So, last class we are discussing about the linear quadratic regulator problem. Let us recall this problem, we have a dynamic system which is described by x dot is equal to A x plus B u and x is the state vector whose dimension is n cross 1, u is the input vector whose dimension is m cross 1 and y is the output vector. So, our problem is to find a control law u of t such that this performance index what we have described this one the performance index is minimized. In other words our problem is to find a control our aim is to find a control law that will drive the state x t 0 t is equal to t 0 that will drive the state at t is equal to t 0 to a finite time t is equal to t f near the optimal near the origin or near the 0 state. So, for that one what should be the choice of u so that it will satisfy the performance index not only this one it must satisfy our given dynamic equation 1 and 2 this one this is our problem. And we have seen this problem what we have considered the performance index if you see this one performance that interpretation of this waiting matrices. And the state waiting q is the state waiting matrix because it is associated with the state r is the input waiting matrix this is associated with that input. And we have a terminal cost that may at time t is equal to 0 t is equal to t f at finite time our state initial state will go to the near the origin not exactly origin, but near to the exogenous near to the origin at finite time t is equal to t f. So, this is the state terminal waiting matrix this one and if you do not consider the that in the performance index that input term that the control effort term. Then if you minimize this one will see or we can say that we do not have any control with the input effort. So, input effort may be extremely high which you cannot directly apply to the systems. So, in other words if you do not consider the state waiting matrix of that one quadratic performance index this part then our we do not have any control on the over the state this one. That is why we are taking the linear combination of state waiting matrix and input waiting matrix control. We are minimizing these two efforts that means control efforts as well as the state waiting matrix effort to this one. So, this is our basic step and the choice of q r what q should be a positive semi definite and r should be a what is called positive definite matrix. And in our linear quadratic regulator problem we have not considered that what will derive it now. We have not considered that is there is no constraint on the u as well as x that x and u are free that no constraint impose on x and u variables. Then when t is tends to infinity t tends to infinity instead of finite time t tends to infinity the state waiting matrix that is x t f it will be assigned to 0. Because it has no physical significance of t is equal to t f the function that is a state waiting matrix value is assigned to 0. Because it has no physical interpretation there because all the states will come to 0 asymptotically t tends to infinity. So, this type of problem when t f tends to infinity this is called this is infinity this is called the infinite horizon problems that also we will discuss later. So, let us see how we are going to derive the what is called l q r problem for finite time regulator problems. Regulator problems means our initial state r in equilibrium position if there is a initial disturbance in the state is there naturally this state will deviate from the equilibrium point. And it should come back to equilibrium point as quickly as possible with the application of control effort that we have to find out that control effort. So, that the performance index what we have considered that is minimized. So, next is we are considering the solution of l q r problem linear quadratic linear quadratic regulator problem for a finite time interval problem bracket finite time. That means once again we define our aim is a driving the state x is t is equal to t 0 to a final state t is equal to t f that means x t f final state t f near about the origin or 0. That is our problem for that one what should be the choice of our control and control input. So, that it satisfy our performance index including the terminal cost that performance index we have considered. So, let us call our problem is like this way x dot is equal to in general it is a x of t u of t and this and x t 0 is equal to x of 0. Since, we have described the system our dynamic system is described in the state piece form that is x dot is equal to a of t x t plus b of t u t and x t of 0 is equal to 0. We have assumed that our system matrices a and b are function of time time varying parameter matrices and if it is time invariant that a of t is constant all the elements of the matrix a of t is constant it does not change with time. So, our output equation this is the state equation state equation and this is the output equation this is the output equation and output equation c into x t plus or you write is simply c of x t. So, this dimension x dimension n cross 1 that u dimension number of inputs is m cross 1 and number of outputs you can p cross 1 though in your regulator problem this output will not come into the picture. We are assuming that we will show you later we are assuming all the state variable information x t are accessible to us or measurable to us or in the sense the information of state variable is known to us. So, then our problem is to find a u such that it will satisfy this power performing index. So, this is the terminal cost which is f t x of t this is the quadratic form in state, but at time t is equal to t f plus half t 0 to t f then x of t q of t x of t plus this is inside the bracket plus u transpose of t r of t plus u of t bracket close d of t. So, I told you earlier that why half is taken into account that in the performing index that this half when you find out the differentiation of Hamiltonian function with respect to u lambda or x then you will see this half and from there it will come to 2 and this 2 and half will be cancelled. Otherwise if you do not consider that 2 numerical value 2 will come through this expression to avoid that one we just multiply by half. So, at what point the optimal value of the function will get it that will not change that as we have seen in static optimization problem that if you multiply a performing index by constant or divided by a constant that what is called optimal point at which the function will be optimal that point does not change it that is we have seen it. So, this you can say as per our notation this is the final what is called terminal waiting matrix and this is the state waiting matrix which is greater than equal to 0 means positive definite. This is the control waiting matrix that value is positive definite matrix that we have discussed earlier. That must be from physical consideration also that must be positive definite matrix it cannot be positive definite because when if it is a positive semi definite control effort applied to the system will be 0 then this is that is why it is a positive definite matrix.  So, we can consider that whole thing that whole from here to here that part is v which is a function of x t u t and d t including half that is v as per our usual notation. So, this part is the integral part of that one. So, this whole thing I can write it t 0 to t f that one this whole thing that is what whole thing will be replaced by that one only you can say. So, let us see what is our Hamiltonian function we know at this moment that how to generate or form the Hamiltonian function form Hamiltonian function you know h is a function of x t u t lambda t and t and which is nothing but a our original system equation x dot is equal to x plus v u. So, I will write it that our integral part of this one integral part of the cost function that is half then your x transpose t u of t x t plus u transpose r of t u of t that part that means first is what integral part of the performance index v of x v f of x is nothing but a v dot x function of what is called u and t is nothing but this plus that in what is called Lagrange multiplier of this multiplied by our x of t x t plus v of u t v function of t this one. This is our Hamiltonian function which is free form x dot that we have discussed earlier that one or if you see more carefully it is nothing but our f of x t u t and this that whole thing is v of this if you see this is nothing but a v x of t u of t and t this one. So, where lambda wave t is a cost state vector cost of state vector of dimension that lambda is dimension n cross 1. So, this is the first step you form that linear quantity regular problem means the system description dynamic system description is given in state space form and corresponding performance index is given that terminal cost plus the integral of the quadratic form of in state and input matrix that is input vector this. So, from this information I can find out the Hamiltonian matrix next step is step to necessary condition condition for optimality. So, what is the necessary condition del h del u of t is equal to 0. So, what is del h of del this is this is you see del h del h with respect to u. So, the u term is involved here and u term is involved here and we know that if you have a x transpose p x if you differentiate with respect to x vector then results is twice p x. So, I will just apply that one that u transpose r t u t I am differentiate with respect to u t that result will be twice r t u t. So, this twice and half will be cancelled. So, it will be half as it is twice r of t u of t I am getting from this part again if there is a function of u of t here. So, it is a lambda transpose b u of t and we know the partial differentiation of a transpose x with respect to x agree that results is a. So, that I am applying here if you apply is here that one then it will come plus b transpose t of lambda t is equal to 0. Because this term you see this I can write it lambda transpose b u t I can write lambda transpose b I can write b transpose lambda whole transpose and I made it into this form a transpose then x means u this. So, this from there we are getting from there we are getting u of t our control input is equal to minus r inverse because r inverse b transpose of t lambda of t. Let us call our equation that Hamiltonian this is equation number one you give it this is equation number one and you give it this is equation number two. So, what in order to get this one what we have used it we have used this two things differentiation of this with respect to quadratic function with respect to x of t if you do this one this result is twice p x of t another we did it a transpose x of t this with respect to x of t is equal to a. So, this two things we have used in order to get equation number two. So, once we get it this one other two necessary conditions are this one if you see the step three. The state and costate equation state and costate equation are given as x dot of t is nothing but a del h del lambda of t. That means h is a scalar function I am differentiating with respect to lambda vector. So, that see this one the lambda is associated with this one only the second part. So, if you differentiate this one with respect to lambda. So, I can write it this is nothing but a a x plus b u this if you differentiating with respect to lambda you see this I am differentiate with respect to lambda. So, this agree so I can write it this is nothing but a whole transpose into lambda that because this is a scalar quantity this and this multiplied is scalar