Recall that we were doing normal mode analysis on the one-dimensional linear wave equation and we had found that the eigen mode in the discrete case goes over to an eigen function. We had called the eigen function a of x and we had found that in this case as well the eigen function satisfies an eigen value problem. It comes from an eigen value problem and in this case only for certain values of the frequency will there be non-trivial eigen functions. Because there are particular boundary conditions which have to be satisfied by the eigen modes. So, that will cause only particular value of the frequency to be allowed. Now, we have satisfied the 0 displacement boundary condition at the left boundary that had caused the cost term to drop out. We had also satisfied the 0 displacement condition a of l equal to 0 on the right side that had caused the frequencies to be only certain discrete multiples of square root t by rho into pi by l. Now, as I had told you before if you compare this formula with the one that we had derived earlier by taking the limit of the finite frequency relation and applying capital N going to 0 and small l going to 0, then we had recovered this. This relation as you can see is I have missed this relation as you can see is the same as what we have got there. Now, you can also notice one thing that we do not have a plus minus and that is because I have chosen not to put a plus minus here. Remember that sin m pi is 0 for plus minus 1 plus minus 2 and so on. But I will remember that and when I write down the most general solution, I will add e to the power i omega 1 t and I will also add e to the power minus i omega 1 t. So, if I remember that then I really do not have to put a plus minus here, but one can put that for the sake of correctness. So, now we have found what are the eigen frequencies or rather what are the frequencies of oscillation. There are an incountable infinite number of frequencies which are given by this relation. What do the eigen functions look like? Because the eigen function is dependent on m. So, I am going to put a discrete index m also on the eigen function corresponding to the eigen value omega i and this is given by some constant into sin. Remember that we only have the sin part in the eigen function, the cos part dropped out because of the boundary condition and so we will have and omega m is given by the formula above. So, if I just substitute it, I just obtain m pi x pi. So, the argument of sin has to be non-dimensional. So, this is a m of x, the mth eigen mode. Once again m goes from 1, 2, 3 up to infinity. So, a countably infinite sequence of frequencies and for each such frequency there is a particular shape of oscillation. Now, can we write the most general solution to our linear equation as a linear combination of these eigen functions multiplied by e to the power i omega mt? Yes, we can. We will follow exactly the same structure that we have done earlier. So, we will follow exactly this structure that I have written where I have written it as a sum of n column vectors multiplied by cm into e to the power i omega nt, except that now our summation will not run from 1 to n, but it will run from 1 to infinity because it is a continuous system. So, I can anticipate that the solution to my wave equation, I will write the wave equation here for completeness. Let me write t by rho. This is the equation. We have done a normal mode analysis of this equation subject to the boundary conditions fixed fixed and we have found the eigen frequencies and the eigen functions. Now, we are going to write down the most general solution of this equation for those boundary conditions as so, some constant into the first eigen mode m is equal to 1. So, sin pi x by L into e to the power i omega 1t, omega 1 is given by the formula in the square bracket. You can substitute omega 1 and get square root t by rho into pi by L. But this, you have to add the complex conjugate part of this. So, c 1 bar again the same eigen function that is just a real function. Similarly, c 2 sin 2 pi x by L, the second eigen function into the second plus its complex conjugate. And you can keep writing this all the way up to infinity. So, in general, if you write, if you want to express this in a more compact notation, you could write this as I am taking into account the negative frequencies also to make the expression real. And so, you can write it like this because for every term, every pair the eigen function is common. So, I can pull the eigen function out and write it as a sum of a complex number plus its conjugate. So, that this, the summation is real. And there are infinite such number of such terms in the expression, it is an infinite series. So, now the question is like before we can ask the question, how do we determine these Cms? Cms are in general complex constants like in the finite degree finite number of degrees of freedom case, the Cms have to be determined from initial conditions. Now, how do we specify initial conditions here? You can specify the initial displacement of the string. Remember that in the finite number of degrees of freedom, we were specifying the initial displacement of every mass. If I had two masses, then I had to specify the initial displacement and the initial velocities of both the masses. Here, I have an infinite number of masses or in other words, I have a mass at every point in space or I have a mass at every x. So, I will have to specify the displacement, the initial displacement of the string at every x. So, I will have to specify what is the value of y x comma 0. This in general is going to be a function of x. Let me call it f of x. The general solution which we have anticipated from the finite degree of freedom case has this structure. If I put t equal to 0, then the entire term in the square bracket, the exponentials just go to unity and I recover. What have we found? We have found that whatever is the initial shape of the string. So, you can give it an initial condition. So, this is my string in the Baye state or equilibrium state. So, suppose I give it an initial condition respecting the boundary conditions. This is not a very symmetric perturbation, but it respects the boundary conditions at both ends. It peaks at some value of x and then goes to 0. If I give it that kind of a initial condition and I call this f of x, this function f of x, this just tells me that f of x can be expressed as a Fourier sine series. This is quite interesting because through this process of doing eigenmodes and normal mode analysis, we have discovered the Fourier sine series. You can see that the coefficients of all the sine terms are real because each bracket has a complex number plus its conjugate. So, each of this is real.  Is this enough? Recall that we are looking at a second order system, second order in time. So, it is not enough to just specify the initial displacement of the string at every x. In the finite degree of freedom, we had to specify the position as well as the velocity of every mass at time t equal to 0. We will have to do the same here. So, we also need to specify what is the initial velocity of every point on the string at time t equal to 0. So, we need to specify if I call the velocity as del y by del t, I will indicate that with the subscript. I also need to specify what is yt of x comma 0, the initial velocity of every point in the string.  Now, if you write it out, you can see that this would have the form i omega 1 c 1 minus c 1 bar into sin pi x by l. I am just taking a del y by del t of this expression and then putting t equal to 0 all the way to infinity. You can once again see that i times c 1 minus c 1 bar is a real number, omega 1 is anywhere real, omega 2 is also real. So, i times c 2 minus c 2 bar is again real. So, once again you are getting a Fourier sine series once for f of x and once for g of x. How do we determine the coefficients of this series? If you are familiar with Fourier analysis, you will know that if I give you a function f of x and g of x, if I tell you that it can be expanded in a Fourier sine series, both of them can be expanded in a Fourier sine series with unknown coefficients, you can use what is known as the orthogonality conditions to take the inner product of these functions f of x and g of x with the respective eigen modes one at a time. And that will tell you these inner products will be 0 for all terms in the expansion except one and that taking step by step such inner products will give you the coefficients of these Fourier sine series for both f of x and g of x. So, that formally completes our discussion of normal mode analysis of the one-dimensional wave equation. It would also be interesting to plot to visualize in space just like we had done for the discrete degrees of freedom case or shapes of oscillation. We had plotted what does mode 1 look like, what does mode 2 look like. One can also do the same here, let us do that. So, shapes and so we have seen