Welcome back. Today, we will start a new topic. So, in this chapter, we study two point boundary value problems. So, for short, we will denote it by b v p. So, in many important applications concerning differential equations, the data on the unknown function is given not at just one point, but many points. And we now discuss, restrict our discussion to two point boundary value problems. So, in contrast with initial value problems, which we have already studied. So, the data on the unknown function governing a differential equation are given just at one point, that is the initial value problem. And this is, when it is more than one point, the data is given at more than one point, then it is referred to as two point or more point boundary value problems. So, our discussion is restricted to two point boundary value problems. And let me start with some examples. So, just to see what are the difficulties, what are the issues. The first example is again u double dot plus u equal to 0. And again recall dot represents d by dt differentiation with respect to t variable, that is time variable and u the unknown function. So, this is second order equation. And for the initial value problem, we give data of u and u dot at one single point. Now, we are interested in two point boundary value problems. So, data is given at two points. So, for example, say u 0 is equal to 0 and u b, b is another point, say it is given as beta. So, we have to find a solution to the differential equation in this interval 0 b, 0 b, which satisfy the differential equation u double dot plus u equal to 0. And in addition to that, it also satisfies these two boundary conditions at 0 and b. So, since this is a linear problem, we know that the general solution is given by… So, that we have already learnt. So, u of t is c 1 sin t plus c 2 cos t for this linear equation. This is general solution. And if we want this to satisfy these two boundary conditions, so let us start with at u equal to t equal to 0. So, u 0 equal to 0 implies that you substitute the value t equal to 0 in this general solution and require that u 0 equal to 0, then you see that c 2 is 0. So, then this cos t term is not there. So, we have just therefore, u t is equal to… I will just now replace c 1 by just c sin t. So, c is a constant. And now, you have to determine that constant c is possible in order to satisfy the second boundary condition u b. So, let us calculate that thing. So, beta is equal to u b, this is equal to c sin b. Now, you see already some difficulties here. For example, if b is equal to n pi, then sin b is sin n pi and that is 0. n is an integer, in this case positive integer does not matter. Therefore, if beta is not 0, there is no solution. So, you just one observation when b equal to n pi, n is a positive integer, then we will not have a solution if beta is not equal to 0. So, that the other the boundary condition at t equal to b is not satisfied in this case. On the other hand, if b is not n pi, then sin b is not 0. And then, choosing c is equal to beta by sin b, we have a unique solution. You have a unique solution for the boundary value problem. So, even in the simplest case of a second order equation with constant coefficients, we may have a solution or we may not have a solution. So, let us continue with one more example. So, this is minus u double dot equal to f t, 0 less than t less than 1. And now, again we have 2.0 and 1. So, instead of u, I will give the data u double u dot 0 is equal to gamma 0 minus u dot 0 is equal to gamma 1. We will see why I am putting minus 1 in a minute gamma 1. So, this represents steady state heat conduction, heat flow in a rod. Physically that is the… So, rod is placed in the interval 0, 1, these two end points and these represent the heat flux. So, that is one physical interpretation. Now, let us… And f is the force interval, f is given to us. And now, let us integrate the differential equation. So, we have integral 0 to 1 minus u double dot t d t is equal to 0 to 1 f t d t. This is from the differential equation. And the left hand side, just we can integrate it. And just you find that this is minus u dot plus u dot 0 and that is gamma 1 plus gamma 1. So, hence we have this equality between the forcing term and the boundary conditions. So, necessarily the forcing term and the boundary conditions should satisfy this. Let me write it. So, 0 to 1 f t d t gamma 1 plus gamma 0. So, now, this relation will tell us which boundary conditions and which forcing terms are possible and which are not to have a solution to the BBB. So, for example, if f is identically equal to 1 and gamma 1 equal to gamma 0 is 0. So, more generally gamma 1 plus gamma 0 is 0. Then, this condition is not satisfied. Then, BBB has no solution because this condition is violated and the left side you get 1 and the right hand side you get 0. So, that is violated. So, there are no solutions. So, on the other hand, so if I keep the boundary condition same, now I take f t is equal to sin 2 pi x gamma 1 equal to gamma 0 is 0. Then, certainly that relation is satisfied. Then, the relation is satisfied and we have many solutions. The solution again you can just take this f t equal to sin 2 pi t and solve the differential equation and you see that you have this 1 by 4 pi square. So, you can check that this is satisfied. The equation in terms so satisfies the boundary conditions. So, there is no problem there and A is arbitrary constant. So, again you see the solution is not unique. In one case, there is no solution and in another case, we have infinitely many solutions. So, these are the typical problems we face in the study of two point boundary value problems. So, with this let me now discuss a general theory first for linear equations. So, how to obtain a solution for a linear second order equation satisfying boundary conditions. So, here so for simplicity, so let me just consider y double dot plus alpha t y dot plus beta t y is equal to g of t. So, this is in A less than t less than b and for simplicity, let me take the boundary conditions as y A equal to 0 y B equal to 2. So, this is the problem here. So, we have this interval A B. So, we are to find a solution for this equation satisfying these two boundary conditions. So, we want a C 2 solution y is a C 2 function, it is twice continuously differential function satisfying this differential equation and these boundary conditions at the A and B. So, while dealing with linear equation, we have lots of tools already developed. So, we are going to make use of that. So, the theory for linear equation is somewhat easier. So, let me start with this. So, let me put some numbers. So, this is equation 1, this is equation 2. So, this alpha beta g are continuous functions. So, some minimum hypothesis defined on this closed interval A B. So, what would like to view this one as. So, if alpha beta are fixed. So, fixing alpha beta. So, what would like to do in analogy with first order equation? So, first order equation it was just one integration was involved and similar thing we expect even for the second order equation. So, there is this integration box. So, we will see what that integration is and here the input g and comes out solution, solution y. That is what would like to view this boundary value problem 1 and 2.  So, this is for some simplification, rewrite 1 as this d by d t of some p t y dot plus q t y is equal to m. So, there is some advantage in this thing. So, let us exploit that thing. So, this is I call it 3. So, what is p? p is a positive function and p is also c 1 on A B. So, it is quite continuously differential function which is positive that is important. So, very easy to see that 1 implies 3. So, first 3 implies 1 that is easier part. So, 3 implies 1. So, if you expand this by this differentiating this product, you see that alpha is p dot by p and beta is q t by p and g is alpha. And for the converse, you have to just find what p is and p comes from this. So, put p t is equal to exponential A to t alpha s. And since this is an exponential, so p is always positive and it is differentiable because alpha is continuous and we are integrating it. So, that will produce a c 1 function. So, you can verify and with this p, you can calculate what q is and what f is. So, now we restrict this our attention to this 3 and again recall the boundary conditions y a they are not changed y a equal to j. So, this is remember that. So, let. So, a procedure. So, let u 1, u 2 be 2 linearly independent solutions of homogeneous equation 3. So, that is in 3 you take f 0 and then you and this existence of these two linearly independent solutions come from general theory of linear equations and we are sure that they are there. Then by using variation of constants formula, a general solution of 3 is given by. So, one part consists of solution of the homogeneous equation and that is a linear combination of u 1 and u 2. And the other one is coming from the particular integral and let me just write that. So, this is A to t f s W s. So, check this one from a bit complicated, but straight forward.  So, this is for the homogeneous equation and this is for the inhomogeneous part. So, this is general solution of 3. Now, we want this y to satisfy the boundary conditions y a equal to y b equal to 0. And when t is equal to a, this integral is no more there and one that integral is there when t equal to b. So, let us write those two equations.  So, let me not write the whole thing. So, you just copy from the previous line. Only thing is I am taking the other side. So, there will be a sign change. So, a b are constants. Now, the a and b satisfy these two equations linear equations and we hope to solve them provided this determinant is non-zero. The coefficient of this coefficient matrix, the determinant of the coefficient matrix is not 0.  So, now you write a and b from and now you say and uniquely. So, find a b substitute. So, let us go back and see what this one. So, let us call this some equation I have put 3 there. So, let me put 4. So, after solving for a and b from those equations you have solved now a b from these two linear equations in form. So, I will let me just write the end result. So, it is bit involved, but very straight forward.  I forgot to tell what w s is.  You also check that I might have done some mistake, but you can verify yourself these are just linear equations. So, there is no problem in verification and this is where that determinant comes u 1 a u 2 b minus u 1 b u 2 a d s and as usual there is other part there is no change there. So, let me just a t and let me just put as it is. So, what is w s? Let me just say what w s is. So, w s r to w t in the Ronskian to add t and since both these they are linearly independent solutions of the homogeneous equation. So, this is by definition u 1 t u 2 dot t u 1 dot t and since they satisfy the same homogeneous equation you can easily check that this is actually given by. So, this we already done earlier for generally linear systems. So, it is constant by p t and remember we have assumed p t is bigger than 0. And looking at this expression let us go back again. So, this complicated let me call it 5 this complicated expression. So, the first integral is a to b and second one is only from a to t. So, we can split this integral into two parts. So, y t is something a to t plus t to b. So, remember this because we are going to imitate this. So, looking at this expressions in the integrand. So, it is convenient to. So, looking at the integrand integrands in 5 it is convenient to introduce the following. Introduce the following functions. So, namely w 1 t is equal to u 1 a u 1 t u 2 a and w 2 t at the other end this is at one end t equal to a and this one is u 1 b u 2 t minus u 1 t.  