quantity. So, I can write it a x plus b u whole transpose into lambda agree. So, it is same because it is a h is a scalar quantity this part is a scalar quantity. So, if you differentiate this with respect to lambda I am getting this expression is a x a t x of t plus b t u of t. You have followed my point this thing is a scalar quantity what I will I take the transpose of that one multiplied by lambda of t. So, this will be same as this value then I am differentiating with respect to lambda t and that results is this one that using that property I mean that expression. So, I can write it now next equation costate equation lambda dot of t is equal to minus del h del x dot x of t not dot x of t. So, now I am differentiate this with respect to x. So, x is involved here x is involved here. So, from there I will set first one I will get if you differentiate with respect to x you will get twice q of t x t 2 2 cancel q of x t I will get it. So, this will get it minus q of t x t the first part then you see this one lambda transpose a x t. So, this I can write lambda transpose a x I can write it a transpose lambda whole transpose because this 2 I am writing a transpose lambda of t whole transpose is same as that part. So, I am differentiate with respect to x. So, it will be coming plus a transpose of t lambda of t. So, this and let us call this is equation number 3 and this is equation number 4 again. So, using equation number 2 means that one this expression you use in equation number 3 3 and with 4. That means using equation number 2 you replace your by this expression and then argument that equation with the costate equation and that will results that one. So, I am writing using 2 in equation 3 and with 4 using it 4 we have. So, x dot of t that means if you write equation number 3 in equation number 3 you are using the expression of u of t and then argument that u of t with then argument that equation 3. So, I am just doing this lambda dot of t is equal to this a of t then b of u t b is your b as it is u of t is what r inverse b transpose and lambda of t and that I am writing x of t and this is lambda of t.  So, this and the this it is as it is u of t say this is I am writing u of t minus a transpose a of minus a transpose of t. So, this dimension is since costate vector and state vector dimension are same each is n. So, this dimension n cross 1. So, now this is called is Hamiltonian matrix Hamiltonian matrix and this whole thing is called Hamiltonian system Hamiltonian system and this matrix dimension is 2 n cross 2 n. Now, look at this expression since our given system a t b of t q of t r of t is the designer choice. If you know the designer what is the designer has taken into consideration to design the l q r problem then this whole matrix is known to us. That means Hamiltonian matrix is known to us and we can find out the its Eigen values only difficulties is there the parameter is changing with time. So, naturally the Eigen values will also will change with time suppose if you consider a of t b of t r of t and q of t is fixed does not change with time. Then this is a constant matrix and Eigen values we can find out and this Eigen values is a closed loop system Eigen values agree the x dot is there lambda dot of t is there and we have a in addition to this there are n Eigen values are there which is closed loop Eigen values and another n Eigen values are there which is associated with the costate vectors. So, let us see what is this represent what is the Eigen values of this one what my main stress is here without calculating anything if you designer has selected r of t q of t and system matrix is known I can find out what is the closed loop system matrix Eigen values. So, this we can write it more compact rather simple form in the sense this I am replacing by another variables e of t plus minus q of t minus a transpose of t this equal to x of t dot lambda of t. So, let us call this is equation number 5 now I want to show you here with a similarity transformation that this Eigen values are nothing but a Eigen values of closed loop system Eigen values closed loop system Eigen values and other values Eigen values are Eigen values of that lambda dot costate vectors Eigen values of the system matrix of costate vectors. So, use a transformation and this transformation I have used it I 0 I p of t and p of t is a matrix whose dimension is n cross n is a matrix whose dimension is n cross n. That means this dimension is n this dimension is n this dimension is n naturally all matrix dimension you know and this is invertible by look this one this is invertible diagonal matrix blocks are unity and it is non zero that all columns are linearly independent columns are there. So, their inversion is exist. So, I am using that transformation x is transform to x bar lambda is transform to lambda bar of t and that is equal to x of t and lambda of t. So, if you differentiate this thing both side what we can write it first is I this p of t then x of t is equal to x of t lambda bar dot of t lambda bar sorry x bar dot of t this plus another term is differentiation of this block with respect to 0 then 0 then 0 then p dot of t. So, this is that one. So, this into that your x bar of t and x of t is equal to x of t and x of t is equal to lambda bar of t is equal to x dot of t right hand side x dot of t lambda dot of t. So, I know what is the lambda x bar dot of t lambda bar dot of t. So, I will put it this expression in this side and then we will make some manipulation and simplification. We will get it now this is the equation number we have given up to equation number 5. So, let us call this is the equation number 6. So, from 6 6 so from 5 and using 6 from 5 and using 6 what you can get it. So, what I told you that in place of lambda x dot lambda dot I will replace by this equation using 5 x dot lambda dot I will use that one. So, right hand side equation is x dot lambda dot is replaced by a of t dot partition e of t minus q of t sorry not transpose or you can write transpose because it is symmetric matrix minus a transpose of t. So, this equal to x of t lambda of t this is the right hand side I will retain and left hand side will be as it is as you have seen it I 0 p of t I then lambda bar dot of t lambda sorry x bar dot of t lambda bar dot of t plus 0 p dot of t and 0 this multiplied by x bar of t lambda bar of t and this I have written. So, after simplification this thing you bring it that side right hand side this part you bring it that side and x and lambda t you replace by transformation matrix that you what we have in a how they are related x of t lambda of t related to x bar of t lambda bar of t that we know with this expression. If you recollect this is the expression we have considered for transformation this is the transformation. So, replace x of t lambda of t by this one in the right hand side of this part and ultimately if you do it that what will get it that one I just after simplification lambda dot x bar of t lambda bar dot this is dot of t is equal to I 0 p of t I whole inverse. Then this multiplied by 0 0 p dot of t 0 then x bar of t lambda bar of t this is my because this term I have taken right hand side then this inverse I have taken both side I multiplied by inverse of that one. So, this is the that and this part will be what see this will be inverse of that I 0 p of t I 0 p of t I this is I whole inverse then a of t minus e of t minus q of t minus a transpose a transpose of t multiplied by this x and lambda t is replaced by x bar and this. So, if you replace by this one this will get it your I 0 I p of t multiplied by x bar of t and lambda bar of t this is the expression we got it x bar of t lambda bar of t. So, after just this and this you club together and if you take this common then this multiplied by this matrix this matrix multiplied by this matrix and result and you will get a matrix of 2 by 2. Before that I have to know inversion of this one I have to get it because I know the inversion is the exist because this matrix has a n linearly twice n linearly independent because from this structure you can say twice n linearly independent vectors are there. So, this inversion is exist. So, now using what is called matrix inversion lemma one can one can get this values are like this way matrix inversion lemma is what I am just writing it here matrix inversion lemma. So, if you have a matrix A suppose we have a matrix A B C D and their partition like this way and it is assume that A and D inverse is exist we have partition in such a way that this are the square matrix and their inversion is exist. So, you have to find out this inversion of that one.  So, what I we have a matrix A B let us call A matrix is partition the matrix into 4 block in such a way that A matrix this block and this block which will be a square matrix and inversion is exist. Then I can write p 1 is equal to A minus A this one C sequence A minus then B D inverse D inverse C p 2 p 2 p 2.  When I have taken this p 1 2 you see p 1 2 I starts with A minus A inverse B then p 2 this one p 2 already I have calculated.  So, if you put the matrix inversion lemma here agree this places and similarly this one ultimately I will get it final expression I am writing x lambda bar dot of t this what I will get it I will just write it final expression please see the final expression what final expression this you use the matrix inversion lemma use the matrix inversion lemma then multiply this one multiply this and this this three matrices multiply and then this and this you add it. Then finally, you will get it this matrix A of t minus B or inverse B transpose B inverse B inverse B inverse B inverse B inverse B transpose of t p of t this is the first block you will get it and second block you will get it minus B transpose R inverse B B transpose B inverse B of t R inverse B transpose B of t.  So, this plus plus this is inside the bracket this one plus p B R inverse of t B transpose of t into p of t plus q of t. So, this is the two one block then the two block what we will get it minus B inverse B inverse two block I am writing minus A of t minus B of t R inverse of t into this is continuation B of t R inverse of t into B transpose of t p of t.  