that our eigen mode AM of x is CM sine and with the corresponding frequency. So, now I can visualize the first mode A1 of x is C sine pi x by L. Let us plot it. So, these are the two walls separated by a distance L. And how would it look like? This is just a sign at x is equal to L, x is equal to 0 is here and if x is equal to L is there, then at x equal to L this goes to pi. So, this is a half sign wave starts from here like this. The CM is not relevant because whatever CM I can choose CM to be plus 1 or minus 1. So, if you multiply this by minus 1 this will get inverted and you will have a negative sign that is also an eigen mode just as we have seen earlier. So, this is mode 1. What is the frequency of this mode? It is square root T by rho pi by L. If you initialize the string by giving f of x to be this shape or some scalar multiple of this shape with 0 velocity everywhere. So, I am choosing in these conditions, I am choosing f of x to be some scalar multiple of sine pi x by L and I am choosing g of x to be 0. So, a 0 velocity everywhere and a displacement which is just proportional to the first mode. Then the string will oscillate purely in the first mode of oscillation and its frequency will be given by the formula that we have written down there. Similarly, what is the second mode? So, a 2 of x c 2 sine 2 pi x by L. So, again I draw the wall separated by distance at the base state at x is equal to L this goes to 2 pi. So, this is a full sine wave this is x is equal to. So, you can see that if you initialize the string like this it will oscillate this is mode 2. So, if you initialize the give the initial shape f of x to be some scalar multiple of this function sine 2 pi x by L with 0 velocity everywhere. It will set up an oscillation these are all standing modes and the frequency would be given by which is just twice of the first mode. Similarly, you can work out all the other modes a 3 a 4 and so on and you can also work out what is omega 3 omega 4 and so on. There is no reason why the system should vibrate only in a pure normal mode. So, in general if you choose your f of x to be an arbitrary but well defined function like something like what I have drawn here then fx will have projections along each eigen mode. The eigen modes are this, this, this and so on and so the coefficients by projection I mean the coefficients are nonzero. The coefficients c 3 plus c bar 3 is nonzero if fx has a projection along the eigen mode sine 3 pi x by L. So, if you choose an arbitrary shape like the one that I have drawn in general you will end up exciting many normal modes simultaneously and the system will vibrate in a superposition of many normal modes. The resultant motion may look extremely complicated and it may not even be periodic in time just as we had seen earlier even in the discrete case. The most important difference is here that we are dealing with an infinite series. Similarly, you can do many things you can start with zero displacement but nonzero velocity. So, you can give fx is equal to 0 but you can choose gx not to be equal to 0. This will also have an effect and depending on which modes you excite the system will vibrate in a linear superposition of each of those modes. An important point to remember is that because these are linear systems each mode behaves independent of the other. The amount of energy that is contained in a given mode is purely determined by initial conditions. If initially if your initial condition does not have projections along a certain mode that mode cannot appear in the system at any later instant of time. This is a property of linear systems. So, now having done our 1D linear wave equation let us go into slightly more complicated examples. We will stretch this discussion of partial differential equations and doing normal mode analysis slightly further because this will introduce us to some of the essential mathematical tools that we will require when we study waves on fluid interfaces because those are all of them are continuous systems and we will be dealing with partial differential equations there. So, in our next example we are going to take the same wave equation but we are going to take our 2D wave equation. So, because now I want to have 2 horizontal directions until now we have only had del square by del x square. Now I want to have del square by del x square and del square by del y square. So, I will choose the dependent variable to be eta instead of y. It represents the displacement in this particular case we will take a membrane. So, let us say we have a membrane. Once again we are going to look at the simplest boundary condition which is the membrane is clamped at all sides. So, we are let us say we are taking a vibrations of a square clamped membrane. So, by clamped I mean it is attached on all four sides. So, let us say this is the x axis, the y axis and the z axis and the membrane is something like this. So, this is my membrane and let us say the coordinates of this point is 1, x is equal to 1, y equal to 0, z is equal to 0. If this is x equal to 1, y equal to 1, z is equal to 0. This is x equal to 0, y equal to 1, z is equal to 0 and this is the origin. So, my membrane is clamped at all sides at its edges and it is under tension. So, in the equilibrium state or the base state this is an elastic membrane you can think of a tabla membrane we will after this we will soon do the actual case of a tabla membrane where the membrane is circular. So, membrane is under the membrane is flat in the base state and it is under tension. So, you can intuitively see that if I give it a kick it will start vibrating. The equation one can derive it, but I am just going to use the same equation that we have derived and I will call the displacement in the vertical direction of this membrane as eta. So, eta by definition can only depend on x, y and t, it cannot depend on z because eta itself is the displacement in the z direction. So, eta is a function of x, y and t and eta is governed. One can also show this by doing a force balance of a certain part of the membrane applying Newton second law and then doing a small displacement approximation. We are going to avoid that process and we are just going to use the same equation written in coordinate free notation. So, I have told earlier that the wave equation is governed by eta tt is equal to c square eta xx. Now, in this case eta is a function of x, y. So, it will be grad square eta where grad square is the scalar Laplacian. So, grad square in this case would be del square by del x square plus del square by del y square the 2D scalar Laplacian. So, that is my governing equation. Once again the wave equation the only difference being that I have two spatial dimensions x and y and so this is a partial differential equation with three independent variables x, y and t. Once again we can do a normal mode analysis on the base state because we expect oscillatory solutions. So, I am going to write eta of x, y, t like before is going to be my normal modes a of x, y into e to the power i omega t. This is my normal. Now, what do I do? I substitute as usual I substitute this into the governing equation. Now, before I do that I would like to do one process which is called variable separation. This comes because of the coordinate system and the boundary conditions which have been specified. The membrane is clamped from all sides and so the nature of the boundary condition as well as this particular coordinate system allows me to do variable separation. I hope all of you have seen variable separable solutions of the Laplace equation. This will be in the same spirit. If ASO with variable separation in mind we are going to say that Axy is a variable separable can be written in a variable separable form. So, it is some function capital X of small x and capital Y of small y. So, this is my variable separable assumption and so my problem of determining my eigen modes or the eigen functions. So, instead of having you can see that because my eigen function here was A of x, y. If I did not do this variable separation, my equation governing A of x, y would continue to be a partial differential equation. This variable separation technique allows me to split it into x which is a function of small x alone and capital Y which is a function of small y alone and derive separate equations for capital X and capital Y. Those will be ordinary differential equations and that is one of the advantages. Now, if we substitute this into the governing equation, we would obtain. So, if we substitute this form of A of x, y into e to the power i omega t into the governing equation, we obtain minus omega square capital X, capital Y into c square y, this is x. And if I divide throughout by x, y, then I can write it as 1 by x t square x by dx square plus 1 by y d square y by dy square plus omega by c whole square is equal to 0. We are going to analyze this equation using variable separation arguments in my next video.