So, they are linear combinations of u 1 and u 2. So, therefore, w 1 w 2 are also solutions of the homogeneous equation 3. So, right hand side is 0 and moreover if you look at these expressions. So, moreover and this is the advantage we take now moreover w 1 a is equal to 0 and w 2 b is 0. So, they are the solutions of the homogeneous equation and each one of satisfying one boundary condition. So, w 1 satisfy the boundary condition at a and w 2 satisfy the boundary condition at p. And now you just forget whatever calculations we did and start afresh from this w 1 w 2 that is just to get a motivation how to obtain this w 1 w 2. So, now let us start with so afresh. So, let w 1 w 2 be two linearly independent solutions of the homogeneous equation 3. We have to remember that homogeneous equation 3 satisfying w 1 a equal to 0 and w 2 b equal to 0. So, if you have a more general condition this is what we have to do. You have to find two linearly independent solutions of the homogeneous equation 3 satisfying one of them satisfies boundary condition at one point and another one at another point. So, for simplicity we have taken this simple boundary condition here that namely y a equal to y b equal to 0 and w 1 satisfy the boundary condition at 1 point a and w 2 satisfy the boundary condition at b. Now, define so g of t s it has two parts. So, let me draw a picture later. So, this is w 1 s w 2 t if a is less than or equal to s less than equal to t and other way around w 1 t w 2 s t is less than s less than equal to. So, if you take the square a b. So, this is the line t equal to s in one portion this is s less than equal to t and here t is less than that is a. So, this is the first portion and that is what is happening and define and put and little comment later just look at the definition of g. So, g has two parts one in a t. So, this integral splits into two parts a to t and t to p similar to the one we did for t and we expect this y 2 satisfy the differential equation and also the boundary condition. And this is the integral box we are talking at the beginning and. So, see this integral box is just manufactured with the help of these two linearly independent solution nothing else and that comes from the just homogenous equation and now we put this input f the right hand side and we obtain corresponding solution. So, this is what we have obtained and now we will verify that y t indeed satisfies the differential equation 3 and also the boundary conditions. So, this is the in the next 10 minutes we will do that thing. So, so cling under suitable normalization we will see what this normalization is y satisfies d e 3 differential equation 3 and boundary conditions. So, it is very easy to verify. So, remember y t is given by. So, let me just write that.  Just remember this every time we have to do that thing and looking at this expression it is very easy to see that. So, clearly y a y a y 0 because w 1 a 0 a 0 and y b 0 because w 2 b 0. You see the way we have chosen the two linearly independent solutions of the homogenous equation they are helping us in satisfying the boundary conditions. And since we are assuming w 1 w 2 are also linearly independent. So, since w 1 w 2 are linearly independent their Ranskian is this we already seen is constant divided by p t and the normalization. So, we normalize. So, normalize means you just multiply w 1 w 2 by constants normalize w 1 w 2. So, that the Ranskian is 1 by p t. So, we want this constant to be 1 and that can always be achieved by multiplication by some constants. So, there is no problem there. So, this is the normalization we are talking about. So, now we directly verify that y satisfies 3. So, again let me recall what that 3 is the differential equation. So, it is d by d t of p t d y by d t plus q t y is equal to f t and w 1 w 2 satisfy the homogenous equation. So, that means d d t p t w i dot d by d w i by d t plus q t w i equal to 0. So, i equal to. So, remember that they satisfy this. They are linearly independent and their Ranskian is just 1 by p t. So, that also you remember. Now, y is given by that again let me not write it. So, just go back here. So, y is given by this. Remember that thing and now we will just get this. So, differentiate. So, you have to be bit careful there because the integral limits also involve p. So, you have to just be bit careful there. If you already done it differentiate y. So, y is given by. So, let me just write it. So, a 2 t plus t 2 p recall that. So, d y by d t is equal to. So, let me just write it a 2 t w 1 s w 2 dot t because t is only here f of s d s. And since this t is there in the limit. So, you have to also differentiate that. So, that we get. So, w 1 t w 2 t f t and if you do for the other integral similarly. So, now there is t in w 1. So, w 1 dot t w 2 s f s d s and now t is in the lower limit. So, get a minus here. So, w 1 t w t and this and this cancels. So, and now you are looking at equation 3. Now, multiply by p t. So, therefore, p t d y by d t is equal to a 2 t. Now, just p t just goes inside there that is all. So, there is no problem there that is it. And now again we differentiate this. So, d by d t p t d y by d t and this is similar to what we did in the previous step. So, just we have now a 2 t. So, w 1 s d by d t of p t d w 2 by d t f as it is. And now because of the presence of t in the integral limit. So, we have this p t w 1 t w 2 dot t f t and similarly from the other integral t to b.  And now I have minus p t w 1 dot t w 2 t and f t. And remember w 1 w 2 they satisfy the homogeneous equation 3 and this is. So, simply this let me write here this is minus q t w 1 and similarly that one is minus q t w 2 t. So, and q t that nothing to do with the integration variable s. So, that q t just simply comes out and what is remaining is just minus q t and if you look at the expression this is just y of t. So, the integrals are taken care of now that portion is coming here and now about what about this one. Now, you just simplify them. So, you get p t w 1 t w dot t minus w 1 dot t w 2 t f t. And this nothing but the Ranskian of w 1 w 2 and we have normalized. So, that the Ranskian is equal to 1 by p t and this p t p t goes away. So, you have just plus f t. So, indeed. So, therefore, y indeed satisfies equation 3. So, I already checked that this y has already satisfied already and already seen. So, therefore, therefore, y is indeed a solution. So, in fact we have just remaining 5 minutes let me just say what we have done. So, we have started with just let me recall. So, w 1 w 2 w 1 w 2 are two linearly independent solutions of homogeneous equation 3 with. So, we have normalized Ranskian is equal to 1 by p t also. So, w 1 a equal to 0 and w 2 b equal to 0. So, if there are more general boundary conditions. So, you have to choose w 1 w 2 appropriately and then we define this g. So, it has a name. So, this is w 1 s w 2 t if a less than or equal to s less than or equal to p and other way around. So, g is called Green's function bound to value problem. So, it is very much dependent on the boundary values that is very important. So, if you change the boundary values if you take more general thing then the green function also changes and this g then gives us the solution of the boundary value problem. So, next time we will consider some examples of construction of this green functions and you are seeing that we are taking the advantage of the linear system and existence of linearly independent solutions and more generally the fundamental matrix if you are dealing with a first order linear system and that is going to help us in construction of the green function and which will eventually give solutions of our boundary value problem. Thank you.


The world is experiencing one of the most fundamental shifts in recent history. So many of the rules have changed when it comes to business in the world today. In a world that's a little bit more complex, that's technologically different. The norms are no longer the norms. In all corners of the world, we are seeing growth from Africa to South America, from Asia. This is the first thing I think. We know we can't continue doing things the way we've been doing them. The name of the game has changed. We have to start thinking as real citizens, beyond governments, beyond borders. Those cultural differences will also bring a different solution. It's not enough to sit in the back row and watch and observe. Today's leaders want to actually drive the discussion. Sometimes you have to break what exists to move to a better system. So in a sense this opportunity to reinvent everything, redesign everything. I want to welcome you all to the annual meeting of the new champions. The new champions are living the shift. They are the shift. Global growth companies, young global leaders, technology pioneers. All individuals in organizations that are challenging conventional wisdom. There are enterprises which are not just protecting the environment. They are actually producing the environment. They've looked beyond profit and they say, how do we generate value? We basically decided to become the first company in the region to become water mutual by 2012. Imagine a world where you can save 50% of agriculture, then you have enough water for everything else. Now our irrigation system save almost 50% of that water. We are a CO2 positive. Through our forest we capture more CO2 than with our production generates. The crisis that we're facing is going to be fixed by innovation, by leaders that are different. I hope to peak your curiosity with a vision to the future of how we might enhance brain function as we know it and possibly change our sense of self. How can technology, robots in particular, help make medical care accessible to more people? It's not just kind of convening people, catalyzing the conversations. It's also helping to architect the action that comes out of that. Medical problems are multi-faceted, multi-dimensional problems. Would there be a side effect to increasing your capacity by 20%? The people who will end up doing best are those that jump first, those that recognize first, those that get in there, the head of the game.  We have to continually improve ourselves. We have to forget yesterday, forget the past, forget the past.  We have to continually improve ourselves, we have to forget yesterday, we have to think of today and tomorrow. Because our mission is live this world better than you found it. And we're not content to just reproduce yesterday, we want to produce and co-author a new, more inspiring world for tomorrow.