And other two A 1 2 block 1 2 block 2 2 block is this one that whole bracket multiplied by what x bar of t lambda bar of t. Now, this is the equation after transformation we got it this one. Now, I am telling you you this is the you see I you select p of t in such a way. So, that p dot of t minus of whole expression p A transpose p of t p of t A t all these things will be 0. So, you find out the p of t value in such a way. So, that this is assigned to a 0 it will be 0 or you can say I will assign this quantity is assigned to a 0 agree for that you find out what is the solution of p. That means this quantity I will assign to a null matrix of dimension n cross 1 agree this whole thing I will assign for that one you solve it p such that this equation is satisfied. So, if this is the so I can write it that A of t minus B of t R inverse of t A of t minus B of t B transpose of t p of t this is 0. And this is B of t R inverse of t B transpose of t agree this one and this one is minus of A of t minus B of t cross this is 0. This is the cross multiplication R inverse of t B of t and p of t p of t mind it this is just same as that one only p c d with minus. So, this whole thing I am writing this whole bracket after this because I have assigned this is 0 assigned to this is 0 in other words assign this one find out find out solution of that what is called matrix equation. So, that this expression will be satisfied find the solution of p for which this will be equal to 0. So, that whole thing multiplied by x bar of t that lambda bar of t agree. Now you see the this is the block diagonal form the Eigen values of this one this whole matrix Eigen values is nothing but Eigen values of this one and the block 2 to block Eigen values whatever the Eigen values of this block the Eigen values of this block will be same with opposite sign because it is special with a minus sign it will be opposite sign. So, this we can conclude this one that Eigen values of total state and costate vector Eigen values of this one is nothing but Eigen values of this block and union of Eigen values of this block and this Eigen values are same only difference is Eigen values of this one with preceded with a minus sign means opposite sign of that Eigen values will be here. So, let us call this is equation number 7 this is the equation number 7. Now we can see this one. So, we got it what we made it a conclusion that one that if you have a costate vector if you do the transformation of this one which we have seen the augmented cost state and costate vector can be represented into a upper block form the Eigen values of x star is nothing but Eigen values of this one Eigen values of lambda dot is nothing but a lambda is nothing but a Eigen values of that one with preceded with minus sign that is why we have seen it. So, our general boundary condition if you see boundary condition is given by H we refer our the terminal cost all this thing boundary condition t is equal to t f delta t f plus del s of del x t minus lambda of t this is minus lambda of t minus lambda of t this whole transpose t is equal to t f and delta x f is equal to 0. Since our what is called t f is specified since t f is specified because we have consider our problem that our aim is driving the our initial state x of t 0 to a final state x of t f t is equal t f near to the origin. So, t f is specified therefore, delta t f is 0 and our x t f near to the origin means x t f is not specified near to the origin and therefore, delta x f delta x f is arbitrary. So, then what is our boundary condition we are getting it here just see this one. So, this if you just put it here x delta s of this differentiate with respect to x t put t is equal to t f minus delta t is equal to t f this equal to 0. So, this therefore, we can write x t f is equal to if you differentiate this one if you see with x or if you go back to this one if you differentiate this thing that s term with respect to x and put t is equal to t f this you are differentiate. So, what will get it this one twice f x t and put t is equal to t f then it will be a it will come like this way. Therefore, lambda t f is equal to half twice f t f into x t f. So, this this cancel. So, f t f into x t f. So, if you do the block diagram representation of this one now we can find out our control law our control law if you see our control law is minus r inverse B transpose. Of lambda t solution of lambda t if you know it lambda t then I can find out the control law. Let us draw the our block diagram of this representation our reference input we have consider 0 because due to the initial condition what is this we are showing it this is B of t. So, this is our star and this is our integrated and this is x dot of t the output is x of t. Then this is coming is from here the state a of t and this is a if you just relate this one x dot is equal to a x a x plus B that must be u of t. Then this is this from there then this is this from there what is lambda u c lambda expression this is q of t. Then this is coming to here this is lambda dot of t lambda dot of t and you see the lambda dot of t what we got it here minus q x if you see this one lambda dot of t here lambda dot of t minus q x x t. So, x t is coming this sign is either you put it minus here or you put it minus here. So, this then a transpose lambda t. So, this is a integrated and integrated output is your lambda of t from there you are taking a signal a transpose minus a transpose of t. Then it is coming here or if you this agree. So, there is that lambda of t now coming here r inverse this is the r inverse of t agree this is the r inverse you see because what is this u of t. Just now we have calculated u of t by boundary condition not boundary condition u of t is equal to just we got it page number 3 that is u to t minus r inverse b transpose lambda of t. So, we have got lambda t r inverse b transpose. So, this is a minus sign if you keep it here agree if you keep it minus sign here or here it does not matter agree then this will be a u. So, that things are there. So, this is the our controller part if you see this is our controller part and this part is our system our given system and what is this one if you see this integrated we have a initial condition x t 0 is equal to x of t 0 sorry x of 0 x of 0 this one. We have a just now we have seen we know just now we have seen we know only what we know only our final costate vector final condition we know it just now we have seen it just now we have seen it this costate here this you see costate vector final condition we know it. That means we know lambda t f is equal to f t f x t f because we have we know x t f where we want to keep the final state agree near the origin near the our 0 that we near the origin we.  So, now this is corresponding to the costate system and this is corresponding to the state system state equation. So, now see this one how will you get the solution of this problem because we have to solve I told you that what we have to do it this now this. So, in order to solve this one we have to solve that final condition. So, note the final condition on lambda t and together with final condition on lambda t f on t final condition on lambda t together with x of t 0 and the Hamiltonian matrix to neon system. The Hamiltonian matrix to neon system what is the Hamiltonian system x dot of t and lambda dot of t that expressions at augmented system is the Hamiltonian system. Hamiltonian system of equation form that means final condition on this together with x t 0 initial condition of the state and Hamiltonian system form the 2.2 point boundary value problem. So, we have to now solve this equation knowing the lambda t and final condition on t f agree and together with the initial condition x t 0 and Hamiltonian system and Hamiltonian system is what x dot of this lambda dot of t from this augmented system what is the expression we got it with this we have to solve this. So, it is called 2 point boundary value problems. So, now look carefully see this one. So, how will you solve that one how you can solve that one that x t of that things because x lambda t f if the final condition of this one is known to you that lambda t f then we can solve this one in backward integration form. Now, see this one lambda t f t is equal to t f final condition t is equal to t f that if you know the lambda t f value lambda t f value then I can find out lambda t f minus the what is called previous state of that one that what is called if the step size is capital T f minus t I can find out by solution of differential equation in backward process and this whole thing is dependent on x 0 x t 0. If x t 0 is changed then it is also changed that solution of this one also change it. Now, how do you solve this one next question is how you will solve this problems that is our next. So, solution of this one is a if you see carefully this one this is a open loop solution in the sense it dependent on the solution of this one dependent of x t 0 x t 0 means x 0 of that one. So, now how to form it that remarks you can write it remarks that t p 2 point boundary value problem must be solved again if the initial condition change. If this initial condition is change we have to again you have to solve this one. Now, what is this one how you will get it this one x t f let us call the x t f is known where we want to keep our final state. Because I told you at t is equal to t is equal to t f it is specified that means we are looking for a control law u that will drive the initial state x t is equal to t 0 to a final time at t is equal to t f final time at t is equal to t f the state x is equal to t f will be near to the origin in final time. That is our problem so now question is this problem you have to solve in backward integration. If you know the x t f backward you have to integrate and solve this one and that solution depends on the x t 0. So, this is the if it is change. So, now we are looking for a closed form solution step 4 the closed loop optimal solution. So, how will you do this one we know how lambda is related at time t is equal to t f how lambda t f is related with x t f. So, assuming that structure of 8 we have what is the equation number we have given equation number let us call this is equation number 8 this is the equation number 8. Assuming the structure 8 lambda t f is equal to bracket you can write it that which one is x t f into x t f to relate the state and costate for all time for all time. We have lambda t is equal to f of p of t into x of t they are because they are at t is equal to t f is f of t f t f. So, you are telling that for all the time t is equal to f it is related with this one then at t is equal to f what should be the p t f same as f t f. At t is equal to t f p t f is same as f t f we know this relationship we got it from the boundary condition of that one. So, that is the boundary condition and that x t f will be near to the origin mean equilibrium point. So, if you consider this equation number 9 then differentiating this one both side we will get p dot of t into x of t plus p of t x dot of t put the value of x dot of t in the expression. Then we will get it lambda dot of t in that expression what is lambda dot of t it is nothing but a minus what is lambda dot of t we got it minus here lambda dot of t you see lambda dot of t from equation 3 possibly that you are 4 lambda dot t is nothing but a q of t into x of t minus a of t lambda of t. So, I will put it this values is there. So, it is q of t x t q of t x t minus a transpose of t lambda t again this equal to p dot p dot of t x t plus p of t and what is x dot a of t x t our system dynamic equation b of t u of t. So, after simplifying this one I can write it p of t after simplifying after simplifying we can write p dot of t plus p of t is equal to minus a transpose of t p of t plus p of t into a of t minus p of t b or inverse b transpose of p of t this product p of t plus q of t is that one this after simplifying we get that expression. Now, you see the solution of this one is not dependent on the initial condition of that one the solution of this one is not dependent on the initial condition. Whereas, when you have found out that this one lambda t f this one when you will solve this one when you will solve this equation in the backward integration the solution of this u is dependent on the x t x of 0 this one. So, and this equation this whole equation is known as matrix differential Riccati equation. In short m d r e is equal to m d r e is matrix and it is a non-linear differential equation that our problem is solve this non-linear equation differential equation. So, we must know our terminal conditions we know p t f is equal to f t f terminal condition is given from there we have to get the solution. We will discuss the solution of what is called matrix differential equation in details next class. So, we will stop it here now.