Hey everybody, it's Hari Swaminathan from option tiger.com. It's Friday, July 12th and I wanted to show the swing trade signal service and this I've added this new indicator here called the custom RSI so the regular RSI indicator actually tells you when something gets overbought or oversold however this indicator has been customized and when it goes into into this zone what I call the bullish zone it is likely to remain there for a while but you know obviously it cannot do that every time but what I'm saying is if you take a bullish trade you're likely to remain in the trade for much longer thereby you're maximizing your profits so whether it's on the downside or the upside you're likely to stay in the trade for much longer. Now in the swing trade signal service I just introduced this last week and I was testing it before that it's working very well and so some of the trades that we had in the last one week I think Costco was one of them where we took the trade somewhere here and then we hang on to the trade for about a week or so and when it came to the 268, 269 level we exited because we had a great profit but you know if you had looked at the custom RSI it was telling you to remain in the trade from somewhere here itself. Granted there was a little bit of a dip over here and maybe we would have hedged a position but regardless it's completely in the bullish zone. So this blue area is the bullish zone the red area is the bearish zone and whether you take a call trade or a put trade the custom RSI really gives you a fantastic insight into when to exit the trade. So this is actually very critical because many a time we leave money on the table and this custom RSI actually maximizes the ability to make profits on your trade. The custom RSI indicator is also going to be used in the proprietary swing trading signal services and it can also be bought as an algorithm so if you're interested in the custom RSI indicator please send us an email at info at optiontiger.com. If you're interested in the swing trading signal service you can come to the OptinTiger website right here and if you click on the algorithm based swing trading signals that will take you into the swing trading page and then you have two options here you can get in for the monthly service or there is now a new annual plan which will give it to you for 99 dollars per month effectively but this will be an annual plan but if you have any questions you can send us an email at info at optiontiger.com. Thank you.


I'm a professor. Hi! Congratulations! Thank you very much. Very nice to come by. I'm very happy. I'm still, still can't believe. Yeah. Well, just goes to show, I guess, that, you know, somebody has to win. Yeah. This morning at my class, 9 a.m., I went to my class, and then the whole news. David Kahrt, winner of the Nobel Prize, and I was so happy. So I just wanted to drop by and say big congratulations. Being a Berkeley Economics major, this is one of the best news yet. I've been in classes with so many professors, and they all brought up David Kahrt's of examples and papers, and I've always studied him, like, in my classes or along my full years. And this news is just amazing. I'll be, I've been messaging people already at home and all over the place, and I'm still, I'll still be doing that the whole day today. He's one of my main advisors. I talk to him really often, like, every time that I have a question about my data, about the things that I'm trying to, to take a look at. Every time that we schedule a meeting for 10 minutes, 10, 15 minutes, we end up talking about one hour, one hour and a half. And I think that's something that happens with most students. Once you get time to talk to him, he really cares about the details. He really cares about what you're doing, and he really cares about getting the whole story and also discussing the whole thing that you're doing, because it's not only about the minimal detail, but it's also about the big picture of what you're understanding and what you're trying to find these whole five years, six years in Berkeley, which has been the best experience of my life. And having the opportunity to meet people like David has been one of the most wonderful experiences here. I think what impresses me the most about his research is that it sometimes it runs counter to normal economic intuition. And so I think he just takes the question to the data and see what the data says. And if that runs counter to previously, what was previously considered economic theory, then that means that we need to have a new economic theory about how things work, like the labor market. So I think the fact that he's kind of interrogating these old ideas, that's been a real inspiration to me. Yesterday, I was showing some friends around campus and I showed them the Nobel Prize parking spots. And I was telling them there's a possibility that my advisor might win.


What's the first three things a fighter loses is speed agility his reflexes his legs and his friends Why does Justin love watching MMA there's something primal to it? And I'm just a big fan of the athleticism and a lot of the skill the truth is He really just likes to watch a couple sweaty men rolling around and and all the heavy petting that goes on So I'm pretty sure that's the real reason that he's drawn to it. These guys names are just they're too long now Is it Kovalkovich? Is it Koval Kovic? Is it Boahovic? Is it Blackovic? You know what I'm saying? Where's the Matt Hughes and the BJ's and Chuck Liddells, you know I'm saying there's no more fighters like that anymore Okay, yeah, let's do it. All right. We got a chair over here Do I have this mic close enough to me? Yeah. No The entire industry has to relook at this and we have to relook at how we're investing into our key people and our key Personnel that represent our industries and our brand Adam Zedlak seems to tower over Adam Schaefer He's a big guy, you know very formidable Yeah, I was kind of curious why he brought a bodyguard with him today. So Adam Adam Zedlak came in today Really, we actually didn't really want to talk to him We really wanted to talk to BJ Penn and knew that we would have to let Adam Zedlak back on the show If we were going to talk to BJ Penn, so So he walked in the door and he had this guy in you know He had a little bit of cauliflower ear going on so I could tell that he was a serious fighter But why is he bringing a bodyguard and I discovered oh, this is BJ Peng guy He was my favorite fighter of all time BJ was Incredible to watch great fighter. I loved it when he would he linked his gloves after fighting Sean shirk I was one of the fights where he did that the first time Uppercut him. He's doing flying knees. He's throwing elbows in there. The guy's just choking motherfuckers out I mean the guy was just amazing to watch at what he did and come to find out that he is a real big deal He is currently number one in the world BJ and so we said hey, why not just throw him on a mic Coming along. Yeah, that's great. You're which island are you from you from from big eye from he long here You know, yeah, why is the best fighters in the world?  I don't know. I haven't been we're slowly starting to get him out with the media now that he's played a bigger role If you have see Jim, how did you grow up and then what made you choose to fight as a career? I mean I've seen every one of his fights, but I just so maybe this is because I smoke too much weed Bro, I got it really big I got back off the weed so much because I don't recall like each one of his fights I got remember him fighting Matthews both times. I remember when he won When I when I beat Matt Hughes the first time I wandered out I think that was the last time and that's when I think I think my Prime was 25 years old and That's that's when I just really loved it loved the whole thing You brought up the Diego Sanchez fight. I remember that fight You know when I got into jiu-jitsu I just I just um it was just something fun I think before desire before dedication I just starts with love and I just love what I was doing and just wanted to you know wanted to be somebody and People asked me how you got into fighting and I'm like well I wanted to be on TV, but I couldn't sing I couldn't do Basically, he's a quiet guy. He's not really a type of guy that I feel like would dominate a conversation That's it. I don't talk much so thank you very much for coming out And so the guys were asking him a lot of questions who went from one question to the next question to the next question We were kind of machine gunning BJ with questions and you know We want to have air feel filled at all times silence doesn't really work well on a podcast in my opinion If he could get the 170, why wouldn't he why would it come people get it if he could yeah Why wouldn't he go be loose and if he could I think we all know why yeah I thought