm going to post up this link right there. You see that little QR code that's popping up on the top left hand corner Just grab your phone and you could scan it right there And we're at 12 o'clock today. I'm going to be doing a an event teaching you how to trade today's markets with level 3 and level 4 And uh, like I said, if you missed it if you're watching this recording You could always watch the recording it will be recorded But you got to register and then for everybody else. Uh, josh is putting up the lesson classes that we got going on at 10 30 So for everyone to hear that's a student of cyber trade university You got the you got the link right there.  All right. Remember got to learn before you could earn Good luck today. Everybody happy trading be safe and uh, like we always say you see something you trade something Uh, you let us know about it. All right, we'll see you all in the trading room in the meantime everybody else We'll see you back here at 12 o'clock. Just make sure you click on that QR code to register


Thief River Falls police are saying that an elderly man who went missing Tuesday morning has been found dead. 80-year-old Orvin Sund was reported missing from his home on the 400 block of Connelly Avenue South around 11am. Tuesday morning, according to authorities, he was wearing a black artichoke jacket and glasses. Around four in the afternoon, someone on the outskirts of Thief River Falls reported that they had seen him. Then late Tuesday night, the Thief River Falls Police Department said they had located Sund. Police say that Sund died of natural causes. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


Pastor Darry Adeboye, the first son of the General Overseer of the Redeemed Christian Church of God, RCCG Pastor Adeboye is dead. Pastor Darry reportedly died in his sleep on Wednesday night in his home in Eckett Aquibom State. Before his death, Pastor Adeboye was a youth provisional pastor in Eckett Aquibom State. G.O. Adeboye had sometime last year during his 42nd birthday, described the deceased as a miracle child.


They told us they're gonna utilize us. It could be any inning. So you just got to be ready and depending on the starter I mean it could be any day, but we feel confident with any of them going in each day. So we'll just take it as it goes Did you expect that they were gonna lean on you as much as they did tonight? I told them in the past. I mean whatever they need in this playoffs I'm willing to give them and they kept asking after each inning am I good am I good and I told them It felt good. So just kept going. What do you think led to your success tonight? Obviously a solid performance two and a third I would say a lot of times getting ahead in the count and just more or less just staying in the zone and I've been a lot better Lately over the last few oddings or so getting back to into the zone and I feel like the last two months of the season I wasn't there. So Having my command back a little bit is definitely gonna help me. So going along the way I want to be able to just you know maintain this and just get it like a rhythm going more or less You pushed you pretty far. Do you think you'll be available for game three? I think so for sure. Yeah with a day off I'll be good But you're feeling going home one one three games in a row home now Yeah, I mean we feel super confident. I mean we're going home to The place that we love playing at and our fans are gonna be just as jacked up as we are and we couldn't have it any other way


My name is Cialing. I'm a volunteer and also a master's student in international development. I really enjoy being part of this conference. It was nice to see people from all around the world and it was very good to see how everyone interacted with each other and especially during dinner that we had a great time together and people are really connected I think. Yeah and I think after Covid I think it's good to bring people back together and that we don't do everything online. I think I spoke to some people about that and they really appreciate it as well. And I would love to be part of something like this in the future as well, if that's possible.


What's up everybody, Jason here from JaspysCaseBrakes.com 2022 Diamond Icons, 1 box break, picker teams number 12 just sold out with this random number block here For the Tigers, White Sox, Mets, Nationals, Orioles, Twins, Guardians and Rockies These are the last teams available, put them all together in a serial number break Everybody gets a random number from 0-9 and of course we distribute the hits out if there is any of these hits that pop up for these teams By the first number on the left side of serial number dash, those are your examples there in the item description Here's the dice roll, let's click dice roll It's a 4 and a 1, 5 times 1, 2, 3, 4, 5 So 5 times, 4, 1, 5 Rub at the top, down to Brian at the bottom 5 times, 1, 2, 3, 4, 5 From 8 down to 1 So Rob you have 8, 6, 5, Travis with 9, Brian with 3, 2, 4 7 for Rob, Christopher, Annie in all redemptions And Brian, Annie 1 on 1s for these teams will be yours And there you go guys, so coming up next in a separate video guys is to break us off Good luck everybody