Your Excellency Ambassador Betty King, the permanent representative of the United States of America to the UN in Geneva, Thierry Ray, the Deputy Director of the United States Patent and Trademark Office, and ladies and gentlemen, it's really a great pleasure for us to be joining with the permanent mission of the United States and also the United States Patent and Trademark Office in being able to display some of the ingenuity of Steve Jobs in this exhibition called the Patents and Trademarks of Steve Jobs, Art and Technology that Changed the World. It's an exhibition which is very much in keeping with the theme of World Intellectual Property Day this year which will be held in April and which is on, as you can see from the banner behind you, Visionary Innovators of which of course Steve Jobs very much, Jobs very much was one. He was of course one of the most influential technology thinkers and actors of his generation and it's interesting in a recent survey that was done by Lemonson and the Massachusetts Institute of Technology of some 1,100 young Americans. Steve Jobs was voted by them as the second greatest innovator of all time after Thomas Edison and some 40% of those who responded, the young people who responded to the survey said that they could not imagine life without one of the devices of Steve Jobs, namely an iPod or an iPad or a tablet or an iPhone. What we are very fortunate to be able to display here thanks to the generosity of the United States Patent and Trademark Office is over 300 of Steve Jobs's patents, most of which come under the iconic Apple brand that Steve Jobs was responsible for. You'll notice on each of the representatives, representations of an iPhone that there is the time 9.41am and this is just one of the mysteries that Steve Jobs introduced. Nobody I think really knows why that time 9.41am was chosen. Some say that it was because the iPhone I think it was was revealed at a conference in San Francisco at 9.41am. Let me extend my thanks to the permanent mission of the United States on behalf of the organization as well as to the United States Patent and Trademark Office. We're really very grateful to them to have this opportunity to display Steve Jobs's work. I'd like to thank of course Ambassador King for her presence here personally tonight but let me extend also a special thanks to Terry Ray who's the Deputy Director General, a Deputy Director of the United States Patent and Trademark Office. Terry has come all the way from Washington or from Alexandria in order to be present with us tonight so it's a very great effort and we are very deeply indebted to you Terry. Thank you very much. Finally let me thank the creators of the exhibition who are known as Invent Now, Inc. which is a non-profit organization dedicated to fostering invention and creativity through its many programs and Invent Now also runs the National Inventors Hall of Fame and Museum which is on the campus of the US PTO in Alexandria, Virginia. Thank you very much. Thank you and thank all of you for coming and I want to add my words of welcome to those you just heard from the Director General and we welcome you because we think that this is a very exciting and important exhibition that honors the work of a true giant of our time, Steve Jobs. As most of you know, Steve Jobs was the ultimate icon of inventiveness and sustained imagination. He knew that the best way to create value in the 21st century was to connect creativity to technology. He will forever be remembered for the company he created where leaps of imagination were combined with remarkable feats of engineering.  Secretary Clinton just a couple of weeks ago called all of the ambassadors, the American ambassadors around the world to give her final charge for her final year to those of us who work for her and the person that she brought to inspire us at this meeting was the author of the Steve Jobs book Walter Isaacson and he regaled us with stories that we could spend the rest of the day talking about but the thing that I remember most, the example that I remember most is Mr. Isaacson talking about how compulsive and obsessive he was with perfection that the engineers when he was doing one of these things behind me, I'm not a computer person but anyway, iPod or whatever, they would bring the glass that's on top of it or it's not really glass but the plastic and he kept asking well does it have to be this thick, why can't you make it thinner and the engineers kept saying well this is the thinnest thing we ever have and he says no it's not and you just go back and you have 24 hours to find something else and this went on and on for every aspect of this whatever invention, whatever new thing that he was coming out with and so the reason she wanted us to hear that is that she thought that if we all could be imbued with just a little bit of his determination and his desire for perfection that maybe we could all be better diplomats and I have to say that we know that his reach, Mr. Jobs's reach was very broad because someone like me who I never saw a computer I ever liked, I didn't like the equipment because it looked bulky, never fitted with my furniture, I didn't want it seen anywhere in my house and then he opened an Apple store not far from my apartment in New York and I found myself like most New Yorkers in that downstairs in that iconic building on Fifth Avenue at all hours of the night and you could go there two o'clock in the morning it was full of people, you could go there ten o'clock in the morning it was full of people it was really he really did change not only the style and all of that but brought a lot of us sort of late bloomers in the field of our technology to this work. Next month as you know wiper will mark World Intellectual Property Day with a very appropriate and relevant theme visionary innovators and we've all heard that he is the epitome of one of these. I think it's entirely appropriate that we celebrate the work of a man who embodied the spirit of innovation at the headquarters of WIPO because the raison d'etre of this organization is to foster innovation and to protect and defend the products of such innovation. So we would like to thank WIPO, the director general and all of his staff and the USPTO for their excellent work in bringing this exhibit to Geneva. We hope that over the next month many people will have the opportunity to visit so we want you to go out and tell the rest of Geneva that they are indeed missing something if they don't come to visit too. Thank you. Thank you so much for giving me the opportunity to speak before you today. I have to tell you that this what you see behind you was in the atrium of the US patent and trademark office and at first it was primarily intellectual property attorneys or patent attorneys who came to look at the exhibit and as the days and weeks went on more and more visitors who have never thought about intellectual property who would have never imagined that they would have come to the US patent and trademark office people were constantly in our lobby and you could go to the lobby of the US patent and trademark office 24 hours a day. So if I worked very late into the evening and I was leaving at 10 p.m. there would be people in the lobby of the US patent and trademark office reading each one of these patents that you see behind you because people partially they realize that they lost that this planet this world lost a true artistic director somebody who wanted to make each one of our lives as best as it could be and in particular our US patent examiners are very very proud of this exhibit and they can tell you how many times their names appear on these patents that you see below me. So this exhibit was very personal to our patent examiners and our trademark examiners but Steve Jobs was personal to everybody in the world and he touched each one of our lives with those of us who are here today and it's important to remember his beginning he was an adopted child who dropped out of college I don't think you could say flunked out but I think theoretically if you looked at his last semester grades that description he was asked he would have been asked to leave if he did not leave. He was a great thinker he was highly focused he realized that we needed information and we needed it in a more efficient manner than what our standard libraries and written print and paper would have given us and he actually wanted to change the world and change things and in my mind he is one of the foremost leaders in what I call disruptive innovation. So incremental innovation is great it improves each one of our lives but disruptive innovation, innovation that changes how we do our research, innovation that changes how we listen to our music and how we keep track of our music, innovation that changes how we do our work whereas everything is conveniently computerized. I am sort of consistent with Ambassador King's I always wanted the smallest computer in my office possible because I viewed it as visually and artistically ugly. Steve Jobs said no you can get all this information and it can look good it can look beautiful. So at any rate I wanted to give you a quote what Steve Jobs had said and he said design is not just what a product looks like and feels like design is how it works. So function and design are one and are critical and for that I thank him. Another thing about Steve Jobs is he was a highly focused intense individual he was a very good businessman but he was a dreamer and he was never afraid of failure. Now he obsessed to try to avoid failure but he was not a success with everything that he did so when I speak to people in universities and young people you cannot be afraid of failure because frankly failure is something which you can learn from and will benefit you later in your career and Steve Jobs knew that everybody could fail at coming up what he considered to be a computer but to actually succeed he planned on taking things to the next step and he didn't worry about failing and he wanted to get each one of us to understand better his vision. In my mind he was the ultimate dreamer. There's another story that I'd like to share with you and that is unfortunately close to the end of his life when he was in a hospital he was with his sister and he was in a hospital bed with all of the equipment the medical equipment and gadgets around him and he was sketching out with a pen and paper with his sister new designs for medical equipment. So his creativity, his innovation, his yearning to make life better for each one of us was constantly and through to the very end. I think of this exhibit behind us as a true memorial to his vision he has he just he liked life he liked mankind he wanted to get to know each one of you but not talking to you not personally he wanted to give each one of you an iPad an iPhone a computer and he thought that if we all talked to each other in a more efficient way it would take us to the next level. So I applaud his vision I I view this as somewhat of a solemn moment that he is no longer with us and I am hopeful that there are other people throughout the world that will take that same level of leadership and innovation design and somebody that's looking out for us will help take us to the next level and make us more efficient in what we do and make each one of us better people with what we do if we have the tools to do our job and then we all could help society in a better way. Thank you so much thank you Francis thank you Ambassador Kim.