the guys would all come with really good questions, especially Sal But I think he just found another opportunity to talk about how good he is at jiu-jitsu And he hits me on the shoulder. He wasn't trying to hit me hard, but I could feel You should like timestamp when the jiu-jitsu Purple belt conversations gonna come up. You know I had a purple belt She's where were you that I should have seen way back. I was this was let's see I was in my this seems to be the theme right whenever do we have somebody like this that comes in is any time that he can insert What color belt he was he definitely is quick to let us know and the audience know so there's a few kinds of guests That we'll get on the show that I know I'm gonna have to carry the interview so one is MMA guy just because I have Background and training Adam and Justin, you know, they did zero of that Unfortunately, it's not as good questions that I thought we're gonna come from him But we do know that Sal was a purple belt and kicked a lot of ass Anybody who's intellectual so if they're smart then I know I'm gonna have to carry the podcast and ask you know Questions and you know kind if they ask a question for us Sometimes I'll say a word and I could tell Adam's eyes. He'll look at me like like what is what does that mean? And I'm like that's an amino acid Adam or something like that. Whatever Sal, of course Dominated the conversation He had a lot of questions of course Sal has a lot of experience in the world of jujitsu and that type of thing and So he has a lot of good question to ask he seemed to know a lot of the same people that DJ knew So, you know no man no man No man's great, man. So that's the guy that got me signed up dude. They seem to run in the same circles I feel like Sal kind of felt like that kind of validated who he was is a is a grappler I've learned that word grappler And he so he's he's a grappler and a purple belt by the way So, you know, I do the warm-up and everything and then and then when there's time to roll He says, you know, you're kind of a big guy. Why don't you go against me? And you don't know me He's not big guys.  I'm tapping like I couldn't believe I got up I threw up after five minutes And I came and I signed up.  This is legit, man I say no, I know him. I knew how I rolled with him. Oh, yeah I think it's interesting watching people, you know brutalize each other on screen However, I'm not the type of person that if there wasn't somebody else watching the show Or the fight I probably wouldn't turn it on myself. It's just not my thing. I'd rather watch You know the crown on Netflix Learn about the royal family. That's fascinating. That's kind of like a disaster waiting to happen right there. What? This is it. This is the resistance training revolution. Get it now at the resistance training revolution.com Hey, did you get the book? Do you have my book? Yeah. Yeah, Amazon. Best seller. Very good. It's easy. Resistance training revolution You just go to Amazon. The resistance training revolution.com. That's where you want to tell people to go It's quite an amazing book.  Really, he took most of my ideas And some of Justin's, mostly my ideas. Did you get Sal's book? No Wait, wait, am I supposed to look at the camera or you? No, I got it. In case you didn't know Sal's written a book called the resistance training revolution And he's and he got a ghostwriter and then together they put together this book and I went out and I bought the audiobook version as well as a hard copy version He's calling it his book, which is fine.  I'd rather be the guy behind the scenes. So I don't know if Adam and Justin bought it He's right. I didn't buy it They're a little jealous. Ever since this all happened I feel like they've been talking to me all weird. You know what I mean? I've seen it. Yeah Doug Eggy, Adam Schaefer and Justin Andrews. I'm grateful for their support and friendship Notice how I was listed first. Yeah What's the website? TheResistanceTrainingRevolution.com Do I just Amazon set? TheResistanceTrainingRevolution.com If you want to put a dollar amount on it, that could be tough because it is priceless, however He reads it in the middle of our meetings now. Anytime that man can read his book, he will I'll read a little bit of the, let's see, priceless I was shocked when I read the statistic from a recent large study How much would you pay for this book? They are not doing the one activity that best assures them an attractive, fit body and a happy, healthful and youthful life Well, the question is, how much do you want to change your life?


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So if there's one example, there will be others Don't let the other be you clean up your metadata if you haven't already Who am I? Well, I am George Papa George George Sunpai and many other names you the beautiful freedom family has given me I am the CEO and founder of freedom For freedom and the freedom family and all the adventures and new business contacts We will make here in Dubai. 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Chief Petty Officers, hopefully you have read, seen, or heard about my zeroing in on excellence initiative and the three focus areas of developing leaders, good order and discipline, and controlling what we own. Zeroing in on excellence does not distract from or add to existing individual roles and responsibilities. Rather, it is the framework around which we can build sound, durable readiness in order to functionally support the CNO's sailing directions. I believe developing leaders, fostering good order and discipline, and controlling what we own will help us build an environment where our entire organization gets stronger, now and in the future. These are not single actions. They are deliberate mindsets that permeate our process and procedures. Each directly advances the CNO's tenets of war fighting first, operating forward, and be ready. Each already falls within our assigned swim lane and can be a powerful engine of influence if it becomes a heightened part of our consciousness. If we grab zeroing in on excellence and maintain a steady strain on the ideas that it entails, we will have a positive impact on readiness and get after some of the issues tainting our navy, including sexual assault, suicide, domestic violence, and drug and alcohol abuse. Through your leadership and support, we will make this initiative work, support the CNO, and continue to make our navy, the world's preeminent maritime force. Thank you, and I will see you in the fleet.


My name is David Questonberry, and I play offensive line. Cancer has affected my life pretty dramatically. When I was 23 and 2014, I was diagnosed with non-Hodgkins T-cell lymphoplasic lymphoma. I went through a pretty intensive regimen of chemotherapy. It lasted about three years. And it was a fight. It was a tough fight. It was a long fight.  And it's been a battle just to get back to where I'm at today. I felt like something wasn't right. Mine was a little different because I had a very aggressive form, so it kind of happened fast. But I probably knew for about a week, a week and a half before I got diagnosed that something really didn't feel right with me. And so that's why I tell really anyone, like, hey, if something doesn't feel right or something is bothering you and not getting better, like, go get it checked. Because if I wasn't in the position I was at in Houston, you know, with the Texans and being surrounded by, you know, fantastic medical doctors, you know, even if I just waited another week or two, my story could be completely different. You know, I had a dream of gold to be a starter in this league and play good football and play a lot of football. You know, I really didn't want to let cancer take that from me. And it has definitely not been an easy journey. It hasn't been a quick journey. It's been a long, kind of brutal road.  But I never gave up the belief that I couldn't get to where I'm at. You know, it was just kind of an everyday climbing that mountain, an everyday fight, even after the chemo was done, even after I was in remission. The fight wasn't over because there was still a level that I wanted to get back to. And that's what really I was working for, and that's what I'm still working for. My advice for anybody fighting the fight, going through it, is fight it your way. Like, this disease and the regimen you go through, it takes so much from you. It takes your hair, it takes your well-being, it takes sleepless nights, it takes your nights away, it takes years or months or anything out of your life. But don't give it more than it takes. Don't give it your hope for a better days. Don't give it your outlook to still try to see the beautiful things around you or miracles that happen all around you. It is tough what you're going through, but don't give it anything more than it already takes from us.