Hey guys, welcome back to come again. I'm Shannon and today we're gonna be taking a look at the pop movies big trouble in little China number 156 Lightning vinyl figure. So stay tuned All right guys welcome back to come again as I said, I'm Shannon and today We're gonna be going over the Funko Pop pop movies big trouble in little China number 156 lightning from the three storms vinyl figure Excuse the lighting. I'm doing this in my office right now I didn't feel like setting everything up out in the living room or out in the dining room and The lighting isn't the best. So I'm using my camera light Right here or yeah my camera light here plus I've got this bar light Plus I got the lights behind me So let's get into this And as you can see I'm holding up this bar light with a few Funkos So anyway This is lightning and for those of you who don't know the Mortal Kombat character of Raiden the God of Thunder was based on Lightning from big trouble in little China and he is by far one of the best of the three He is the best of the three storms my personal favorite. He's peeking up there On the back you have Jack Burton, which is 151 Gracie law, which is 152 low pan 153 rain, which is 154 Thunder, which is 155 and lightning, which is 156 So let's go and on the side here. You got his display side, which is how I display my pops just to save on room So let's go ahead and open them up and take a look All right, so the clamshell it does Snap together Take a look at the detail on this guy. You got the little bamboo hat here Which is very nice all the attention to detail on it They could have made the hat bigger Because if you recall the three storms sorry, I've got my windows open so you might hear a car or two drive by It's a really nice day out. I don't feel like closing the windows So anyway, they should have made the hats a little bit bigger because if you guys recall They the three storms would kind of look through their hats Or they'd have to tip their heads up to kind of look So yeah, these hats should have really come down to about here and been a lot wider maybe out to here But it's still cool.   It's the only Articulation Funko does on their vinyl figures Very nice figure. I do eventually plan on getting the other two storms I'm not really a huge fan of big trouble in little China. I've seen it a handful of times But I've always liked the three storms. I love the design of them You know And like I said before The Mortal Kombat character Raiden the God of Thunder was actually based on lightning The art the creator of Mortal Kombat and Raiden actually stated so in an interview in a few interviews really You got the little tough that's on top of his head his hat there Very nice It also looks like he's got a dagger in his belt, which I completely missed Anything else No, not really Nice silver paint job Nice paint job all together. I have seen on a few people's reviews of the three storms Oftentimes the strap will the paint will bleed off But this one looks pretty crisp Not too bad. There's a little bit of skin tone bleeding Right there But not too much. It's barely even noticeable Unless you have a really keen eye But overall I'm very happy with this This makes my 19th pop figure that I've got I've got a couple more in the coming in the mail. I've got One coming from my wife for mother's day. She's a big doctor who fan if you guys can't tell this is being filmed The thursday before mother's day and it will probably be released on youtube July I believe sometime in july that's how far ahead I am on pop reviews We do pop reviews every tuesdays They're scheduled So that's how far ahead I am on scheduling pop reviews They're already uploaded. They're just pending They automatically Get a published at about 5 a.m. Central standard time on youtube Uh, so yeah, check it out. Check check out our other pop reviews. They're all Linked to a playlist on comic ed and tv So if you really love pops Just click on the playlist and watch it straight through New pops are added like I said every tuesday, so Yeah So thanks for tuning in guys Come back next tuesday when I will be reviewing the phantom Pop heroes the phantom number 67 vinyl figure and of course lightning has fallen down Take care guys


It's now three years since the Scottish Parliament established a committee specifically tasked with scrutinising the effects of the unfolding welfare reforms on the lives of people in Scotland. Our latest piece of evidence is a major in-depth study which provides an up-to-date snapshot of the financial impact and the sorts of groups affected. For us on the committee, the picture is unambiguous. It's getting harder and it's families who are feeling the most pain. This is the first piece of research that the committee has done which has actually looked at the impact of the welfare changes on individuals and households. It's given us a very grim picture which backs up the anecdotes that we've had from people who have come to the committee to tell us about the problems that they are experiencing. It shows that over £960 million will be lost to individuals and families in Scotland through these changes. That's women, children, disabled people, but it also shows that it's going to be impacting on people who are in work, low-paid people. It's an unacceptable situation that this research indicates, something that shouldn't be happening in a modern society and something we should not accept in the 21st century. The paper is the latest in a series of studies carried out by Sheffield Hallam University for us and involved a massive troll and analysis of data from a range of sources. But the figures are stark. Loan parents with two or more children will lose more than £1,800 per year. For loan parents with one child it's slightly less, £1,700. Couples with two or more children will see £1,480 disappear from their budget. Well, for those with one child it's not much better. And for a single person the annual loss is £490. The work carried out by the committee constitutes a substantial and comprehensive body of work, tracking reforms as they've happened. We on the Welfare Reform Committee hope the evidence and technical research like this latest report, which is freely available to public and experts alike, will be used to stimulate informed public debate on the subject and also to formulate policy in the future. What the evidence shows is that a lot of anecdotal evidence and the experience we have had as elected representatives is that this is having a significant impact on people. It's very frustrating that that doesn't seem to be recognised by the Westminster Government. While the Scottish Government should be commended for mitigating against some of these effects of the welfare reform, it's very regrettable that that mitigation is necessary. What we would want to do is that the people that are making these decisions about the future of people in Scotland take a licence of what the evidence is telling them that this is having significant impact on the most vulnerable in our society. This latest research and other material gathered by the committee can be accessed via our web page and you can join the debate on Facebook or Twitter.