From San Francisco, it's theCUBE, covering OSISoft, PyWorld 2018. Brought to you by OSISoft. Hey, welcome back, everybody. Jeff Frick here with theCUBE. We're in downtown San Francisco at the OSISoft called PyWorld 2018. They've been doing it for over 15 years. There's about 3,000 people here from all types of industries, really sharing best practices, about using this software solution and the data that comes out of it to basically find inefficiencies. And we're excited to have for our next guest these Josh Reigns, a senior metering engineer from MIT all the way out in Boston. Josh, I'm glad we could get you out of the snow. Great to be here. Absolutely. So a little bit about what you do at MIT. I deal with the campus metering, campus energy metering. MIT brings in electricity and natural gas and then makes electricity, chill water and steam and then distributes that to the rest of the campus. I deal with all of the physical meters in the building, the data acquisition hardware, as well as the PI system that hysterizes all of that information forever in a day. And just for people, kind of general scope, how many buildings, you know, what are some of the kind of top level numbers of all the systems that you guys are keeping track of buildings, et cetera? We've got about 120 buildings, I believe. At the moment, we aren't metering that many. However, we are pushing out a lot more meters within the next three years to do exactly that, to really get a good solid grasp on exactly what every single building is using, every watt that goes through the wall, every BTU that goes through the wall. So it's interesting, because buildings are kind of a living organism. I think most people, if you're not in that business, right, you see the walls, you see the glass, you think it's pretty static, but there's actually a whole lot of stuff going on. And I wonder if you can talk to some of the, you know, obvious inefficiencies and opportunities to make those buildings perform better, performs the right word, and maybe some of the less obvious ones that you've discovered using the Pi software or just other ways that you've discovered opportunities. Calling a building a living entity is actually a really great example. We'll have buildings that will almost completely shut down between the hours of about 10 o'clock at night and maybe about six or seven o'clock in the morning. And then you can actually watch and using the Pi software is phenomenal for this. You can watch the building wake up in the morning and come alive. You can see in the summer, the doors start to open, the internal temperatures start to rise as people come in and out, and the chill water usage go up as that air conditioning starts to kick on. Some of our newer buildings, we have done some predictive analysis on in the building management side of things. So the air conditioning, I should come on about 30 minutes before people start to come into the building and try and pre-cool and get ready for that influx of heat as people start arriving. It helps maintain the overall temperature of the building and you don't get some of those big swings that would then propagate back to the central utility plant. This allows the central utility plant to even out their chillers, maybe bring on a larger chiller a little bit ahead of time and not have to then bring on two or three chillers in order just to deal with that surge of heat coming back in. Just curious, one of the really interesting topics is happening all over right now, right? With the rise of intelligent machines and artificial intelligence, as you know, are the machines going to take over the world but really, consistently we hear, it's really humans making better decisions with data that's provided by the machines and the system. So I wonder if you can share some examples of that where you've been able to take some data, find the pattern without maybe some really crazy big data analytics or running all kinds of crazy analysis but actually relatively straightforward trend lines or anomalies that really pop out of the data once you have the data presented in an easy way to consume. There are actually two scenarios we had on campus within the last year that popped mine real quick. One of them was in a building where we had simultaneous heating and cooling we found. In the same building. In the exact same building. How big was the building? It's actually one of the central buildings on campus. I can't remember the square footage but it was. Like two stories, eight stories. About four stories with a large mechanical subbasement to it. And we found that, we actually found the simultaneous heating and cooling and were then able to track it back and find a three-way valve that was completely broken and allowing both hot and chill water to float into the coils at the exact same time. Just by finding that, fixing the valve, we were able to bring that under control and reduce the wasted energy going into that building. By how much? Or is it back to 10%, 100%? I want to say it was 5% on that one. Okay. One of the larger improvements we made. We had a building that was returning a chill water delta temp of somewhere in the 0.2 to 0.4 degree range. So we were supplying chill water at 42 degrees and getting it back at roughly 42 and a half degrees. Ideally, we're striving for a 12 degree differential to actually pull the heat out of the building and bring it back to the plant. So it should be hotter water coming back. Exactly. To the air conditioning, okay. Once we found this, we realized that the control valve was not working in any way, shape, or form that we were supposed to, it was basically stuck open. Once we were able to identify that, we were able to fix the valve, start controlling the building better. The savings actually necessitated the amount of chill water on a gallon per minute basis going into the building was roughly 1200 gallons a minute, full flow. We dropped that down to close to 150 gallons a minute. That necessitated, almost shutting off a chill water pump at the plant. Estimated savings over the course of a single year, I believe, anywhere from $60,000 to $80,000. Wow, but what's interesting about that story, because the actual valve itself that was broken had no sensor on it, right?  But you're able to determine, based on the other data, to track it down. Yep, correct. That's a great story. And it really ties to another factor, which I'm sure you already talked about kind of evening things out and we hear a lot now, right? In the popular media about Tesla batteries, you stick them on the side of your house and now you can kind of manage your consumption off the grid when it's cheaper and put it back on when it's expensive. Because it's not a single price that you pay for that kilowatt, right? It's just a highly variable. So I wonder if you've been able to really take advantage there, too, to avoid some of that peak consumption patterns that's going to cost you a lot more than if you can even it out. Actually utilizing the Pi data in the past was one of the pushes towards MIT creating or revitalizing their cogen system and bringing in an entire new cogen building, increasing their existing electrical output from 25 megs up to theoretical 40 megs in order to reduce how much we are pulling off the grid at any one time. Wow. So what's next? What's next? What are some other opportunities that you see that you can leverage these tools to go find some more inefficiency? One of the things, and actually one of the reasons I'm here at this conference this year is to work on a way to pull in high speed PMU data. And be able to analyze that after an incident happens or as an incident is happening to determine where analytical fault may be occurring, whether it's in our system or whether it's coming off the grid and make determinations as to, do we need to replace equipment? Do we need to go into island mode and do we need to disconnect and just source all the power directly? Are there particular buildings that we need to isolate and figure out why are they performing so badly immediately and could be a detrimental cost to the campus? So it's really interesting because you're finding all kinds of opportunities just to fix things versus I would imagine at some point somebody looked at a number and said this is completely inefficient like your other building, we need to overhaul the whole system. Yes, and we've got an entire system engineering group that is doing exactly that. They are taking data after the fact that they are analyzing it over the last year, two years, 10 years and determining how a building was operating 10 years ago. We may have made full building renovation. How is it operating now? Did we do better? How, if this building is almost equivalent in usage, in size, in location on campus, direction of where the sun is and they renovated this building but they haven't done this one yet, can we expect to see the same energy improvements on this other building or should we do this other building in order to get to the same energy profile? Right, really cool stuff. So Josh, I really appreciate you taking a few minutes to stop and buy. Happen to be here. All right, he's Josh, I'm Jeff. You are watching theCUBE from OSISOF PyWorld 2018 in downtown San Francisco. Thanks for watching.


My name is Celeste Jude Sable, come on rock my palm and she is the most patriotic woman in the entire world აღღზ ღღსყჄკგვგპვს჊ჟჺ  tissue koy kakw  같板 ಕ್ Gingerallow a is  JJonak폰 destac Dart ಕೋಲೋUI  wondಲೋಮರ ಕ್ರ Luiza ಅನ್ಱಿBLEEPಮ್ಸ configure ವರ್ಯರницаತ್ಯರ್ಸಿೆ ಲ್ರಿಣದಟ ಜಾಮಮರೝ�  ಮ� instant happiness ವೈರರೇಳಕ ಸೕರ್ �二 scheme आप अाप आप अ pesos ज conceptsं न आप न घथ प्यश वो ईप बान पdioं तझो ke आप न औग ㅋㅋㅋㅋ जदे व нажब जद � वग tablej de ऒो उआप उचऎण बण अचँचच वर वख of నియ్హాలింి నిఆరినినిని నిఋత౧ాపి నిపింటకికిఇతారడికినితి నినిఆడికికినియంకింటిక౿నితానికి.  masculinity                                                                       dul  orient                           duty day because she put herself on the on the battlefield and she went and she faced the lair leader and you went to Giaclar and all there are so many people so far today or me is RL so say that day and me become RL and RL means Republic of Liberia wow yes wow and how long have you been dressing like this? I've been dressing like this for 12 years why because I love my country and also that women made the flare and the flare is important to Liberia people our time those day flare is to important October 24 is a day for women in Liberia and that day reach every houses can get flare car can get flare human being can get flare we can celebrate from in the morning until in the evening but say nothing nothing walking flare be dying so I have look at you and say no I can't be leaving of course they are setting with me die and flare die though I can't be leaving for flare to be die so now I start to bare put the knee on me that I will be Republic of Liberia because of the war of the peace we put down in Liberia so I will take the responsibility for me to well flare through my life until I die so you die so all your clothes are flare my digital flare my everywhere you see the flare even the chair you see my chair that same flare you can see no difference something there my flare I love my flare my three colors in my whole life until I die I already saw myself in my young age well close I used to wear and forget but in the same day nothing nothing walking I decide that I'm okay my flare I love my country you are the most patriotic woman in the entire world yes that's me here and I'm so happy that you love Liberia so much so I love Liberia to my deep on my heart you caught my blood so so Liberia come from there the way I love Liberia I love Liberia will love the die Liberia will shine and shine and will go let's sing the Liberia national anthem oh hey Liberia hey oh hey Liberia hey oh hey this growing land of life but they shall not be here don't need any grippy of me and my teddy bear don't need any grippy of me and my teddy bear and my teddy bear and my teddy bear one two three four enjoy enjoy enjoy there you go happy to see you but you know what I want to say something like thank you so much for watching this amazing episode this is the most patriotic woman I've ever met all you need to do is to share this video let people know that there are people who love their country with all their heart and mama RL yes I'm a woman I don't educate them you see me so I don't know book but my talent where God gives me is in love with myself everywhere I behave people respect me I don't know book it's too big for me but you my second step with your degree again I can make it before you so I try to tell the world that you know everything no I don't know book but I get talent I can feel fresh you know I can feel liquid so I can feel cool I can feel gentle I can feel cool I can feel breeze I can feel at the same time I'm a century so I don't know I don't know book but I know things my knowledge is working like a clock so I'm proud to myself that I'm working in it again for this one number eight I'm a candidate ran for 2017 for the day straight as representative I ran a representative for the day straight for 2017 election we pass I'm one of the candidate who are 22 candidate running in the day straight but I went as independent candidate in a king face so I'm proud so I'm proud I can make it anywhere anywhere I can make it so thank you very much thank you so much


Thank you, Mr. President. Dr. Hewitt is a search officer, Mr. President. Other billers in the White House side, Mr. President, how are you? Like this way, sir. Thank you. Well, thank you very much. I shall move forward to it. Dr. Teller, would you like to have it with us? Dr. Bill Fischer, thank you, sir. Good to see you. Nice to see you. Thank you, sir. It's all right. Thank you for everything you've done, Mr. President. Mr. President? Mr. President, thank you. Nice to see you. It's all box-bomb. Chairman of the White House side. It's a pleasure to see you, sir. Thank you. Thank you very much. Professor Singer and Latina. Good to see you again. Thanks. Good to see you. Bill Adlian from Duke. Hello. I have a new shirt for you. Thank you. Well, thank you. Ed Freeman from San Diego. Nice to see you. Good to see you. Good to see you. Good to see you. Good to see you. Good to see you. Sandy McDonald. Well done Mr. President. Thank you. Nice to see you. Very good. Joe DeSutter. Thanks to President. Good to see you. Yeah, I want to get this time off the call for great years. Yeah, it's fine. And if everyone could just tighten up as much as you can on either side. Yes, yes it is. That's the sprint. Keep it from the curb over a little bit. That's it. I couldn't get any of the time. Okay, great. Everybody can look right here. Big smiles. Thank you Mr. President. Thank you Mr. President. Thank you. Thank you. Thank you. Thank you. Ladies and gentlemen, science being interesting to know. With that operation through the Duperson Contracts from here up to here, took 2 ½ hours. I couldn't believe it. I went into the hospital with a picture that I'd be sitting on the corner of a desk or a chair with Planned shirt and a pair of slacks and watch them work on that for a few minutes and get up and walk out No, I was stretched out in the hospital suit. I couldn't see it. They put something in here Stayed there and I stayed there and then the horrifying thing I heard the doctor say well It seems that there's a lot of little nerves in the hand Yes Well as a matter of fact we probably know is that the history that after World War one There's a great neglect of hand wounds because of more serious wounds that they thought were life-saving so far and then The record is it developed the hand wounds and hand injuries and so forth Let the army then to set up and declare they were going to become specialists in surgery And I don't think there's any higher level today There at the Yard like at Walter Reed Hospital on that particular subject I Decided these military gentlemen, maybe I just take it for granted Well, you didn't come here to ask have me tell you about my operation But I do want to make all of you Counsel Well, and I thank all of you for the service that you've rendered Best of everything well And