Hey guys, Ryan here, and I've got my son. What up? And we just checked out Ghostbusters, because we're on a journey to check out all the movies that I grew up with, to see if he enjoys them. And I do. Who you gonna call? So you all know what Ghostbusters is. Three guys team up to fight paranormal, against ghosts, kicking butts.  It's a bit of comedy, it's from the 80s. I loved it as a kid, I grew up with it. I loved the action figures, I had toys, now growing up I have the proton pack, I have everything you could think of. So obviously I wanted to get writer into it. He bought a t-shirt recently, and he knew he hadn't actually seen the movie, but he liked the symbol. So I thought, well, we probably should check it out. And why not take a little journey on checking out those movies that I grew up with, see if he liked them. So what'd you actually think? I think the movie was good. You thought it was good? Yeah. Mike, what was your favorite part, do you think? Uh, when they all went down from the museum. From the museum, from the library? Yeah. From the ghost at the start? Yeah. So I thought that was going to scare the crud out of him. That's ghost at the start, the big pink ghost talking about little ghost. And then they go, yeah. I thought that part was going to scare because I thought me and your mom had been talking and we were like, all right, we should probably skip that part, but you were fine with it, weren't you? Yeah, I was like, I thought that was pretty funny. You were laughing your head off, especially when they ran out of the building and stuff. So Ghostbusters is a pretty scary movie. It's meant to be. I mean, I knew I saw it when I was like four and I told you it was my favorite movie when I was like six and I watched it all the time, but it's meant to be a bit scary. Were you scared? I don't know. Out of like? I was scared of the big dogs. Oh, the big dogs, yeah, the big terror dogs? Okay, who brought- Yeah, they were kind of scary, but I wasn't like super scared. I was like kind of, the one who was on top of that big building and the girl that came out of there was like, that kind of scared me a little bit. Okay, out of like five terror dogs, how many terror dogs were you scared? Just two, actually, just one. Oh, just one, that's not really scary at all, really. So were you carrying behind things like this? No. No, no. Well, I was like scared kind of like I feel my brain went out, but not. But not heat? Yeah.  Do you think you'd want to watch this again over YouTube or do you think you'd watch YouTube instead? Watch this over again. You'd watch Ghostbusters again? Yeah. You're very good. So come to the Ghostbusting, yes! Do you like the music in it? Uh, yeah. Yeah? Bzz bzz bzz. What do you think Ghostbusters is gonna be like before you saw it? I just thought that they were just gonna be chasing around capturing ghosts, but all they were doing is like walking around talking to people and capturing ghosts both at the same time? So there was a lot of talking in the movie you didn't like? Yeah, I mean not likely, but it didn't really understand to me. Oh, that makes sense, that's fair enough. I think that's something that Ghostbusters does that it has a lot of humor when you're a kid, But then it also has a lot more when you're an adult, but that's that's fair. Yeah, because I didn't really understand what all of it means right But you thought some of the stuff they were doing was funny, but yeah Cuz some stuff some stuff don't people say I feel like I don't really know about the stuff that they say Yeah, I understand that because it's like you said This guy's like a bully. How could I know? Don't what would believe me like if he said saying there's a way to hold on or saying there's a way to That's a really good point. So be good for goodness sake Somebody's coming out of here. We've got to find a judge or something. Hey, wait a minute. Hey, hey, hey, hey Hold it. I'm sorry. I I was expecting just It'd be just like now. Okay, so more like you wanted a more running around chasing ghosts and capturing ghosts Yeah, but it was a lot of talking. Yeah, because I don't really understand it. Okay. All right All right, so we're gonna do a star rating normally people do five out of Five stars out of some some people do ten stars out of things or ten out of ten I reckon we do something to enjoy. So what's your favorite thing you like to eat? Cheese. Yeah. All right.  Sausage, okay, and what's like that's something to kind of think it's okay Cara, yeah, Cara. All right, and what's like your all-time favorite foods?  All right, so thinking about all those things these ghost buses is where would you put as like good as sausages as good as Tarot is as good as cheese or is as good as watermelon and grapes. Which one? It's good in watermelon and grapes Top rating. Oh, that's good So like I like like I like super like the watermelon and the grapes So that's like my favorite food and then like my favorite TV show and my movie is Ghostbusters Cha-ching! Somebody ring the Ghostbusters bell. We got one! Do you know there's a sequel? Do you know Ghostbusters 2? Yeah. Do you want to watch Ghostbusters 2? Yeah. Okay. There's going to be a new movie called Ghostbusters 20 or whatever it is GB 20 coming out in 2020 Maybe we can go see that. Okay. Yeah Cool. All right. Well, I'm Ryan and I'm Michael and we just checked out classic movies with classic dudes


lose control cause everything that you thought I would be is another mistake too and every second I waste is more than I can do


We're working on a reform of the whole dental system in Wales to make improvements for both patients and the profession. These changes are based on the principles of prevention, improving access and quality of services. We know prevention is really important when it comes to oral health. If you look after your teeth and mouth, you may only need to see a dentist every 12 to 24 months. Rather than relying on routine six months check-ups, we're ensuring dentists provide needs-based care. The capacity released by this change will allow those who want continued care from an NHS dentist and those patients that need urgent dental treatment to have the support they need. We've taken steps to improve our dentistry workforce. We've incentivised future dental trainees with a potential £5,000 salary uplift to complete their foundation year in dental practices across parts of rural Wales. We've also increased the capacity of our existing workforce. We've made changes to regulations that prevented dental therapists, hygienists and clinical dental technicians from playing a full role in NHS care. In September 2022, we also opened the North Wales Dental Academy combining general and community dental services with education. This is providing dental care for around 12,000 to 15,000 patients every year. We're even trialling a mobile dental unit on the site of a scholar-molewin in Blaynife, Stignog giving children advice on oral health and providing dental check-ups. Around 80% of dental practices have chosen to work under these reforms and this has allowed nearly 300,000 new patients to gain access to an NHS dentist across Wales. I'd like to thank our fantastic dentistry staff who've worked so hard to make this possible.


a key point you make in the book is that if we look across cultures, this pattern of monogamy is clear. So I know all of us are bringing a cultural context to this conversation, and that cultural context could be religious influence based on the way we are raised, the communities we're a part of, you mentioned another culture, the elites, but I just want to point out that what is clear in the science is this pattern of monogamy in humans is prevalent across all cultures. Religion builds morality upon monogamy and the nuclear family in a lot of different instances of different religions completely. So there is a signal that is present in human nature that science is measuring across all of these cultures that leads to this conclusion of monogamy. Yeah, I think it's one of our great social achievements as a human race.  And so some of the people point to that and say, we're just kind of like more advanced chimpanzees. One of the things that we often don't recognize, how good we have it as human beings, do either of you have just to guess if we applied our notion of say domestic violence to chimpanzees? Do you have any estimate or guess at what proportion of female chimpanzees at some point in their lives experience what we would frame as domestic violence? Nearly 100. Yeah, 100%. And I would say that those are linked. And a lot of times violence is used by males to control reproduction and reproductive access and so forth. And again, I totally agree with you, AJ, that we do have a deep capacity for monogamy and what anthropologists would call long-term pair bonding. We also have a capacity to not to kind of disregard that. I think it doesn't take long to look around the tabloids and see examples where people are behaving in other ways. It's obviously a sensitive issue. I think it's going to be good for society. It's going to be good for children.  It's not easy, especially with some of the cultural changes that have happened in the last decades, at least in the West. But I think it's a fight worth continuing. In a sense, it requires us to overcome a deep kind of propensity within human nature. To bring it home and to get back to this idea of what actually is the purpose of existence, to me, it seems that the way that nature has shaped us leaves us pulled in these different directions. We have these differing capacities within us. And when you combine this, again, my conclusion is that on some level, we have this ability to choose free will. To me, it seems like life is a test, that we have to choose between these competing impulses within us. And it seems at least on some level that life is a test. We've had on Dr. Robert Waldinger to talk about the Harvard Adult Developmental Study, and I know that's a key chapter in the book. So I'd love to segue into how does this look from purpose from a personal level, but then also what is this good for society level that is linked, obviously, into human nature, because it's clear through all of this that we have thrived as humans in civilizations. It's not been on our own, completely isolated, and it's not been in small tribes trying to fight off woolly mammoths and saber-toothed tigers. We've been able to survive and strengthen in forming civilizations. And a lot of this meaning and purpose is tied to the human nature around creating these civilizations. Yeah. And also at a fundamental level are immediate social groups. When you ask people what is most meaningful about life in these large series that, say, the Pew Foundation does, and you give them a blank answer so it's not necessarily multiple choice. They just can write whatever they want. Most people list in some form their personal relationships. And I think that is revealing. As you've noted, a lot of people will just say, well, should I just work as hard as I can, give as much money as I can? And there are some cognitive illusions that nature has in a sneaky way built within us, because we're not good at one of the psychological principles that is really interesting is this notion of affective forecasting. That is the ability to predict how we're going to feel in a given situation. And what that means by extension is that we're not great at predicting what's going to make us happy. Let me qualify it a little bit because we're mostly good at predicting whether a situation is going to help us to feel positive or negative emotions. But the intensity and the duration of those emotions were not great at. So this was driven home by an influential study in the 1970s with the provocative title of lottery winners and accident victims, where researchers, they went and they assessed these two very different groups of people, ones that had suffered terrible accidents that left them quadriplegic or paraplegic, and the other group, those who had won the lottery. This wasn't immediately after the event of interest, but some time. And so if I ask you, would you rather win the lottery or suffer an accident? You say, well, of course I'm going to win the lottery because my happiness is going to be better. But in terms of the ability of these two different groups of people to enjoy everyday things, there wasn't really any difference. And that is because of a related principle called hedonic adaptation, this notion that for a lot of things, after a period of time, our kind of happiness set point goes back to where it was. And that's certainly the case with things like money, getting a promotion, that sort of thing, is yeah, they make us feel better for a period, but then we kind of settle back in. In a way, there's a good part about this because it also means that we can adjust in the other way, and that if we go through some sort of adversity, that we can adapt and prove resilient and adjust to difficult circumstances. So it's not all bad, but there is a kind of a maddening aspect to it that depicts us almost as like hamsters running on this happiness treadmill. But the key exception is relationships. And again, for good and for bad, a positive, warm, intimate relationship can really increase our happiness set point, whereas a toxic one, you don't really adapt to that. Toxic relationships kind of have this enduring negative impact on well-being.