What's going on guys it's your boy DPJ here today with another Destiny video and in today's Destiny video I want to talk further more about the fawn exotic hand cannon and whether or not this weapon should be nerfed because it's general control over PvP, Iambana and the trials of the service. Now last week I uploaded a video asking you guys if you think the fawn should be nerfed or not I created a straw pole in that video and in today's video we're going to check out the straw pole we're going to see how many of you guys want this bad boy nerfed and how many of you guys do not want this bad boy nerfed. Now taking a look on Reddit and watching other people's YouTube videos there is a massive problem with PvP and it's not just the fawn it's also the last word and shotguns blinking shotguns the range of shotguns and so forth and if you guys don't know we course you know that old does destiny he created an amazing video which I will link in the video description which you guys should definitely check out in this video he talks about all the problems with PvP and what's causing and ruining PvP at this current moment in time and that is he talks about the fawn he talks about the last word he talks about blinking shotguns he talks about the range of shotguns and he also talks about the foul winters life now all of these things are major problems with PvP whether you like to admit it or not it's making PvP really unbalanced the time to kill in PvP with these weapons and you've heard me say it before it's too damn quick we expect a lot longer of a time to kill in destiny the way it was before even when also rifles had the error of PvP you still weren't dying in a blink of a second now you do and this is with hand cannons hand cannons should not be this powerful and this was the point of my video which I posted last week and this was the point of that old video which I will link in a video description if you do want to check it out so basically I uploaded a video asking you guys if the fawn should be nerfed while giving you guys my personal opinion on what could be done to the fawn to fix it to make it basically balanced but I ain't gonna go into all of that now like I said you can check that out in the video I posted last week but we're gonna check out the straw pool and see how many of you bad boys wanted this weapon nerfed and how many of you guys did not want this weapon nerfed okay so we have all that 11,000 volts which is incredible and by quite a big majority more people do want the four nerfed than don't we have 6,000 plus volts people want it nerfed and we have 4,000 plus volts people who don't want it nerfed it isn't as one-sided as I thought it would be seeing the amount of people who are basically bitching about this weapon on Reddit and on YouTube etc me included but it's still a mass majority 57% of people at this current moment in time I mean the straw pool will be updating it's getting thousands of volts daily so it's probably changed since me recording this video but it does seem as though the mass majority of the Destiny community want the four nerfed and they agree that the fawn is in control of PvP now so like I promised in the last week's video I will forward this to Brunjie directly I will DM Deej, I will DM a few of the devs making sure they see this shit and making sure they do something about the fawn and all this video is gonna get disliked I know a lot of you guys want the fawn to stay the way it is I know a lot of you guys can't perform in PvP without the fawn which is a bit of a shame to be honest but in my opinion and a lot of people's opinions it is a ruining PvP really is the fawn the last word the range of shotguns and blinking shotguns all need to be sorted out somehow but guys I hope you enjoyed the video thanks for stopping by as always thanks for voting if you did and peace out until next time Peace


In this session, we shall be talking about Renessa Humanism. As you know, in the first semester of MA English program, we have a paper. We are already introduced to the first three units of the first paper, which is about social and intellectual history of England. In the very first paper, Unit 4, we deal with Renessa Humanism. And in this session, we shall be talking about some of the very important aspects of Renessa Humanism. And while dealing with this Renessa Humanism, we shall be talking about what is Renessa and what is Humanism and how literature emerged out of Renessa and Humanism. So before going into the details, let us have a look at what the term Renessa means. The famous 19th century historian Jacob Buchhardt describes the essential spirit of the movement in the discovery of the world and of man. This is the name of the book, and where Buchhardt talks about the very spirit of Renessa. So he says, to the discovery of the outward world, the Renessa added a still greater achievement by first discerning and bringing to life the full whole nature of man. At this period, as we have seen, first gave the highest development to individuality and then led the individual to the most jealous and thorough study of himself in all forms and under all conditions. Indeed, the development of personality is essentially involved in the recognition of it in oneself and in others. Between these two great predecessors, our narrative has placed the influence of ancient literature because the mode of conceiving and representing both the individual and human nature in general was defined and colored by the influence. But the power of conception and representation lay in the age and in the people. So in this quotation, Jacob Buchhardt beautifully describes the very spirit of the Renessa. Now, let us try to have a look at what Renessa means. Renessa represents a turning point in the history of European society. However, we must also note that our influence here has to be quantified or modified by the views of the recent scholars who prefer to call the Renessa as the early modern period. While the medieval scholasticism put the stress on metaphysical speculation and abstract logical reasoning, the 15th century humanistic learning was concerned with the elevation of the position of man in the universe, his dignity and his creative powers. So these are some of the very ideas of Renessa we can have. Then if we try to understand the very idea of Renessa, we can understand the term or understand the very idea of Renessa through the concept of medieval scholasticism. So what does it mean? Medieval scholasticism can be looked at through the very idea of humanism. So this necessitates us to understand what humanism means. So what is humanism? Humanism refers back to the culture of the 14th century extending beyond the 16th century Europe, which was based on Greek and Roman learning. Ethmologically, the word comes from the Latin word humanus, which signifies centered on human beings. So in the context of the 15th and 16th century post-medieval Europe, humanism means the rise of a new learning in which the central area of interest is man and his relationship with the universe. Humanism is used in a broad sense, which implies a world view with a set of values revolving around the human rather than the divine. So this means defining the human without any reference to God and focusing on human potential and human achievements instead of theological doctrines. So humanism mostly talks about the position of man in the scheme of things. Humanism or humanistic education of the 15th and 16th century Europe with its central focus on human passion, ambition, and action exerted a tremendous transforming influence on the contemporary arts, history, and politics. This intellectual movement is known as the Reneza in the cultural history of Europe. That's why my friends, whenever we look at the very concept of Reneza, we cannot do away with the concept of humanism. So as the title of the unit four in the MA English course, and the first course of the MA English program, the first semester, where we have kept a unit called Reneza Humanism, unit number four. So when you read through this unit, you must be reading about Reneza and humanism in parallel terms. When we talk about the changes that we brought up, brought in the context of Reneza thought, how humanism and Reneza thought came to influence the society of the people of the medieval age, we must look at this following authors. But behind the bud of humanism in Europe lies the intellectual contribution of a number of thinkers who adopted a humanistic approach to the acquisition of knowledge. And for them, the cultivation of knowledge signified the development of the potentialities of men in the universe. So it's an every time we are referring to the position of men in the scheme of things, in the society, against theological beliefs. So some of these very important humanists were, I hope you will remember these very important names. They are Petrarch, Dante Elegieri, Picodella Mirandola, then Lorenzo Valla, Frasua Ravella, John