Hey friends and welcome to my channel I am Yoshida and this is Norris Cove so today we have this situation going on here this is my micro if you follow me on Instagram I am at Norris Cove on Instagram and if you follow me you've been seeing me do little show them little inserts little daily pages that I like to do I mainly started using this for work in the beginning I didn't know what I was using it for I basically let me see let me see if I can find one of my very first pages in here yeah this is how I was doing my income I was just writing it down this way well this was a little boring and actually you see I tried to you know dress her up but I just wasn't getting it and then you see I left a few little pages and that's what I was doing but I wasn't really consistent with this away and I'm actually take those out so then I decided hey why not make it like a daily page and then that's when it came to life that's when I started using more often so here is a little snippet and small flip through I even have a grocery list which needs to go in this area and I just started doing more like daily pages and basically for work some days it's not pretty because I don't kind of plan right so I had two days where I just didn't have a chance to put stickers in it and then I mainly use it for work well Anika my good friend Planner Bay Anika she did hers and she showed how she did hers and I'm always inspired by her channel if you're not following her you need to follow her you'll get some great inspiration well she put the jelly pockets and and I've had some jelly pocket paper I've been holding on to for months I mean months I even have some yellow where's the yellow one at so I have this yellow one I've been holding on to and then I had this blush kind of color one naked or whatever and it was just sitting around and when she showed how she put that in I said you know what let me try that let me give that a try and gussie up my little micro note so today without further ado and rambling we're just going to set it up on camera I don't think it'll take them on because I've already made cut the paper I will leave Anika's video on how to cut this paper if you have a silhouette she'll show you how to do it on your silhouette portrait I had one and to my I swear I didn't know that you could cut paper will cut you know anything without I was wondering how those registration marks work but I found out today needless to say so I have some vellum here that I like to use and consider when using I have my puncher here I have some disk I have extra notes I've had this maybe a week or two now and I've just been holding on to it because I need to go in and just set this baby up so first thing I'm gonna do is take off these bags let's take this okay so now we have a disk on I have the regular business rose gold disk and I wanted those to match that I actually kind of bought them for my face planner but I'm just gonna go with something else and I'm gonna take a few pages or paper from this new one and I do like the rose gold just the mini ones here but I didn't think they would be big enough so I'm gonna see if they're big enough I may just kind of switch back to them so I'm just gonna basically start setting up my sections and I'm not certain but I'm almost positive that you could take some half no paper but cut it down to size but that would be a lot of cutting I guess because I know this is not exactly like a half a sheet so with this section that is my affirmations I'm gonna stick that there affirmations are in the back let me do a couple more pages of that oh and then let me explain this so here where the tabs are with this one I just took some I shot my stash I had some old sticker paper here and I just wrote in affirmations let me zoom in just a little bit more so I wrote in affirmations so then now let's take a little bit more paper I think I'm just gonna alternate with some of this paper so my next section should be I was gonna say list my grocery shopping so basically this tab says again shot my stash and it says grocery and I put a little cart there but basically this is what I'm gonna keep grocery list and just list period so I'm gonna mix in a little bit of this paper so any kind of list and I know that it's any kind of list but it's mainly for grocery list and I'm just gonna put that there and then here's my grocery list and then this was on there I'm gonna slide that on in and then I have a Walmart list here as you can see slide that on this is like a running Walmart list so I love their trash bags they're cheap so it's like a running list okay let's see what else we have the next one is this week now this week wait I'm gonna miss someone hold it hold it hold it when it's all the same work oh here it is I'm like wait a minute something's missing work so work it's pretty much I like this so I'm gonna put this here this is actually that's gonna be part of this sweet Kegel work and I think I'm gonna take these first pages I need to keep this one because this has that's a note and that has my tax information on it and like the other day I could not remember like what I made on a certain day I was able to come right back here in my micro and write down what I mean I keep my income in about four different places but it's very helpful for me so here we go and that says work so there's work and then let's get a nice cover for work flawed and still worthy and this came from Goman and Coco there we go and that jelly piece is over it my daughter souls and I'm trying to get her to make me like a little pocket so I can add things to it and then this is this week so this week I'm trying to figure out what this week will basically consist of this week I'm thinking will just consist of like basically I may turn it into a daily you know planning a little bit so I might be able to daily planning this and it kind of goes into my work week so that's what I plan to kind of do with this week at least that's what I have in mind and again I'm just mixing up these pages any color that way I can just kind of go in and add any color that I want a flip to work add some more paper here and work since I did these little pages I'm gonna kind of hold on to these because sometimes I like to look back over stuff and see like what I made and see I want to add a little gold section as well I like to carry my goals with me but this is what it's looking like isn't she pretty and I gotta have some you know embellishment so I'm debating on this bow is it too big let me see me slaughter and he on my little jelly pocket these little jelly dashboards are too cute I would have never thought to do that because I was just always I don't know what I thought really to be honest with you so I could do that but I think she's kind of big for her but she's really cute I have this one I'm thinking I'm just kind of leaving her really cute and kind of simple so I like this bow here and I had something close so I'm just gonna put the extra aside I was gonna put in some angel paper I mean some vellum I'm gonna take this out real quick and being that she's pink I think I'm gonna use this okay so I decided to put this pink vellum over top of this so that you can kind of still see it but it gave a little bit of how I like to mention a little bit and then just in between randomly so affirmations so affirmations I'm gonna look for a great quote here and quote so I have faith in quotes for my affirmation I'm gonna go to quotes and then I'm gonna I'll for affirmations daily I'll probably be looking up some if I can't it says courage is grace under pressure I like that and right now we're doing here we go just so that'll be our opening page to our affirmations okay courage is grace under pressure I just had something I wanted to add to this but this is what she's looking like these as well and I need to get to my work that's pretty much what I need every day is to get to my work so I'm gonna keep this paper clip here so that can get me there a little faster and then also I'm just gonna stick this thing there and here she is she's so so cute look at her let's back out just a little bit so we can appreciate her oh that bow I don't know she's cute but I just don't know let's take the bow out and see and let's slide this here like I said my work is what I mainly use this for so we just gonna slide this on so I can be able to get to her oh that's just cute enough that's really cute I feel like I need something else on I don't know why y'all know I love a little juicy planet so we've used up all of our paper and I think the classic this allow you to be able to add to it like I said I probably after a month of dailies I will probably just like take it out or you know me putting in my my work budget and everything so this is it and I think I want to kind of add another section like a to buy section I have list but I just want like a to buy section I think so this is oh this is so cute I just don't even know what to do okay you guys so this concludes my video I hope this video has been helpful I hope you enjoyed me showing you my setup of my micro oh and the disc match the words and oh this is so so pretty I need more okay thank you all again so much for watching I will see you in my next video if you're new to my channel you enjoyed today's video and you would like to see more things for myself please hit that subscribe button don't forget to share and like this video comment in the comment section and also hit that notification bell so that you are notified whenever I upload content I will see you in my next video bye


Good morning, Hank, it's Tuesday. So this is Tetris, a video game developed by Alexi Pajitnov that arrived in the United States in 1989 for the Game Boy and the Nintendo Entertainment System, aka the NES. Tetris became a phenomenon. In fact, it is still the best-selling video game of all time. And lately, I've been wondering, why are humans suddenly getting much better at Tetris? First, a little background. There are two, like, great white whales of NES Tetris. The first is a max-out score. If you get 999,999 points, the game stops being able to count your score. The second is level 30. So in NES Tetris, the blocks fall faster as you level up, and once you get to level 29, they drop so fast that it's almost impossible to move them left or right, making level 30 seemingly impossible. Back then, there was only one player, Thor Ochreland, who claimed to have achieved a max-out score in level 30, and lots of people thought he was lying, which, as it turns out, he wasn't. We now know that Thor was just, like, much better at Tetris than all other humans. Anyway, the weird thing about NES Tetris in 2008 is that far fewer people were playing it than played back in 1990, and you would think a larger player base would mean higher top scores. Like, in 1990, hundreds of millions of people were trying to solve the problem of getting to level 30. By 2008, very few people even still had a Nintendo Entertainment System, let alone regularly played Tetris on one. But a few people never stopped playing NES Tetris, and as tends to happen when you do something for 20 years, they got pretty good at it. Also, by 2008, the world's Tetris players were much better connected to each other than they had been back in 1990, partly because the internet has connected all of us, and partly because smaller communities can be more tightly knit. Like, when 100 million people are talking, it's hard to hear anything but noise. So Tetris players started to learn more from each other. Together, they figured out that you should always build your well of empty space on the right side of the screen, except as you approach level 29 when you should build it in the middle. Also, some of them developed a new strategy for moving pieces called hypertapping. And then in 2010, a tournament started, the classic Tetris World Championships, which brought the best players together in real life and motivated them to improve via competition. The quality of play at the tournament has improved every year, like this year several people achieved max-out scores in qualifying, and eventual champion Joseph became the first person ever to reach level 30 in front of a live audience. And then there's live streaming. Tetris players around the world now share their games on Twitch and YouTube, which allows other Tetris players to learn from them. Even people who've been top-level Tetris players for decades are changing their playstyle to reflect new discoveries and strategy. And as a result, dozens of people have now maxed out. And Joseph recently made it to level 31, a land previously only visited by the legendary Thor. Now, I want to be clear that getting a max-out in Tetris is still, like, ridiculously hard, but it's possible. So why is humanity suddenly getting better at Tetris? Because a group of enthusiasts built spaces, both online and off, that allowed people to connect with each other over what is usually a very solitary hobby. And because small groups of deeply passionate people can often be more productive than large groups of casually interested people. I've been thinking a lot about that, which is one of the reasons Rosiana and I ended up starting the Life's Library Book Club, which thanks to your overwhelming response is now open for enrollment, link in the doobly-doo below. But more generally, I know it's fashionable these days to say that the internet is a festering cesspool of toxicity, and, you know, it is. But the internet is also many other things, including one of the primary drivers of humanity's improved performance at a 29-year-old video game. Really, there is no THE internet, especially in the era of personalized feeds. There is only for each of us OUR internet. I don't labor under the delusion that I can make THE internet better, but I do want to make MY internet better. And on that front, I think Tetris has a lot to teach me. Hank, I'll see you on Friday. P.S. next week. Pizza Mrs. Coming. You know what that means.