A night in March, by Duncan Campbell Scott, read for LibriVox.org by Bruce Kachuk. At eve the fiery sun went forth, flooding the clouds with ruby blood, uproared a war-wind from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow-slipped singing over the wall, and ever, when the wind would cease, a lynx cried out within the cold. The spirit walked the ringing rooms, passing the locked and secret door, heavy with diverse ancient dooms, with dreams dead laden to the core. Thou art too deep with woe, I have no harbour place for thee. Leave me to lesser griefs, and go, go with the great wind to the sea. I faltered like a frightened child that fears its nurses very brood, and as I spoke I heard the wild wind plunging through the shattered wood. Thou betrayed the rest of kings, with tragic fears and spectres won. My dreams are lit with pure-er things, with humbler ghosts be gone, be gone. The noisy dark was deaf and blind, still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Art thou the fate for some wild heart that scorned his caverns, curve and bars, that leaped the bounds of time and art, and lost thee, lingering near the stars. It was so still, I heard my thought, even the wind was very still. The desolate deeper silence brought the lynx-moan from the lonely hill. Art thou the thing I might have been if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul. The wind rushed down the roof in wrath, then shrieked and held its breath and stood, like one who finds beside his path a dead girl in the marish wood.  Art thou the spirit ministry that hovers round the newly dead, the auroras rose in solitude, and wanly paled within the room the window showed an ebb and rude upon the blanched and ashen gloom. I heard a voice within the dark that answered not my idle word. I could not choose but pause and hark. It was so magically stirred. It grew within the quiet hour, with the rose shadows on the wall. It had a touch of ancient power, a wild and elemental fall. This rapture had a dreaming close. The dawn grew slowly on the wall, spreading in fragile veils of rose in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace, and folded in the fading night I felt the dawning sink and cease. A night in March by Duncan Campbell Scott, read for Libervox.org by Chad Horner from Polly Clare in Coney under Northern Ireland, situated in the north-east of the island of Ireland, at Eve the fiery sun went forth, flooding the clods with ruby blood, uproared a war went from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow slipped singing over the wall, and ever when the wind would cease, a lynx cried out within the cold. A spirit walked the ringing rooms, passing the locked and secret door, heavy with divers ancient domes, with dreams dead laden to the core. Spirit, thy art too deep with woe, I have no harbour place for thee. Lead me to lesser griefs and go, go with the great wind to the sea. I faltered, like a frightened child, that fears its nurses very brood, and as I spoke I heard the wind, wind plugging through the shattered wood. Hast I betrayed the rest of kings, with tragic fears and sceptres weighing? My dreams are lit with pure things, with humbler ghosts be gone, be gone. The noisy dark was deaf and blind, still the strange spirit strayed or stood, and I could only hear the wind go roaring through the ribbon wood. Art thou the fate for some wild heart, that scorned his caverns, curve and bars, that leaped the bounds of time and art, and lost thee lingering near the stars. It was so still I heard my thought, even the wind was very still. The desolate deeper silence brought, the links moaned from the lonely hill. Art thou the thing I might have been, if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul. The wind rushed down the roof in wrath, then shrieked and held its breath and stood, like one who finds beside his path a dead girl in the marsh wood. Or have I ceased, as those who die, and leave the broken word unsaid? Art thou the spirit ministry, that hovers round the newly dead? The auroras rose in solitude, and wainly pealed within the room. The window showed an ebony rod, upon the blanched an ashen gloom. I heard a voice within the dark, that answered not my idle word. I could not choose but pause and hark. It was so magically stirred. It grew within the quiet hour, with the rose shadows on the wall. It had a touch of agent power, a wild and elemental fall. Its rapture had a dreaming close. The dawn grew slowly on the wall, spreading in fragile veils of rose, in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace. Unfolded in the fading night. I felt the dawning sink uncease, and of poem this recording is in the public demand. A Night in March by Duncan Campbell Scott Read for LibriVox.org by Newgate Novelist At eve the fiery sun went forth, flooding the clouds with ruby blood, uproared a war wind from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow slipped singing over the world, and ever when the wind would cease, links cried out within the cold. A spirit walked the ringing runes, passing the locked and secret door, heavy with diver's ancient dooms, with dreams dead laden to the core. Spirit, thou art too deep with woe, I have no harbour place for thee. Leave me to lesser griefs, and go, go with the great wind to this sea. I faltered like a frightened child that fears its nurses fairy brood, and, as I spoke, I heard the wild wind plunging through the shattered wood. Hast thou betrayed the rest of kings with tragic fears and spectres won? My dreams are lit with purer things, with humbler ghosts, be gone, be gone! The noisy dark was deaf and blind, still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Art thou the fate for some wild heart that scorned his cavern's curve and bars, that leaped the bounds of time and art, and lost thee lingering near the stars? It was so still I heard my thought, even the wind was very still. The desolate deeper silence brought the links-mone from the lonely hill. Art thou the thing I might have been if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul? The wind rushed down the roof in wrath, then shrieked and held its breath, and stood, like one who finds beside his path a dead girl in the marish wood.  Art thou the spirit ministry that hovers round the newly dead? The auroras rose in solitude, and only paled within the room. The window showed an ebb and rude upon the blanched and ashen gloom. I heard a voice within the dark that answered not my idle word. I could not choose but pause and hark, it was so magically stirred. It grew within the quiet hour, with the rose shadows on the wall. It had a touch of ancient power, a wild and elemental fall. This rapture had a dreaming close. The dawn grew slowly on the wall, spreading in fragile veils of rose, in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace. And folded in the fading night, I felt the dawning sink and cease. End of poem. This recording is in the public domain. A Night in March by Duncan Campbell Scott. Read for LibriVox.org by Harman Busby. March 7th, 2020. At eve the fiery sun went forth, flooding the clouds with ruby blood. Uproared a war-wind from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow slipped singing over the wall, and ever when the wind would cease, a lynx cried out within the cold. A spirit walked the ringing rooms, passing the locked and secret door, heavy with divers ancient dooms, with dreams dead laden to the core. Spirit, thou art too deep with woe, I have no harbor place for thee. Leave me to lesser griefs, and go, go with the great wind to the sea. I faltered like a frightened child that fears its nurses very brood, and as I spoke I heard the wild wind plunging through the shattered wood. As thou betrayed the rest of kings, with tragic fears and spectres won, my dreams are lit with purer things, with humbler ghosts, be gone, be gone. The noisy dark was deaf and blind, still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Art thou the fate for some wild heart that scorned his caverns' curve and bars that leaped the bounds of time and art, and lost thee lingering near the stars? It was so still I heard my thought, even the wind was very still, the desolate deeper silence brought the lynx-mone from the lonely hill. Art thou the thing I might have been, if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul? The wind rushed down the roof in wrath, then shrieked and held its breath and stood, like one who finds beside his path a dead girl in the marished wood. Or have I ceased as those who die, and leave the broken word unsaid? Art thou the spirit ministry that hovers round the newly dead? The auroras rose in solitude, and wandily paled within the room. The window showed an ebb and rude upon the blanched and ashen gloom. I heard a voice within the dark that answered not my idle word. I could not choose but pause and hark it was so magically stirred. It grew within the quiet hour, with the rose shadows on the wall. It had a touch of ancient power, a wild and elemental fall. As rapture had a dreaming close, the dawn grew slowly on the wall, spreading in fragile veils of rose in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace, and folded in the fading night I felt the dawning sink and cease. A night in March by Duncan Campbell Scott, read for LibriVox.org by Larry