Colette, Thomas Moore, and Desiderius Erasmus. These are some of the very important personalities who changed the human history during the time of the Renaissance. Humanism and Renaissance thought. Now let's have a look at how humanism and Renaissance thought influenced the 15th century society. Among the English humanists of the 15th century, John Colette played a very significant role in bringing the glorious world of classical literature out to the English people or introducing the old classical literature to the people in England. He was primarily concerned with the religious literature of the classical antiquity. One of the best known figures of English renaissance was Sir Philip Sidney. He is often called the archetypal renaissance because he was greatly talented and had many accomplishments to his credit. Not only was he a poet and scholar, but he was a stitchman, a courtier, and a fine soldier. Among his friends was the poet Edmund Spencer, who wrote The Fairy Queen, the very famous fairy queen. Sir Philip Sidney also wrote a pastoral romance. The name of that was The Countess of Pembrokes, Arcadia, and the most famous sonnet sequence, Astrophil and Stella. Sidney's epilogy for poetry is recognized as a subordinate text of literary criticism even now. It is said to represent the first English synthesis of the different stems of renaissance thought, particularly in the field of literature. As you know, you should be considering, you should look at Sir Philip Sidney as a representative of the renaissance man and you should situate his very famous sonnet sequence, you know, Astrophil and Stella in the context of renaissance literature. Now, let us quickly ponder over the very idea of the history of renaissance in Italy. During the period, between 1490 and 1520, the renaissance emerged as an intellectual movement, which was Italian in origin, but it was very much European in scope. Now, the question is, why in Italy and not elsewhere? In fact, the 15th century social and intellectual atmosphere of Italy was conducive for such a movement or such a change. At the material level, Italy had ample resources to patronize the study of art, literature, and moral philosophy. The curriculum in the universities of Italy was not predominantly theological, unlike the universities in France and England. Italy experienced the growth of an urban culture when in the other part of Europe, the feudal setup was still retaining its stronghold. The Italian cities like Florence, Venice, and Padua flourished both economically and intellectually. The Italian Martian class actively patronized the study of classical art and literature. So, gradually, a scholasticism was evolving. So, we can quickly have a look at a kind of a map where a very spirit of renaissance roamed around, in fact. And this is the map of 15th century Italy, which experienced considerable development of libraries at places like Florence, Neples, Cassina, Venice, and elsewhere. Just have a look at this map and see the important places which were becoming the center of learning. The mass production of manuscript texts followed by the printing of various editions of ancient classics brought about the revolution in the field of renaissance studies. The Italian academics also played a major role in the curriculum of the humanist ideas because these academies provided the humanists and with the opportunities for exchange of ideas with their fellow scholars. The members of the Platonic Academy made a conscious attempt to receive ancient forms of cultural exchanges as manifested in Plato's dialogues and leaders. They attended the informal meetings of scholars for philosophical discussions and the exchange of ideas on classical scholarship. Then, of course, Mnistar is also associated with the fall of Constantinople in 1453 due to the invasion of the Turks, which led to the entry of a number of displaced Byzantine scholars into Italy. It resulted in the intellectual cross-partalization between the East and the West of Europe, creating a conducive atmosphere for the present humanistic studies. So, fall of Constantinople in 1453 is a very important incident. Influence of the renaissance, the cultivation of humanistic ideals through the regeneration of classical studies reached the height of momentum in the 16th century Europe. But in England, the movement continued after the 17th century. And ultimately, it set the stage for scientific revolution and enlightenment of the 18th century, about which we shall be studying in the next two units of this MA English program. The in England, the enthusiasm for ancient classical art and literature was combined with a renewed focus on religious studies resulting in an endeavor to reconcile classical learning with the Christian tradition. English humanism succeeded in achieving a successful compromise between the excessively rhetorical preoccupation of the Italians and the narrow framework of theological studies thus becoming Christian humanism, which will be dealing elaborately on the very idea of enlightenment in the next two videos, probably. But we also need to understand how renaissance and the exploration of the new world took place while also discussing the emergence of literature during the time of the renaissance. The exploration of the new world by the navigators and professional explorers received the new impetus during the renaissance in England. The spirit of imperialism fuelled many time adventures and besides the extensions of its imperial frontiers, it also gave birth to numerous tales of distant explorations and success. Richard Hackleuth's work published in 1589 and the name of the book was The Principal Investigations, Voices and Discoveries of the English Nation, a notable example in this regard. It's a kind of the many-time adventure. This is the picture of the many-time adventure that was taking place during the time of the renaissance. Just you can have some ideas of how it took place, what was happening at the time. Then of course, when we talk about renaissance humanism, we cannot but refer to the literature part. So what were the very important works that came up as part of literature at the time? So these are the works. Roser has come schoolmaster. It was published in 1570. Plutarch's Lives of the Noble Gratians and the Romans 1579. Baldiser, Castiglione's Decotierre, Nicolome Chiaverde's The Prince, whose influence can be very well seen in Marlowe's play, The Jew of Malta. So these are some of the very common representative texts. But if we come to some very important and very specific examples, we can see the works of the university wits, the works of Seneca, how it influenced Elizabethan tragedy, or most particularly, the works of Shakespeare. So what we need to do is, while studying this unit, what we need to do is to have a look at the different literary reforms that emerged such as drama, such as non-fictional prose, such as in this regard, let me remember Francis Bacon, who wrote Essays, then of course, in a poets like Philip Sidney, who wrote Solace. So this renaissance was an excellent time for the flourishment of literature and different literary genres like drama, non-fictional prose, and of course poetry flourished during the time of the renaissance. And due to renaissance scholarship and due to hemanistic thinking, which foregrounded the significance of men or the position of men in the scheme of things, and because of that, people were talking more about the affairs of men and their position in the society. So before winding up, I think we can recapitulate some of those issues that we have discussed in this session. Those are the all-round development of the individual was the central issue in the 15th century humanistic studies in Europe. Humanism forced their reaction against the medieval scholastic thinking. The renaissance was a humanistic movement since it aimed at cultivating human concerns through classical scholarship. Although it has its historical roots, so to say, in Italy, the renaissance in England exhibited a distinctive character of its own. Humanism was champion in England, both by the court and by the universities. And let me tell you, this was also the time when emerged some of the very prominent universities of the world. And of course, we have to look at some of the books that we need to study as part of our MA English program. So these are some of the books that we have to study as part of our understanding of renaissance and renaissance of humanism. So please read Asa Briggs' book, A Social History of England, then Boris Ford's Pelican Guide to English Literature, The Cambridge Modern History by Dennis Hayes, and Z.M. Trevelyan's English Social History. These are some of the books that you can find very handy while reading about, while studying renaissance and renaissance of humanism. So friends, we are going to wind up here. See you again in the next video, in which I shall be talking about enlightenment. Thank you so much and all the very best.