football fans. Welcome inside the Fandals sportsbook here at the Meadowlands. It is week four and we are here to bet it. Thanks for hanging with us. I'm Lisa Kearney. We've got a huge show for you today, including actor, comedian Anthony Anderson joining us to talk about his Raiders and his Super Bowl pick. That's ahead. But right now, gotta give all the love to my teammates. What's up guys? Our experts breaking down the biggest games of the week. Of course dropping their best bets on the board. Plus we've got your best value. DFS plays as well. It is go time. So make sure you download the Fandals sportsbook app right now. Sign up for your new account. Do not forget plug in that promo code right there at the bottom of your screen. More ways 1000. You will get a risk free bet up to 1000 bucks. All right, they're calling this first game. We're getting to the return. Bucking ears at Patriots or Tom Brady at Bill Belichick. Yes, it's being referred to that as well. We've all had this one circled on the calendar. The goat returning to Gillette Stadium for the first time since leaving New England. Brady said he's quote not going to be thinking about 20 years of history here. He's going to be thinking about one night of football. Gotta respect that both the Bucks and Patriots coming off double digit losses here. Tampa Bay is a seven point road favorite in Brady's former home stadium. Dave and Ed got to get you guys in here to bet it. It's going to be an emotional one on Sunday night football. There's no doubt about that. Dave, which side do you like here? Well, my problem is where Tom Brady is returning from this week in particular coming from California research every game of his career. He's only gone from California back to the east coast and consecutive road games twice he's owned to against the spread. If you count Vegas last year, he went to New York after that didn't cover. This is just a tough spot for Tampa. I think with all the travel that they've had to do and I don't think Tom Brady is really going to be on the field that much. Anyways, Tampa Bay's defense just has not been stopping teams on third down. The Patriots are very good at converting first down. So I think Bill Belichick really wants to limit Tom Brady's opportunities and it's going to do everything he can to control the ball. This number is too big for me. I like the Patriots. I'm getting so emotional just talking about this game, right? All the emotions. I don't care. I really don't care about the emotions. All the familiarity back and forth. It doesn't matter. Focus only on this game at hand. And to me, the Buccaneers have a much more sophisticated offense than the Patriots do when it comes to pre snap, shifting and motion. The Buccaneers run it 53% of the time. That is 12th most in football. The Patriots run it 26th most in football. So I look at this and I say, Okay, sophistication matters a lot. Tom Brady has a PhD in the NFL. Mac Jones. I mean, he's doing football one on one at this point. Pre snap, shifting and motion. Buccaneers are way more sophisticated. Patriots won 12 personnel to Titan personnel. Much more. That's not good when you're playing from behind. I don't think the number is too big. I'm going with the box. Okay, well, speaking of sophistication, let's get the right take on this bucks Patriots matchup for that. We had to Chicago bring in our NFL expert. Hello, Cole, right? Cole. Brady said it is a homecoming, but he's not expecting cheers for him. Which team do you have winning it by how many points? Well, Lisa, someone needs to queue up that Adele track because it's going to be one heck of a homecoming. It's going to be all eyes on Foxborough on Sunday night football and Tom Brady. Well, he's in Drew Brees's front yard when it comes to kicking in the door when it comes to that passing record. So we'll see Tom, of course, makes some history, but it's hard to imagine that he's going to break that record in Foxborough as a member of the Bucs. But either way, it's also hard to imagine that the Pharaoh threw for over 400 yards on 41 of 55 passes and he lost to the Rams. So it's going to be more than a tall task for the teacher, Bill Belichick to beat his former student. We know how that usually goes and no James White. That's going to be a huge setback when it comes to New England's playbook. So you have to go with Tampa here at 31 to 14. Tom terrific. They roll. Okay, go ahead and tail Cole here. If you roll with Brady in the box, a winning $50 bet at the Fandals Sportsbook means you're going to collect more than $93. Hit up the app, Fandals Sportsbook app. Now to a huge NFC matchup featuring two undefeated teams. The NFC West looks good early, right? The 3-0 Rams hosting the 3-0 Cardinals. Arizona tied for the league lead in points. The Rams ranking second. A lot of offense here in this one. Tony, the LA Rams, a four and a half point home favorite. Which side do you like? Well, I know Dave's going to tell me about how historically the Cardinals stick against the Rams. The Rams have won seven in a row in a series. Going to go to those notes from three or four years ago. I look at 2021. The Cardinals score 30 points in every game. So you know they're going to be a high scoring unit when the line is this big at four and a half. I want to take the points. I mean, they got a really good chance of going into LA and winning this game. So why not take a team that's getting more than a field goal? Give me the Arizona Cardinals. I don't have to go back to 2018 or 2019. You can look at last year where the Rams dominated Arizona. Look, there's going to come a week where I pick against the Rams. I want to actually, but I just couldn't do it here. There's seven on one against the spread. Last eight against the Cardinals, but not only just covering the Cardinals are averaging about 11 points a game the last four seasons against the Rams. The Rams are scoring over 31, seven of the eight times. Look, Arizona's, you know, they've been sloppy, but they've been able to get away with it against Jacksonville and against Minnesota. They can't get away with that against this Rams defense. Too much defense from the Rams. Rams cover. Okay, there you go. There you have it. Time now to dig deep into the NFL's next gen stats. We move on as the NFL analyzes the location, the speed, acceleration of every player on every single play and then uses that information to determine various data sets here and we are using that information to bet this game. So Ed, you're our analytics guy. Got to bring you back in here. Give us a next gen stat that you are using to pick this Cardinals Rams game. Lisa, if you look at weighted opportunity among all Cardinals receivers, you aren't seeing DeAndre Hopkins near the top of the list. Instead, another veteran, AJ Green. Here's his route chart from last week. Green's catch rate over expected, which measures how tough each of his five receptions were. Came in second highest among qualifiers, 37.1%. Notice how there weren't too many yards after catch in that game. Much of his yardage total were air yards. A lot of white there, not much green representing that yards after catch. One of many options for Kyler Murray is AJ Green, and that suggests even a stout defense like the Rams will have problems. I have the Cardinals covering. There you go. Dave, I mentioned Kyler Murray's starting quarterback. No, I'm not going to get into that. All right. Thank you, Ed. Awesome. Next level info from those next gen stats. Ed stated his case, but if you want to fade our guy, go with the Rams at home. Giving the points, you're going to collect more than $97 on a winning $50 bet. Got to do you. And a reminder, you can make your first bet on the app risk free. Just sign up for a new Fandals sports book account using the promo code more ways 1000. You will get a risk free bet up to $1,000. Again, that promo code more ways 1000. Let's move on here. And since we're talking numbers, let's just keep it going. Time now for our DFS download. Of course, that means a chance to win millions in prizes for free. Yes, Fandals hooking it up for you for free. Just head to Fandals.com. Sign up for the weekly free DFS contest and play free each week. Just sign up, set your roster, play and win. And of course, our job here at more ways to win is to help you score as many points as possible. So, Fandal Editor-in-Chief, JJ Zacharyson is in house with his best values here for week four. Hey, JJ. Hey, Lisa. I know he hasn't done a whole lot over the last couple of weeks, but I do like Davante Smith this week at $5,900, going up against the Chiefs. If you look at his peripheral numbers, his usage really hasn't been that bad this year. He ranks in the top 30 in target share on the season at wide receiver, and you have to like him against Kansas City. The Eagles could very easily face a negative game script. That could lead to more passing. And so far on the season, Kansas City has been the seventh best matchup for wide receivers when looking at adjusted fantasy points allowed. So, I think that Smith makes a lot of sense given that he's still under that $6,000 mark. The next guy, he's kind of obvious, but it's Chuba Hubbard. He's $6,300 this week. He's going to be the lead back with Christian McCaffrey sidelined. Hubbard saw the majority of the backfield share when CMC went out last week. He outattempted Royce Freeman 11-5, and more importantly, he outtargeted Freeman 5-1. And I say more importantly because targets are hugely important for fantasy running backs, and it shows that Hubbard could be game script proof. And even though Caroline is the one team this year that hasn't run a single offensive play while trailing, they've got their first real test against Dallas this week in a game with a pretty strong overunder. So even if the game script does get out of hand, Hubbard should be on the field. That's why he's a great play at $6,300. And then finally a little bit more expensive than that is Aaron Jones at $7,400. The matchup against Pittsburgh isn't great on paper, but we should be more concerned about usage and potential game flow with most of our running backs in fantasy football. The Packers are big favorites this week. Jones has now had back-to-back games with at least 70 percent of Green Bay's running back rushes to go along with a target share per game of 14 percent. If Green Bay gets a head in this game against Pittsburgh, Aaron Jones should see a lot of work, and that means he's going to give you some good fantasy output. Awesome stuff as always JJ. There you have it. Go to fandal.com. Sign up for free at DFS competitions right now. And each week of this awesome NFL season, use JJ's info for a chance to win millions in prizes. Of course, follow our guru at Late Round QB on Twitter and Insta. Hit up his podcast, The Late Round Podcast, on Apple Podcast as well. Back to our game previews now as we rip through here and AFC West Showdown is going down on Monday Night Football. The 3-0 Raiders travel to Los Angeles to face the 2-n-1 Chargers. We're bringing in a ringer here to help us bet this one. Actor, comedian Anthony Anderson says Raider Nation will get it done on Monday night. Hey Anthony. Seems as if the Raiders are three and a half point underdogs, but I'm still going for my Raiders. You can play the money line or you go for the spread. I'm going for the spread. That's my pick. Raiders, Chargers, Raiders, Raider Nation, baby. Raider Nation, baby. And Anthony's taken the Raiders, taken all of those points. They're actually getting three. Which side are you backing here in this one? Yeah, a little bit of a move here, but here's a situation where I think this is the game that I'm most looking forward to. Maybe not so much the Tom Brady return. This is the game I'm most excited about because this is a contest with two offenses that are very, very different, but have similar output, similar success rates. When you look at the Chargers, EPA, they're 0.118, which is 14th best in football right around average. The Raiders are just a few hundreds of a percent of thousands, really. 