Wilson. At eve the fiery sun went forth, flooding the clouds with ruby blood, uproared a whirlwind from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow slipping, singing over the world. And ever when the wind would cease, a lynx cried out within the cold. A spirit walked the ringing rooms, passing the locked and secret door, heavy with diverse ancient dunes, with dreams dead laden to the core. Spirit, thou art too deep with woe. I have no harbour place for thee. Leave me till Asa griefs and go. Go with the great wind to the sea. I faltered like a frightened child that fears its nurses very brood, and as I spoke I heard the wild wind plunging through the shattered wood. As thou betrayed the rest of kings with tragic fears and spectres won, my dreams are lit with pure things with humbler ghosts. Be gone, be gone. The noisy dark was deaf and blind. Still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Art thou the fate of some wild heart that scorned his cavern's curve and bars, that leaped the bounds of time and art and lost thee lingering near the stars? It was so still I heard my thought. Even the wind was very still. The desolate deeper silence brought the lynx-mone from the lonely hill. Art thou the thing I might have been, if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul? The wind rushed down the roof and wrath, then shrieked and held its breath and stood like one who finds beside his path a dead girl in the marsh wood. Or have I ceased as those who die, and leave the broken word unsaid? Art thou the spirit ministry that hovers round the newly dead? The auroras rose in solitude, and wonly paled within the room. The window showed in ebb and rude upon the bleached and ashing gloom. I heard a voice within the dark that answered not my idle word. I could not choose but pause and hark it was so magically stirred. It grew within the quiet hour, with the rose-shadows on the wall. It had a touch of ancient power, a wild and elemental fall. Its rapture had a dreaming close. The dawn grew slowly on the wall, spedding in fragile veils of rose in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace. And folded in the fading night I felt the dawning sink and cease. End of poem. This recording is in the public domain. A Night in March by Duncan Campbell Scott Red for LibriVox.org by Nemo At eve the fiery sun went forth, flooding the clouds with ruby blood, uproared a war-wind from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow slipped singing over the wall, and ever when the wind would cease a lynx cried out within the cold. A spirit walked the ringing rooms, passing the locked and secret door, heavy with diverse ancient dunes, with dreams dead laden to the core. Spirit, thou art too deep with woe. I have no harbor place for thee. Leave me to lesser griefs and go, go with a great wind to the sea. I faltered like a frightened child that fears its nursefairy brood, and as I spoke I heard the wild wind plunging through the shattered wood. Has thou betrayed the rest of kings with tragic fears and spectres won? My dreams are lit with pure things, with humbler ghosts be gone, be gone. The noisy dark was deaf and blind. Still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Art thou the fate for some wild heart that scorned his cavern's curve and bars that leaped the bounds of time and art, and lost thee lingering near the stars? It was so still I heard my thought, even the wind was very still. The desolate deeper silence brought the lynx moan from the lonely hill. Art thou the thing I might have been, if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul? The wind rushed down the roughen wrath and shrieked and held its breath and stood, like one who finds beside his path a dead girl in the marish wood.  Art thou the spirit ministry that hovers round the newly dead? The auroras rose in solitude and wanly paled within the room. The window showed an ebb and rude upon the blanched and ashen gloom. I heard a voice within the dark that answered not my idle word. I could now choose but pause and hark it was so magically stirred. It grew within the quiet hour, with a rose shadows on the wall. It had a touch of ancient power, a wild and elemental fall. This rapture had a dreaming close. The dawn grew slowly on the wall, spreading in fragile veils of rose and tender lines of lemon gold. The world was turning into light, was sweeping into life and peace, and folded in the fading night. I felt the dawning sink and cease. End of poem. This recording is in the public domain. A Night in March by Duncan Campbell Scott, read for LibriVox.org by Phil Shempf. At eve the fiery sun went forth, flooding the clouds with ruby blood, uproared a war wind from the north and crashed at midnight through the wood. The demons danced about the trees, the snow slipped singing o'er the wall, and ever when the wind would cease, a lynx cried out within the cold. A spirit walked the ringing rooms, passing the locked and secret door, heavy with divers ancient dooms, with dreams dead laden to the core. Spirit thou art too deep with woe. I have no harbor place for thee. Leave me to lesser griefs and go, go with the great wind to the sea. I faltered like a frightened child, that fears its nurses' fairy brood. And as I spoke, I heard the wild wind plunging through the shattered wood. Hast thou betrayed the rest of kings, with tragic fears and spectres won? My dreams are lit with purer things, with humbler ghosts, be gone, be gone! The noisy dark was deaf and blind, still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Heart thou the fate for some wild heart, that scorned his cavern's curve and bars, that leaped the bounce of time and art, and lost thee lingering near the stars? It was so still I heard my thought, even the wind was very still. The desolate deeper silence brought the lynx-mone from the lonely hill. Heart thou the thing I might have been, if all the dead had known control, risen through the ages trembling sheen, a mirage of my desert soul? The wind rushed down the roof in wrath, then shrieked and held its breath and stood, like one who finds beside his path a dead girl in the marish wood. Or have I ceased, as those who die and leave the broken word unsaid, heart thou the spirit ministry that hovers round the newly dead? The auroras rose in solitude, and wonly paled within the room. The window showed an ebb and rude, upon the blanched and ashen gloom. I heard a voice within the dark, that answered not my idle word. I could not choose but pause and hark, it was so magically stirred. It grew within the quiet hour, with the rose shadows on the wall. It had a touch of ancient power, a wild and elemental fall. Its rapture had a dreaming close, the dawn grew slowly on the wall, spreading in fragile veils of rose, in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace, and folded in the fading night, I felt the dawning sink and cease. And a poem, this recording is in the public domain. A Night in March by Duncan Campbell Scott, read for LibriVox.org by Rumpelt Poetry. At eve the fiery sun went forth, flooding the clouds with ruby blood, uproared a war-wind from the north, and crashed at midnight through the wood. The demons danced about the trees, the snow slipped singing over the wall, and ever when the wind would cease, a lynx cried out within the cold. A spirit walked the ringing rooms, passing the locked and secret door, heavy with diverse ancient dooms, with dreams dead laden to the core. Spirit, thou art too deep with woe, I have no harbor place for thee. Leave me to lesser griefs and go, go with the great wind to the sea. I faltered like a frightened child that fears its nurses very brood, and as I spoke I heard the wild wind plunging through the shattered wood. Hast thou betrayed the rest of kings with tragic fears and spectres won? My dreams are lit with pure things, with humbler ghosts, be gone, be gone! The noisy dark was deaf and blind, still the strange spirit strayed or stood, and I could only hear the wind go roaring through the riven wood. Art thou the fate for some wild heart that scorned his cavern's curve and bars, that leapt the bounds of time and art, and lost thee, lingering near the stars. It was so still I heard my thought, even the wind was very still. The desolate, deeper silence brought the links moan from the lonely hill. Art thou the thing I might have been, if all the dead had known control, risen through the ages, trembling sheen, a mirage of my desert soul. The wind rushed down the roof in wrath, then shrieked and held its breath and stood, like one who finds beside his path a dead girl in the marrish wood.  The auroras rose in solitude, and wanly, paled within the room. The window showed an ebon rude upon the blanched and ashen gloom. I heard a voice within the dark that answered not my idle word. I could not choose, but pause and hark, it was so magically stirred. It grew within the quiet hour, with the rose shadows on the wall. It had a touch of ancient power, a wild and elemental fall. Its rapture had a dreaming close, the dawn grew slowly on the wall, spreading in fragile veils of rose, in tender lines of lemon gold. The world was turning into light, was sweeping into life and peace, and folded in the fading night, I felt the dawning sink and cease. End of poem. This recording is in the public domain.