SEP-A82 Object Class, Euclid Special Containment Procedures SCP-A82 is to be kept in a fluid environment at all times, consisting of no less than 40% seawater. Object is to be kept suspended by non-metallic means, currently caught in fiber line that is to be changed daily. Object is also to be checked daily for any signs of rust flaking. If any part of SCP-A82 appears uncoated with rust, it must immediately be immersed in a 100% seawater solution. Water must be taken directly from the ocean. Reduce concentration only when the object is again coated in rust. No metal may be placed in containment area. Only organic materials are allowed in containment area, and any contact with SCP-A82 requires use of thick cotton gloves. Any metal-making contact with it is to be heat-severed, melted down, and kept immersed in 100% seawater in a separate area. Any auditory issues reported by staff must be reported immediately. An affected personnel must submit to a full psychological examination and, depending on results, either transferred to another facility or permanent containment at ████████. Description SCP-A82 appears to be a random assembly of gears, cables, pulleys, screws, and belts, all made of an amalgam of various metals. Objects size at time of recovery are approximately 87 cubic meters. Current size are approximately 12 cubic meters. SCP-A82 rusts quickly in seawater. No identifiable energy source has been found, but all components will begin to move if not coated in rust. SCP-A82 is completely silent at all times, no matter what level of activity SCP-A82 reaches. Any metal touching the object will become permanently affixed to it, and over a period of a few days, become the new part of the object. Organic metal remains unaffected. SCP-A82 is extremely resilient, with tensile strength and toughness above those of aircraft-grade titanium alloy by weight. Even though its composition appears to be a random alloy of iron, tin, gold, and other metals, some as of yet unidentified, extreme focused heat must be applied over several hours to cut even a small portion free of the main assembly. Persons remaining in the vicinity of the object for prolonged periods have developed auditory hallucinations while near the object, mainly the sound of grinding and clicking. The sound intensifies, and is abated only by throwing metal into the object. Subjects and advanced stages of psychosis have thrown themselves into the object, resulting in almost instant death by crushing. The body is often drawn in, and impossible to recover. SCP-A82 was recovered from a location at the northeast coast of Banks Island. Area was bearing of all metal and metallic ore in a one-mile radius. SCP-A82 was found at the geometric center of the area. SCP-A82 had become submerged in seawater at the time of discovery. A small town was found nearby, abandoned for several years. SCP-A82 was removed, and shortly started to flake off rust, causing the varied parts to begin motion. After several accidents, SCP-A82 was cut down and contained on site. Note, SCP-A82 is not to be brought into the vicinity of SCP-271 or any subject possibly contaminated by SCP-217. Addendum, please review Interview A82-1 for further information. Interview A82-1 Interviewed Richard Wright Interviewer Dr. Gears Forward, Richard Wright is identified as a survivor from the small community near the initial recovery location of SCP-AA-2. Begin Audio Log 1304 Please take a seat. State your name for the record, please. Richard Logan Wright, everyone calls me Rich, though. Excellent. Thank you, Mr. Wright. Do you recall the date when you first saw the object in question? At when was it? I'm not really sure. It was a while ago. Alan found it first, wrecked his boat on it. He told a few of the other fellows about it, said they could sell it for a bunch of scrap. We all thought it was a chunk off a jet or a cargo ship. At what point did the device start operating?  Started spinning slow, then sped up. By the time I saw it, it was really running. Jimmy tried to get closer, try and see what was powering it, or why it was so quiet, but he slipped.  Alan seemed kind of off, kept asking us if we were hearing anything. Miss Parker thought part of it was gold, even tried to jam part of it with a pipe to get at it. That pipe stuck fast, and smacked her a good one when the gear it was on spun around. After that, people mostly kept away. Were there any other incidents of people being injured or hearing noises?  Alan was keeping it in an old storeroom by the dock, and nobody really went out there much. He started looking bad, said he couldn't sleep, that he kept hearing that thing grind away. Father Pat started dropping by, tried to talk to him, told him to get rid of it. He was gone for a couple of days, then suddenly the two of them turned up together, happy as clams. Subject trails off, shaky slightly. Mr. Wright? Subject rubs face and shakes head. I'm fine, sorry. So Father Pat and old Alan show up, fresh as daisies, say they got the thing figured out.  Anyway, they said some damn thing about it being from somewhere else, that God made it, that it was for me, and I left. Did you believe them? What, that it was from God? No, no I don't know. I didn't really know what the thing, this damn machine kept spinning away, no power to it and eating metal too.  When people started getting interested, started listening to Alan and Father Pat, told everyone to bring metal to it, told them the gears were the voice of God, and that it grew louder as we turned away, and softer as we brought it offerings. Did you bring metal to it as well, or spend any extended period of time near the object? Subject is silent for several seconds.  You can hear this thing all over town, got to be folks who couldn't even sleep, just clanking, grinding, screaming at all hours of the night, giving it metal helped.  There's not a goddamn thing wrong with that. Subject bangs table with hands, it's highly upset and breathing heavily. Sir, I will request that you calm yourself, I am asking questions, not accusing, please return to your seat. Weeks several deep breaths, I'm sorry, over a couple of weeks everything got fed to that thing, it was just how things were, we were pretty isolated you know, it's not like we have much else. You just make a couple trips out to the storehouse and toss any metal you happen to find in, I always seem to be people there just watching it. It tore a hole in the roof after a while, Father Pat started getting strange, telling us that it wasn't enough, I think the noise was getting to him, said it needed something more meaningful, subject trails off, Mr. Wright? Mr. Wright is silent for 48 seconds, I came in one night because I heard people shouting from the storehouse, Father Pat was leading a prayer to this thing, but it didn't sound like any prayer I knew, people were coming up and he bent over them, they screamed and then he turned to that big mass of metal, I thought he was giving communion until I saw the pliers in his hand, I'm sorry, pliers? He was yanking out people's feelings, he was pulling out their fucking teeth and feeding them that thing, subject is shouting and apparently highly upset, he started screaming about it not being enough, that it needed more, but there wasn't any more, there was barely any metal left anywhere, then he pointed at Alan, he said that he was hiding metal from the great machine, Alan screamed they didn't have anything, Father Pat said he had a metal joint in his hip, everyone got up at once, oh god, oh god they grabbed him, everyone just grabbed him, he started screaming, subject is crying and shouting, he kept screaming and screaming and nobody cared, I saw his arm go in, saw all his fingers break and pull the rest of the arm in, and I ran, what could I do, Jesus I couldn't stop it, there were too many, and that thing was screaming and screaming and Alan was screaming and Father Pat, subject falls to the floor sobbing and shouting, this interview is concluded, thank you Mr. Wright, security please see Mr. Wright out, and log, closing statement, Mr. Wright attempted suicide shortly after the interview, subject is currently being held on Suicide Watch and for observation.


Okay, welcome everyone. Welcome to the Schubert seminar. Today we're happy to have Professor Andru Weber from Warsaw telling us about the characteristic classes of b-orbit in square zero matrices. Please go ahead. Okay, so thank you. Thank you for the invitation and for letting me present my result. But before, maybe I have to say that this really, this period was not a good time for doing mathematics. You know, I walk up on first day morning and, you know, what happened and it was really the strange feeling like from some science fiction that a big European country attacked another, quite a big European country. And in fact, bombs were sent to the places that I know I visited and also I know people living there. And some bombs were really close to Polish borders so that was, and who knows what would be the next. So that's really not, I had problems with concentrating on mathematics, but slides were prepared so I can continue. And this is the joint work with my student, Piotr Rudnicki, about characteristic classes of orbit of Borel group in square zero matrices. So this is basically for GLM but can be generalized to other types, ADE basically. And there's some extension that is somehow related to my previous work with Richard Riemann, but this is only beginning for the stuff for elliptic classes. So I just basically tell you what was done with paper with Piotr Rudnicki and then we will see how much time is left. So this is really, we can start very elementary that we have square matrices and the condition is that for these matrices is x square equals zero. And I do not look like a variety given by equation because we have not reduced maybe scheme. I rather look at it as a B orbit, orbit of the Borel group and look at the closures of Borel orbits. So the varieties are reduced by definition. And I would concentrate on the orbits of this Borel group. Okay, the action is by conjugation. If you conjugate matrix with square equals zero then get again the matrix with square equals zero and I would concentrate on the matrices that are upper triangular, they are preserved by this action. But some, so this upper triangular case was better already started by several people. So I'll concentrate on that case and some possible extensions are around but it's easier to start with that case. So the first non-trivial is for the matrices of dimension three by three. So the upper triangular by three matrix, it's a matrix with A, B, C here. And the condition of being square equals zero is A, C equals zero. So this is