0.109, 15th highest in football. But they do it in different ways. Raiders are an 11 personnel with three wide receivers, 35.6 percent of the time that is third fewest in football. The Chargers run 11 personnel, 55 percent of the time. That's 19th most in football. And so they do it different ways. Should be a very, very close and exciting game. And because of that, I want points. Give me the Raiders. Well, here's the deal with the Raiders. They have been winning big with that home run ball. Specifically Henry Ruggs has had five catches already for 20 or more yards. Here's the problem. The Chargers just do not give up those home run passes. They're defensive, secondary, both their corners and their safeties.  I think that the wide outs for the Chargers are actually going to have more successful plays than the wide outs for the Raiders. I'm going to go with the Chargers, Lisa. And I know Pony's probably at some point going to reference that painting behind Anthony. It's just going to happen. Yeah, yes. He has that queued up right now. I'm going to get to him in just a moment. The three N.O. Broncos will be watching that AFC West matchup very closely. Denver has given up just 26 points on the season, including a shutout against the Jets last week. Yes, there is that home saying it was the Jets. All right. Denver now gets the Ravens who are coming off that incredible 66 yard field goal to win it in Detroit, which pushed them to two and one pony. You are called into you are called into this match. Broncos are one point home underdog in this one. Which team do you like? How could I not reference that painting? The guy had a furry beard. I've never seen that before. Dave's painting would have a glue ripped up exact and trifecta tickets to it. That would be the Dave Weaver portrait. Look, I like the Ravens in this matchup. The Broncos to me are still paper champions until proven. Otherwise, they've beaten teams that are combined 0 and 9 or yeah, 0 and 9 to start the season. Baltimore gets it done close game, but I like him getting you know, just a point here. Yeah, I'm with you because remember Baltimore, they beat Kansas City in Kansas City a couple of weeks. So I had every reason to regress a little bit last week as they went into Detroit and look, they were also missing for their front seven defensively to the COVID list. So they're getting a lot of their starters back. This is going to be a much different game. Don't worry about them having to doink one in against the Lions to win from 66 yards. Oh, by the way, Justin Tucker might make one from 70 in Denver if he needs to. But I'm with you. I think the Ravens are the better team here. All right, you guys, and yes, hold tight because we'll get more Anthony and we will get more of that painting in just a moment. Great stuff by you guys. And I can't believe I'm even saying this, but the one and two chiefs who are still Super Bowl favorites, by the way, we're going to get to that a little later in the show as well on the road at the one and two Eagles this week. Kansas City last in the AFC West will try to turn around this week against this Philly team that got absolutely embarrassed on money and I football losing by 20 in Dallas. Pony short week for the Eagles here. They're getting seven points at home is seven enough. I think it is. I like them because I think they can win the game. You know, we saw the way that Lamar Jackson is a dual threat quarterback, did such a number on the Kansas City defense. I'll ask why Jalen Hertz can't do the same thing. He's been the Eagles leading rusher through three games. You know, now Mahomes has got to worry about nine year olds giving him the double birds when he goes into Philly this weekend. That's a problem according to Eli Manning. So I'm going to take the Eagles as a big number in that hostile environment. Give me the birds. Well, Lisa Pony, I'm working on getting one of those paintings like Anthony Anderson. It's off to the side right here in my office. But either way, I think go through you guys know that the theme this week for Kansas City is going to be ball security because last week they were flat out sloppy versus a less talented charger team. There's no doubt about it in turnovers. Well, that was their biggest setback. Patrick Mahomes with a pair of interceptions. And we know that Tyreek Hill and Clyde Edwards are there and they spit out the seat as well. And that can't happen. And it won't happen this week versus a Philadelphia team that plain and simple likes to spread the ball out. We know Jalen Hertz was able to hook up with nine different pass catchers and Philly schedule from here on out. When you take a look at it, well, it's a plain old hornets nest. This is going to be a loss one in a string of four straight cheats. They go on to win this one pretty big. 2717 guys. Great stuff, Paul. Hey, Ed. I know you already have yourself portrait hanging up in your office. You also already use these next gen stats to fix the Cardinals Rams game earlier in the show. Now I want you to give us three bets based on that next level data that you think are really good values on the Fandalsports book app right now as I like to say the board is open where you taking us? Well, let's start with Carolina. The offense has its star wide out. DJ Moore crushed it last week against the Texans and here's his route chart from week three. More than a third of the time Sam Darnall targeted him leading to an air yard share for the entire team of more than 54 percent and a catch rate over expectation of greater than 8 percent more than used his explosiveness for a handful of yards after the catch. I'm expecting more more against Dallas and I have the Panthers covering next even a loss Jimmy Garoppolo did some good things Sunday night but here's the deal his passing chart against the Packers win Green Bay you know had some issues there defense sent only four rushers as expected points added was 2.6 not bad given his game is predicated on short throws and having his receivers do the rest with yards after the catch. It's why nearly all of the attempts are within 10 yards from the line of scrimmage Jimmy G will have to work on pocket presence having been sacked four times and having a sub par EPA when blitzed but I still think the Niners can cover in this situation. Finally let's check in on Bill's quarterback Josh Allen and see if we can figure out if he is back to a successful form from 2020 or if he's regressing to me I think he's somewhere in between his throws behind the line of scrimmage are all below league average in terms of passer rating if a defense can force those options or short over the middle throws they just might have success but anything beyond 10 yards that's Josh Allen forget it he will destroy a defense Houston they don't have the defense to contain Josh Allen or the slew of Buffalo receivers even though that spread is mighty I'm still going to take the bills great stuff awesome stuff by you always I love those stat segments so intuitive that information take it now use it to place your bets on the Fandall sports book app right now you can place a wager on the bets we just talked about here or hundreds of others they are available for you right now it's the Fandall sports book app time to speed things up hit our betting markets rapid fire style shouting out your local teams as we rip through the rest of the week for Slate here guys I give you the game you have 10 seconds to give me your picks Pony you're in Pittsburgh the one and two Steelers are not they're getting six and a half at two and one Green Bay how do you play it numbers too big TJ Watt should return for this game the last time he played a full game the Steelers upset the bills on the road I'm going to take Pittsburgh plus six and a half day bringing it back here to New York Giants looking for their first win of the season getting seven in New Orleans it might not win but I think that's too many points they've been a great road dog over the last few years nine and one against the spread I don't think James quite has found his rhythm with those receivers yet I'll take the Giants and you get when you're getting Washington and they're in Atlanta both teams one and two but Washington a one and a half point road favorite in this one we need to have some real talk about this Washington defense they have not been playing well this year I know defense is volatile from one season to the next but now they're getting Matt Ryan and I feel like Atlanta can win I'm taking them on the money line Cole coming to you you're in Chicago one and two Bears had one passing yard last week amazingly they are favored by three points at home against the Lions who you got yeah the offense dead last passing offense dead last but Detroit we know it's the Detroit Lions so there you have it it's going to be a perfect storm for a bounce that game I see the Bears getting this one and cool in that Arlington Heights talk they win 21-9 recently all right speaking of struggling offenses here the winless Jets have scored six total points in the last two weeks Pony, New York getting seven at home against the two and one Titans yeah the Titans don't force a lot of turnovers and as long as Zach Wilson takes care of the ball I think they'll keep it within that touchdown spread I'm going to take the Jets at home right great stuff by you guys that was our rapid fire style we move on now because the Jets will be right here at the Meadowlands on Sunday just across the parking lot from the Fandals Sportsbook where I am standing right now the Fandals Sportsbook at the Meadowlands will be absolutely happen this weekend and of course open all seven days of the week watch wager win with your favorite teams and players right here again located right across the street from MetLife Stadium on game day just hop the free round trip shuttle from Lott G if you don't have a parking pass all good too head to Reds Restaurant and Carl Stat catch the $10 shuttle to MetLife and then head to Lott G for your free ride to the Fandals Sportsbook mass transit of course available as well so many ways to get here and absolutely worth your time mark your calendars as well and get here for the 2021 Breeders Crown taking place right here at the Meadowlands race track that's October 29th and 30th get your friends come out for an awesome time here at the Meadowlands and of course the Fandals Sportsbook and tell them Lisa sent you we'll see here and we continue on here on more ways to win from ponies to dogs time to give some underdogs a little love Cole you're absolutely crushing these Moneyline Moneymakers four for four in your last two weeks of upset picks including the saints and falcons last week what you got here for us in week four well Lisa this week I'm only going to focus on one don't want to give too much good information away and last week as we know the Titans well and Indy they weren't able to take