Taka, mehi muka kutu mwa muka isaka wa jit becameaorshi, karabuna glissu hii maikimu, na kortya muka maikimu, klil jit nasit uti mim double tavya, kuya mika wakil na mama kutu.  Kindly introduce yourself to our audience back at home and tell them who cash is. Yesaya. Onanita cash ano kipenda yela yela. What about now? Live on your TV. Vile inafa. No sense kufkirekilo na fukiria. Acha ni omge kuwanza. Acha ni omge kuwanza. Acha ni omge kuwanza. Acha ni omge kuwanza. Acha ni omge kuwanza. Acha ni omge kuwanza. Acha ni omge kuwanza. Acha ni omge kuwanza. UnSpace fertile in Mango website at shownd Nevertheless, regular don applause you don't want me to Well touch you know gangster I got. Gangster. Gangster. Gangster. How has it been for you? It's been a crazy ride. Jumzi kini pandashuka. Sengini mzuka full, sengini mzuka half, sengini mzuka quarter. Like kini badumzuka border. What are some of the lessons you have picked along the way? You know in those years, it's almost close to 10 years. It's actually 10 years. Kibaw, kwanza, make money. Sifanje tumzi ki. Tengeneza pesa. What is your passion? Passion. Kwa juki mix passion. Nalabda man gama kitringini dina kumzuka. Kwa kika passion, piki ya ki unneza lalanja. Uza gana jina bigi na una kitu. Ewa nganoma. So make it a business. Make it an enterprise. Ewa kifupi. Sifanje tumzi ki sababia wan love. Uza gana wan love, wan love alipi rent. Yes. Alipi bills. Alipi bills. So by making money, unambiawa sana. You know have a brand. You know jiyu eki wukonja maket youself properly. So that's if someone wants to work with you. Tuna nina kwa raisi. And they have something. Even apart from, onaja building a brand takes such an enormous amount of time. Wezi am kwa se mehoya. Mini brand lewa. Amma mini brand kutoka keshosa sana. Nimi amwa kashkutoka lewa ni brand jana si kukua. So like have an income. Have a capital. Have a plan. Okay. So what would you say makes you unique? Nini na fanya kashana standout. Aki sima wakupapuwa, maki sima wakumi imba. Aki drop mga mazake nini na fanya standout. Ananatist. I think kwanza ni mzuka. Vibe. Yes. Vibe ako. A lot of people tell me that I am unique. So I think it's my voice. Yelo wuki iske uta jua. Eh wule nule mchi zi. Wule nisi. See somebody else. Nambi wanga wuki wongia tribit na jua. Aragama tukoni trajone. So I think voice ni unique. Vibe generally. Okay. So the first song you performed it's by you and various artist form in Zealand. Why did you decide to bring those artists together? And are you from that side as well? Yeah, I am. Okay. Zero until 2020 mzuka yukua full but 2020 kuna a media station yukuna start up kisi ni home by the way. So nika get opportunity yakonda kuwa kuko. So nika yake kisi around late 2020. First time I live kuko as an artist but I can go away from music for a while sababu at least wule nimi sama lazimu ifanya biashara. Yes. So zero up until around 2017 kuna ifanya for the love of it. So nika moku get other avenues aku generate na jua ma income ganji ni ni. So nika naka kupe gawera huko. So niki wawera kisi nika interaction a lot of artists wajia kuna asa ni wadop sana wuko. Agini most of them na imba vernacular bati na kuna kitu netogusi urban music so most of them ni wa yo vibe. So nandili feelen ya asa ni wadop mimi hata having been from kisi iskwa ni me stay yukua ni kuna stemji ni sana but some of the artists na wajia kukitambu atu kama kina mzimigi wana ma big nya mfu mweba tuna kina babji wali fanyanga uji inga ni kuna kina jigi. Oni wasa ni way back but kuna wangi na wampi wali kuna come through. So I thought how about niki ya sayote kwangu mwaja nini wa link up at least to show kili yung bogi na zafanya. So nika fanya kama intro na niki executive produce the project. So niki chaza studio time niki chaza video nilink up na tasla tasla at the time wali kwa kisi wali kuna wak close na katapila katapila piya kwa video by there. So yo time wali kwa base duka laki na after shindelia mi ta flani. So na ata time piya tasla piya li hama wuko kwa kakam nani. But it was a good experience at least kwa kawati sote pama waja na mzuka ni full nya na toki feel nya na na kiwa. Onimba kiki kisi lagi nuta baniata ni French. Lahi na flow fresh kwa beat nene. Sana, Sana, Sana, Sana. So we can't ato sachao individual artist uta pata nizi. So we can't matter wadup, waduna projects mengi Sana at least toreki yom nzuka on the map. Yaa.  Are you planning badu kufanya collabo sama you won't do singles as well. Aa Sàiina do As in villain, mesa ma kwanza tato ditua pongokufanyamziki biz adiyo kitamu nukunafanyamziki sababumimi na fanyaki na taka. I was basise yangunni hiphop na rap. jabu, hepopandwata partisi dihond doki tu minna like but later ni li kuja k compatibility kweka, naku ni lem Colorado We made strategic moves So every jam na do na jari bukongali amalita henda Na jari bukongali na target nini Na takakuona ingoma ni kiido ita ni rudishi enini Return on investment no jua Still business is a business Like business is a business Moves ako na zi plepo And on that note Chombi about the most recent song that you have done in the lair In the lair was after Sayotaslami Mubu nil kwa mwa knatasla Sa nata nangu megini ni to tension piya Alini link up na dema ni to sarange Tu kwa do another amazing jam So after I moved to Nairobi Jusai ni currently nko based in Kisi Ni kwa link up na producer Mi gida ni to Samsi Samsi is an old friend by the way Nini audio na video producer piya Na li kwa na waksana na mbuzi gang before Waa piwa li kwa nga wuku Nga kisi In the other place So kuna talent mingi sa mimi me to kwa wuku Wad kwa kiyomoka wana Ona kuja yi Ona kuja wuku Nini link up na Samsi Aka ni introduce kwa jamani to Vinto piya Vinto neskon piya ni vocalist Badoni audio na video producer Actually any of the videos Akez na tamba wuku mad niya Awa Sayotas ni metajapu Ona fanyu videos na demand So to kinda studio ni to free flow Tu kwa jari buku come up na kitu Ni kwa wami na da if I fly nivi So Vinto nili produce beat Samsi aka mix aka master audio Tenna both wuka do video Eh, at least ni kwa na Since Awa ni tu na waka na Awa Sayi Na waka talented as Karibun semileji nambaya Ni wajipu la kumapem Eh, waka talented as Yeah man Yes Okay So atu nesapta piya in the lea And all those other amazing songs wu me fanya Eh, mostly most of them is kwa YouTube So Badoni in the lea Mi akumbiya to turn this venture into a business Transition time Gyuna na gita ma mini kna fanya katumi zuka Nka nalink up studio na jesit No pigatumga ma nai kelepa le YouTube Mi na sama, hkesha nihini Hkesha nihini Agini sa aeja satu nanza kujaribu ku'a piga Na jari buku kuwa Kwaum ja nza Shkwem jinkam jinkak Eh, juun eza, waistiyom zuka So inga to YouTube So after cash forever Kasi amu dendi kwa na ke Na forever ni le forever aka wa idea So ki get cash forever Like, all the other videos are done Videos on the 8 years of the ads I am just a grown woman and will come through In shout outs as we wind up We did a shout outs It was a lot At least i told you Before i shout out I never shut up Big up all the producers of our twit Big up Tassler Big up Samsea Big up Vinto Big up Geshiyote Matib Thank you so much for coming through. We appreciate your time. We get to one final performance. I have a few comments. I want to sample. We want to sample. I'm Adi Sazi na nasema pale Twitter. Can all massive logs end?


Holland I am practicing my Dutch by ordering in Dutch. They have English version and Dutch version We're getting the olives, which is the Porsche olévin and the Porsche Autocas, so now when the lady comes I'm gonna do it for real one is ain Ain, so it'd be Ain Porsche olévin. Olévin.  Porsche olévin Ain Porsche olévin, and I don't know how to say and and and and and one Get a fellow basketball and Ain Shit, here she comes. I'm ready Ain Porsche olévin, and Ain Porsche Autocas The next bit when she brings the food in I have to say this looks delicious and to say that it's Cedar liquor out, which means it looks delicious Cedar liquor out


The Kosovovence models presented from 1960 to 2007 were reviewed and their accuracy for correlating and or predicting the solubility of drugs in water-cosolvent mixtures was assessed. These models can be categorized into three groups, theoretical, semi-empirical, and empirical. The simplest Kosovovence model, the log linear model of Yakovsky, estimates drug solubility in water-cosolvent mixtures by using the aqueous solubility of the drug. The Jui-Banakri model requires only one additional data point, the solubility in neat-cosolvent, to make predictions with an acceptable error rate. Error terms used in the literature were also discussed, along with some general comments about the acceptable prediction error for pharmaceutical applications. This article was authored by Abogas M. Jui-Ban.


I started to promote the Internet Interpol more than 10 years ago. That time people were smiling on me and said, what's that? Internet Interpol. Okay, now it's coming true. Cooperation between Kaspersky Lab and the new cyber division of Interpol. I see it's only one and right way how to address this issue, how to investigate cyber crime in a cyberspace. And I see there have to be, there should be the cooperation from both sides. From other side it's a technological experience. So our ability to read the code, to take the data from the Internet, to trace the steps, traces of the bad guys. And from Interpol it's ability to work internationally, to be connected with cyber divisions in 190 nations. So I think that in this way the computer incidents will be investigated much, much faster. The cyber incidents, they are split into different categories.  Cyber crime is just financial motivated attacks or political motivated attacks to steal confidential data, to have access to their bank accounts, illegal access to bank accounts. Espionage, it's stealing classified information or top secret information, their intellectual property. And cyber sabotage, it's attack on the critical infrastructure, critical IT infrastructure, critical industrial infrastructure and on the telecommunications. To me they are most critical, most dangerous, of course it's cyber sabotage, it's attack on the power plants, power grid, transportation, telecommunications, financial sector, health care. And I'm afraid this is the worst case scenario and these scenarios really wake me up at night.