that free variable. So it looks like two planes intersecting. And here you have zero and you have one orbit. The complement of this line. I'm sorry for my clock, it's late. So three orbits of rank one, two planes without a line, line without a point and the point itself is a zero, the rank zero matrix. Okay. So and why this space of square zero matrices is important? It contains a lot of information about the classical stuff like matrix Schubert varieties. If you have matrix and just K times L, not necessarily square matrix, you can embed it to a square matrices just as a block matrix. You can just make a block here and it automatically becomes a square zero matrix. And moreover, if you act on this by Borel groups from one side, you act by X upper triangular and from other side by inverse of Z. Then this action agrees with the action by conjugation. This is a simple calculus that conjugating this matrix by upper triangular is the same as left and right action by Borel groups. Okay. So it follows that all what I'm saying can be applied in the classical context of matrix Schubert varieties, but maybe I would prefer to say that this is an extension of the classical context. Okay. And the B orbits of square zero matrices were studied by Anna Melnikov quite a I think the 2000 something 2005 maybe the paper appeared. And it's really elementary that every orbit of Borel group among the square zero matrices contains a matrix that has only one somewhere, only one in one column, at most one in one column or at most one in one row. And in fact, this matrix is given by some combinatorial data. For example, you can call it pattern or linking diagram. So here you have row two and one in the row six. So two is connected with six and the matrix in fact says that the sixth vector is sent to the second vector and then the second vector says second basis vector to zero. And also here you have another one in the seventh column seven is sent to four and four is sent to zero. So the Melnikov shown that every orbit contains matrix of that shape and this matrix is unique. And from this combinatorial data, this is just a set of pairs set of these joint pairs and call it in the diagram. From that, you can easily read the dimension of the orbit. So this is the formula. So this is first R is the rank, which is number of pairs. So it looks like a dimension of grass mania, but from from that, you have to subtract the number of intersections. Here you have one intersection and also subtract them. You have some fixed points, those who are not not touched by arcs. So we have three, one, five, eight and over this each point you ask how many arcs you have above. So you have one and you have above two arcs passing over and here you have zero. So maybe another method would be just to draw lines from this and you could in that way you can count a total number of intersections. So in our case, the number the dimension would be the n is eight. So and the rank is two. So two times eight minus two and the number of intersections minus one and there are three. Here you have one arc passing over six points and here you have two. So this is two times six. That's 12 minus four. So that's eight. So it's easy to compute the dimension. Okay. So maybe another example is the, so let's take n equals four and the matrices of rank two correspond to the following patterns. Here you have one, two, three, four and there is one is connected with three and two is connected with four. The other one is, one is connected with four and two is connected with three and the last one one is connected with two and two is connected with three. Okay. So there are two rank two orbits and for the rank one orbit if you have one for example here, so you can show that generating other matrices using borough group you can obtain every matrix in this region. So you get of this kind provided this matrix is of rank one because the initial matrix was of rank one. So generating you still get rank one. Okay. So maybe I got it wrong. So you can almost every matrix of rank one obtain every almost every, but if you take a closure with the space of singular matrices. Okay. And for the orbits of rank two, maybe if you are interested in equations. So this these two configurations are given by equations just the rank conditions. So you can find yourself what is the rank condition if two rectangles are overlapped and then you can have rank two and otherwise rank one and this this this configuration says that everything is contained in the rectangular which is above above the diagonal and this is other case. And here there is extra equally extra extra condition that this matrix if you put here generic things this matrix might be not of square zero for example that one you have a b c d e and if you take a square you get equation of this type. So this is the condition. So to make it short it's in a paper of Anna Melnikov that the equations are the equations of the closure of the orbit are the ideal is generated by rank conditions and square zero with this non trivial for some configurations and for some follow automatically and there is a minimal for the fixed rank in fixed dimension there is a minimal orbit and it looks like this it's minimal because it has maximal number of crossings and also maximal number of can say bridges passing over the over this region every every artist passing over that and it corresponds to orbit that here you have to have to have zero and there you um the closure of the orbit is something that's a linear space and the orbit itself is some is is a consist of a matrices that here on this diagonal are non-zero entries okay and the the pattern is I mean the matrix the representative of the orbit it looks like that and then you generate okay and also there is an algorithm how to obtain a minimal orbit of the fixed rank by applying the simple reflections so the algorithm algorithm goes like this that's okay so here you have some configuration so there is one arc and another arc and the rule goes like this you have to so there are several ways you can do it but there is one at least one canonical then first move left legs to the left so this is a left leg and this is a left leg and you want to arrive to a position when the left leg is a position one and the second left leg is in the position two so just move this first first first left leg left leg is in the good position the second one you have to move so you move and then you have to move the right legs so this this other one should be transported here so you transport it just applying simple transpositions and you arrive here and somewhere on the way you have to jump I mean you have to switch this but that's it has to happen somewhere if they were in a not good order okay so you the right leg is on the second right leg is in the good position and then first like right left you have to still move it a little bit so you land up here so this is kind of algorithm you can do a similar algorithm switching the role of left and right first to move right legs and then left and still there are a lot of freedom the more possible choices in fact if you have this kind of pattern I checked out exactly three ways to three different permutation that's conjugate this one because you can consider this as the first arc this is the second and this third and then you have to skip there or other way around you consider this as the first this as the second and this are the first so you have to skip with this on the left side or there's another way that's something in the middle so the algorithms combination of them between the finding the canonical presentation of the permutation but also some some some positions you can simplify okay so as the singularities of these varieties are for us not I mean we work with singularities but for matrix Schubert varieties we know that for this I'm not sure at least in the type C there's a counter example but at least the singularities are rational and there's this resolution so I will tell about the resolution in the moment but first I have to recall the standard thing that for the g-orbit or important g-orbit you have a standard resolution at least in type E so if you have a matrix with square zero so from this matrix you can extract its image so if this matrix of rank r then the image is the subspace of of rank of dimension r so it defines an element of the grass mania so from a matrix a you you you obtain a element of grass mania and to determine this matrix completely you have to have a map from cm to the image from cm to the image but the square equal zero implies that the map vanishes on the image that's why you have map from the quotient cm by the image to the image so image is the tautological bundle and exactly this guy is a cotangent bundle so that's why you have a smooth resolution even a symplectic resolution of the g-orbit in the potent g-orbit and we are interested not in g-orbit but in the Borel orbit so still the Borel group it's Borel equivarian so Borel group acts on that on that resolution and this orbit is sent to some Schubert Schubert cell here downstairs so it's easy to to guess that you need to resolve this Schubert cell and finally you arrive to a problem of resolving some bundle over Schubert cell and it recently appeared then a paper of Bender Eperon just with a full description of this kind of resolution for the square zero matrices and for the type A D E everything works fine but I would just concentrate on the type A so the what is the what is the algorithm so the statement is that you take the minimal orbit so this is a minimal orbit orbit of Frank R and I already told you that this is a matrix set of matrices of that form so this is vector space so it's smooth maybe I should say for the type B C and G F so this might be non smooth so you would have to resolve it it's another another step to do but for the type E it's a vector space and then resolve like you resolve the Schubert varieties so this is you obtain construction of Botz Samuelson resolution so then you get bundle over Botz Samuelson resolution written that way that is iterated twisted product of minimal parabolic so this is standard maybe I don't have to recall it here so anyway this resolution is of the form of the bundle over Botz Samuelson variety and when this pi is something that's pi times minimal orbit is them that we are interested in okay so maybe I can stop now because now I would move to more homological part there the first was just a description of the situation geometric situation then I would move to the co-homological invariance so let's make five minutes break sounds good thank you very much any questions before the break all right if there are no questions let's take a break for five minutes okay