advantage of Tennessee's to return over so the Colts they also had to deal with King Henry rattling off 28 carries for over a hundred yards rushing in Miles Gaskin well he's no Derek Henry and we know that the Colts are going to button things up on defense they're going to rattle Jacobi percent just a little bit they're going to squeak out the wind get out of South Beach a 21 to 17 you can count on that one and so all they need to do is squeak it out go ahead and tail Colts upset pick or hey make any bet on the Fandall sports book app right now risk free up to $1,000 all you got to do sign up for that Fandall sports book account new users get a risk free bet up to $1,000 just be using the promo code right here more ways 1000 and our experts are giving you their risk free bet of the week here Dave Ed it is week four shout out to you guys though because you've each nailed your last two risk free bets Dave you had a moneyline parlay with the Rams and Vikings a $1,000 risk free bet paid out more than 4,300 bucks yep Ed you had the Rams minus five and a half on an alternate spread you love the alternate spread your risk free thousand dollar bet paid out about 2,800 bucks guys rolling in it let's do it again here Dave where is your money going this week here in week four we're going to keep it as a two teamer but try something a little bit different than the moneyline parlay we'll call this the three yards and a cloud of dust parlay a lot of runs a lot of running clock I love the way the Dallas defense showed up last week Carolina we know has one of the better defenses in the league that game's going under and then the Jets just flat out can't score Tennessee's going to run the ball all day long the clock will be moving in both of these games under and under alternate total in the Colts Dolphins game I don't know what's going on with the quarterback situation in Indianapolis that's a big concern and then with Miami going with the backup quarterback yeah a backup can show flashes but consistency is a big problem I'm going under 39 and a half thousand-dollar risk-free bet nets me more than 2400 bucks I'm going with one of the cool futures that's on the board one of the betting options at Fandle right now is the team to finish with the worst record and the giants 0 and 3 again you look at the gauntlet the schedule they have coming up they could be 0 and 10 I don't think they'll be favored in a game until Thanksgiving so for that reason you're getting great odds right now on New York big blue to finish with the worst record in the NFL there it is they have people in New York don't want to hear that but hey gamblers make sure to sign up for a Fandle sportsbook account right now to place your bet bet with your heart if you want to do your thing and remember use the promo code more ways 1000 you'll get a risk free bet up to 1000 dollars it's easy it's legal it's live you take your winnings if you hit and you get your money money back inside credit if you don't I call it the best mull again in the business not just football on this show we're bringing you news from the track as well the breeder's cup world championships returns in November to where the turf meets the surf in delmar california the world's best to thoroughbred racehorses will compete for championship honors in more than 31 million dollars in prize money it's all happening friday november fifth and saturday november sixth tickets are available at breeder's cup dot com breeder's cup dot com right now and for those of you who can't make it to the track you can watch all 14 championship races on nbc sports or tvg and tvg not only your place to bet the breeder's cup but you can bet every race every day right now by downloading the tvg mobile app and before we go here on more ways to win we're three weeks in so let's get some updated super bowl picks here the chiefs have lost to in a row still the favorite here our guys are giving us their best value picks in just a moment but first we're getting we're bringing anthony anderson right back in here he says it'll be a different afc west team holding up the lombardi trophy at the end of the season take a listen i gotta go with my team they lost vegas raiders and you know what i want to see you know who i want to see them play i want to see the raiders play tamper bay last time my raiders were in the super bowl we lost the tamper bay in san diego i was at that game so i would like to see that again passionate man that anthony anderson raiders are plus 4100 dave i get my whole team in here dave give me your best value bet to win it all who do you got pony shamed him into changing his selfie angle to cut out the picture good job pony i'm gonna go way down the list keep going keep going the bangles at 120 to one look they got the jets coming up they got the lions come up let's just say they get midway through the year with a nice winning record the stealers are down the ravens are down young team get some confidence i'm saying it's a huge value there 120 to one on the bangles now i agree the afc is wide open at this point given what the chiefs have shown us through three weeks but it's not that wide open let's take the baltimore ravens they've been my pick from day one i'm gonna stick with them i was convinced by the wardrobe change the pink sweatshirt i'm gonna take the raiders just like anthony they're three and oh and yet they're still 41 to one to win the superl they've been the most impressive team in the afc so far so you get great odds with them at the moment well you know what i like arizona and kansas city the numbers they look great with the card knows that at plus 3400 but you know you have to hang your hat on what kansas city is able to do i'll roll with them last season and you take a look at all the weapons that patching my homes has nevermind the record throw it out of the window when all the dust settles i'm gonna go with kansas city at plus 600 yeah pony that's a relaxed look that the pink sweatshirt rolling in here um guys great stuff by you all again that was a raiders plus 4100 that picked by anthony anderson great having him on the show today game picks best bets dfs all the goods we covered it all week four is here you can bet it right now check out all the best we talked about on the fandals sportsbook app new users sign up with the promo code more ways 1000 to get a risk-free bet up to 1000 bucks from all of us here at fandals thanks for hanging with us we'll see you right back here next week after an unprecedented year apart the time has finally come to say welcome back to the prestige and excitement of witnessing history firsthand this november beautiful del mar we'll welcome back the world's best thoroughbreds the brightest stars and most passionate fans to the breeders cup one experience that's a breed apart tickets on sale now at breeders cup.com


When God elevates a man or a woman he never elevates that man or woman with the intention of elevating them for the sake of themselves. When God calls you it's not about your call. When God puts you in ministry it's not about your ministry. When God anoints you it's not about your anointing. When he gifts you it's not about your gifting. When God elevates you it's about elevating his word.


Today, I will be discussing about an important and interesting phenomenon to be kept in mind by positioning a patient for radiography. Do check it out. Hi, I am Dr. Indra Neel and I will be discussing about the anode heal effect. This effect stems from the fact that x-ray photons are produced not only at the surface of the anode, but also at deeper levels within the substance of the anode. X-rays are isotropic in nature. That means they are emitted equally in all directions. Now imagine a group of people say around 10 people had to run a 100 meters dash on a road with less traffic and obstacles, then all of them would cross the finish line. But if the same were to run a 5K long distance marathon on a busy road filled with traffic, probably only a few of them would make it to the finish line. Applying the same analogy, the number of x-ray photons that emerge nearer to the target surface which is facing towards the cathode side will be high as they travel a shorter path compared to the x-ray photons that travel a longer path through the substance or the heel of the anode. And during this process some of the x-ray photons get absorbed. As you can see, some of the x-ray photons are absorbed while traveling the longer distance through the anode atoms. As a result of this, there is a variation of intensity across the projected x-ray beam and this is called the anode heel effect. As you can see when the relative intensities are measured, we have a central ray as a standard 100% intensity and those towards the anode side have lesser intensities and those towards the cathode side have higher intensities. Now we all together cannot eliminate the anode heel effect completely, but we can make use of this during patient positioning such that the thicker body part is placed towards the cathode side and the thinner less denser part is placed towards the anode side which consists of less intense beams. Thereby we achieve a uniform exposure. For example, when we image the abdomen, the less dense upper abdomen can be placed towards the anode side and the more denser pelvic girdle can be placed towards the cathode side. Similarly in mammography, the more dense chest wall end is placed towards the cathode side and the less dense nipple end can be placed towards the anode side. Also, we can reduce the severity of this effect and make it less pronounced in three ways. The first is with the help of polymeters. These are like our window curtain blinds that restrict the size of the primary beam projected towards the patient. Lesser field size means the extreme values or the ranges of the X-ray beams on ether ends are cut out and the beam is made less diverse and the central field is allowed to be focused on the patient. Again, when the field size increases, the beam diversity that reaches the patient increases and anode yield effect becomes more pronounced. Second is by altering the SID. SID is the source image receptor distance. We can reduce or increase the anode yield effect by altering this SID, also called as focal film distance. Notice when the film is close to the source, it is exposed to beams of both extreme ends, a wider range of beams and thereby the anode yield effect increases, but when the film distance increases, the diversity of exposure is less. Finally, the anode angle also plays an important role in increasing or decreasing the yield effect. When the anode angle decreases, more X-rays are made to traverse through the substance of the anode, through the heel of the anode, thereby increasing the effect and increasing the anode angle The path away from the main substance of the anode reduces the heel effect. Summarizing the anode yield effect, the beam intensity is high towards the cathode side and less intense towards the anode side. We can take advantage of anode yield effect and position the patient accordingly such that the more denser parts are placed towards the cathode side and the less denser parts are placed towards the anode side. The anode yield effect is inversely proportional to the anode angle and the source image receptor distance, also called as focal film distance and anode yield effect is directly proportional to the field size. That is, if field size increases, the anode yield effect increases. Thank you.