Assange exposes the empire's true face, notes from the edge of the narrative matrix. Julian Assange is a journalist who's been imprisoned for doing journalism on war crimes by an empire that claims to defend journalists and oppose war crimes. Assange and his persecution expose the giant plot holes in every story the western power structure tells about itself. About its love of free speech and the free press. About its opposition to tyranny. About its wars and why it wages them. Assange exposes the empire's true face. And in that sense it's interesting that the empire made the decision to jail and silence Assange. Since in doing so it exposed its own tyranny and criminality far more than WikiLeaks ever could have hoped to. Assange said, it is the role of good journalism to take on powerful abusers. If you accept this as true, you must also accept that there are precisely zero good journalists anywhere in the western mass media and that Assange is the greatest journalist who has ever lived. The moderate position on Ukraine is to hold both Russia and the US empire responsible for their respective roles in starting and continuing this war. That's the middle ground position. But this position is regarded as freakish fringe extremism in the western mainstream and you'll be accused of literally conducting scyops for a foreign government if you voice it because the western mainstream is just that freakishly extremist. The mainstream position in the west is that Putin invaded Ukraine solely because he is evil and hates freedom and that Moscow is 100% responsible for this conflict in every way while the US is just an innocent little flower who just wants to protect freedom and democracy. When you actually spell out what the mainstream position on Ukraine is, it sounds like a silly fairy tale for children but that's what all the most influential western pundits, politicians and government officials are actually saying. That's how batshit insane things are. The Overton window has been shifted so far in support of NATO warmongering that this middle ground position is now regarded as fringe extremism so they just debate things like whether or not cluster bombs should be used to fight this war that is obviously 1,000% Russia's fault. As is often the case, this dynamic has already been well described by the elderly scholar who we all love to share our thoughts and opinions about Noam Chomsky. The smart way to keep people passive and obedient is to strictly limit the spectrum of acceptable opinion but allow very lively debate within that spectrum, even encourage the more critical and dissident views. That gives people the sense that there's free thinking going on. While all the same, the presuppositions of the system are being reinforced by the limits put on the range of the debate. Here's a tweet by Katelyn. Ukrainian flag usually just means US flag. 99% of the time you see someone flashing a Ukrainian flag or saying I stand with Ukraine. What they really mean is I support the US proxy war and hope Washington succeeds in its goals to use Ukraine to hurt its long-time geopolitical rival. The claim that NATO is a defensive alliance that set up to promote peace is a lie that's refuted by a swift glance at recorded history. In terms of evidence, it's crazier than saying there are alien aircraft in our skies, but you constantly hear respected pundits saying it. The US presidential race is that wonderful season American liberals set aside to remind socialists that they hate them far more than they hate the right and would cheerfully burn the whole country to the ground before they'd share one iota of power with them. Here's a tweet by Ian Bremmer about Cornell West. Presidential candidate Cornell West, more closely aligned with Putin than Trump is, not easy to pull off.  It's trippy how people pour such effort into disputing whether the planet is warming when the biosphere is showing us many, many other signs of looming collapse. They completely ignore the ocean dead zones, plummeting insect populations, loss of wildlife trees, fertile soil, etc. I mean, what specifically is the claim here? That there's a big evil plot across the entire scientific field to lie about warming, but all the other signs of environmental collapse are legit? Or are those fake too? If so, why only focus on the one message that benefits fossil fuel companies? Obviously, there are powerful people looking to exploit global warming to shore up wealth and power. That's to be expected. It would be surprising if it wasn't happening. None of that changes the need to drastically change the way humanity operates on this planet right away. One reason it's so hard to set up beneficial systems is because in negotiations, manipulators always push for the absolute maximum amount of gain they can possibly grab, while good people only push for a normal, human-sized amount of space for themselves.  People come to the negotiation table with demands that are viewed as reasonable by those in power and then are negotiated back halfway from that point of reason as a compromise, while those with the power grab up everything they can get their mitts on and walk back only if forced to. This has a ratchet effect over the years, which sees ordinary people losing more and more power to the ruling class. That's not going to change until normal people stop letting the manipulators set the bar at what's reasonable and start pushing out space for themselves with as much force and entitlement as bad people. People are going to have to stop coming to the negotiating table with their compromise and instead show up with the demand to take back everything that was stolen from them and more with as much force as necessary.


Hey Psych2Goers and welcome back to another video. We wanted to thank you for all of the love and support that you give us. It helps us make psychology and mental health more accessible to everyone. Now, let's begin. Psychologists and researchers have long been developing studies to find out what exactly it is that makes someone attractive. Think about it. What are the questions you might ask yourself when you ponder on what attracts a possible partner? Is it good looks or is it displaying confidence in having a good, healthy attitude? While these are good and basic qualities for dating, what about the little habits that you can use to help charm your crush even further? Behaviors that can make a potential partner admire you so much that they're willing to chase after you. In a non-creepy way, of course. Here are six behaviors that will make someone chase you, backed up by psychological research. 1. Compliment others and in turn, people will associate those compliments with you. Have you ever heard someone speak so highly and kindly of another at a party, and you admired them for doing so? This can leave you with the impression that they themselves are kind-hearted because of how they spoke so kindly of others. When you shed others in a positive light, people will associate the traits you use to describe that person with yourself. So, if you have kind words to say about your best friend or your crush, like, she's so energetic, fun, and lovely, and your crush may start thinking that you happen to be energetic, fun, and lovely too. This is something called spontaneous trait transference, and it occurs when communicators are perceived as possessing the very traits they describe in others. 2. Spend more time around the person you have a crush on. The mere exposure effect can be a very useful way to get someone to like you. According to the psychological study by R.B. Zajonk, the mere exposure effect is a psychological phenomenon in which people find themselves preferring someone simply because they developed familiarity with them. When someone is repeatedly exposed to a certain stimuli, they develop familiarity with that stimuli and therefore prefer its presence. The more familiar your crush is with you, the more they'll start to notice you. 3. Play copycat and mimic your crush. Do you find yourself subconsciously mimicking the gestures, movements, postures, and facial expressions of your crush when you're talking to them? This instance is called the chameleon effect. It boils down to people like people who seem familiar to themselves. If you subtly mirror your romantic interest when you interact with them, they might just start to develop a natural pull towards you. 4. Say their name often to grab their attention. Have you ever noticed that you can pay attention to a single conversation, even when in a crowded and noisy room? This is a form of selective attention called the cocktail party effect. It's when you're able to focus your auditory attention on a particular conversation, while simultaneously filtering out the other noises and distractions in the room. Like, for instance, when someone says your name and you immediately snap to attention so you can hear what the speaker is saying about you or what they're asking you. This effect can also be used to help your crush notice you better. While in conversation with them, try saying their name often and at the beginning or end of questions. This will grab their attention and also add a bit of charisma to your normal conversations. This offers them the sincere impression that you are interested in them and what they have to say. 5. Come across as capable and intelligent, but still human. Has it ever occurred to you that clumsiness and a little lack of grace can make you more attractive to your crush? Researcher Elliot Aronson from the University of Texas found that if you make some mistakes but still show that you're capable and intelligent, it may make others see you as more attractive. In the study, he had people rate fake test takers based on their attractiveness. Test takers were graded as great, mediocre, or poor. Some test takers would act clumsy and spill coffee at the end of the interview. People rated the test takers who spilled coffee as highest on the attractive scale. The research paper states, a superior person may be viewed as superhuman and therefore distant. A blunder tends to humanize him and consequently increases his attractiveness. This means that people want to see your human side. When you show that you're just a regular human being who makes common mistakes, your crush can relate to you better. 6. Hang around with a group of friends Research shows that people tend to find others more attractive when they're in a group over being by themselves. This idea is called the cheerleader effect. Researchers Edward Voll and Drew Walker of the University of San Diego, California conducted five experiments where subjects would rate people based on photographs of them. They found that subjects rated people more attractive when they were pictured in a group of the same gender compared to an individual photograph of someone pictured alone. As the study suggests, individual faces will seem more attractive when presented in a group because they will appear more similar to the average group face, which is more attractive than group members' individual faces. So if you see a cute individual at a party, try getting them to notice you first when you're chatting with your group of friends. Are there any behaviors from this list that you want to try out on your crush? Let us know in the comments below. If you enjoyed the video, give us a thumbs up and share it with someone who might find it helpful too. The studies and references used are listed in the description below. Don't forget to hit the subscribe button for more Psych2Go videos and as always, thanks for watching. We'll see you soon.