So, in our discussion on the second order partial differential equations, so far we have considered partial differential equations second order in two independent variables. In this lecture and the next we are going to discuss second order partial differential equations in more than two independent variables. The first concept that we are going to discuss is what is called characteristic surfaces. This is a generalization of characteristic curves that we have seen in the discussion of second order equations in two independent variables. The outline for today's lecture is we first recall the characteristic surfaces and classification which was done in two dimensions which is same as in two independent variables whatever we have covered for the partial differential equations where we called it was a characteristic curves and we have of course classified based on characteristic curves. So, we will recall that and then we generalize that to higher dimensions and they are now called characteristic surfaces for obvious reasons because they are going to be one dimension less. For example, characteristic curve it is a curve in R2. So, now here we will have to imagine things which are just one dimension less. So, that is why we will come to that then we will understand what this means and then we classify the linear equations in more than two variables. So, linear PDE in D dimensions this how we call it is an equation of this form. This is a most general linear partial differential equation in D independent variables. Often we call that D dimensions PDE in D dimensions means there are D independent variables. Sigma ij equal to 1 to D aij of x dou 2u by dou xi dou xj. This is often called what is called a principal part of the PDE, principal part of the PDE. So, it is that part of the PDE where the highest order derivatives appear. The highest order derivative appears with power 1 coefficients may depend on x, u and first order derivatives does not matter. So, this is what is called principal part. In the context of this D dimensional linear equation the principal part is precisely this because this is where the second order partial derivatives of u appear. If you recall in when the in the case when D equal to 2 the classification and the characterization of characteristic curves is actually based on the principal part. So, similarly it is going to play a role even in higher dimensions. That is why I have introduced the word formally that what is the principal part of a linear partial differential equation. It is that part where the highest order partial derivatives appear and some people call this one as lower order term sometimes because it involves derivatives of u not of second order but of orders less than 2 that is 1 or no derivative. We have to make some place some assumptions on the coefficients without which we cannot do the theory. So, we are going to assume that aij, bi, cd of course they are functions of x defined on a domain that is x belongs to some domain in Rd we also assume that these are continuous functions for simplicity. We most importantly assume that aij equal to aji because aij is a coefficient of dou 2u by dou xi dou xj aji is a coefficient of dou 2u by dou xj dou xi and if you are expecting a twice continuously differentiable function as a solution to this equation then dou 2u by dou xi dou xj is same as dou 2u by dou xj dou xi the order in which you take the second order partial derivative does not matter. Therefore, we can always make this to be symmetric aij equal to aji. So, this is the condition that we must place. So, let us assume this and this x which is in the bold phase actually stands for x1, x2, xd in Rd. So, what is the Cauchy problem for the equation dL that is d dimensional linear equation this is a shortcut form of calling d dimensional linear equation we just call dL. So, what is the Cauchy problem? Take gamma subset of Rd which is a regular hyper surface. Let u and all of its partial derivatives namely ux1, ux2 up to uxd be prescribed on gamma this is often called Cauchy data. Cauchy problem for dL consists of finding a c2 function defined in a neighborhood of gamma because that is where the function u and the partial derivatives are prescribed or even a part of gamma now we are used to this idea that Cauchy problem need not have a solution around entire gamma it could be a part of gamma such that u solves dL it should be a solution of the partial differential equation and the given Cauchy data should be satisfied by u. Now, what is the meaning of gamma inside gamma subset of Rd is a regular hyper surface there are 2 words regular and hyper surface normally hyper surface means somebody who just we just one dimension less in the whole space for example in R3 a plane would be a hyper surface 2 dimensional plane or a sphere that will be hyper surface because a sphere can be described using 2 parameters whereas in R3 we need kind of 3 parameters. So, that is the meaning of the hyper surface and what is regular it is something about smoothness we will see that. So, when d equal to 2 how did we define gamma is a regular curve first of all we consider gamma which is a parameterized curve to start with and regularity meant that at every point of gamma there is a well defined tangent. Equivalently it means that a well defined normal exists at every point of gamma even in higher dimensions gamma may be taken as a parameterized surface parameterized by d minus 1 parameters when d equal to 2 the curve prescribed by 1 parameter when you are in Rd it will be prescribed by d minus 1 parameters. So, parameterized by d minus 1 parameters. Regularity means that at each point of gamma in the case of d equal to 2 we said well defined tangent now that it becomes well defined tangent plane exists. Therefore, equivalently a well defined normal exists at every point of gamma. We will come back to this discussion towards the end of this lecture. When d equal to 2 the function u and only its normal derivative were prescribed right recall lecture 3.1, but we found that it is equivalent what is equivalent prescribing function u and only its normal derivative this is equivalent to prescribing u and all its partial derivatives. Why is it so because gamma was a regular we can determine all derivatives if you knew the function and the normal derivative. So, even in higher dimensions one may prescribe the function u and its normal derivative on gamma it can be done. In such a case what do you have all tangential derivatives are completely determined on gamma why is that because the function is given on gamma and they are d minus 1 in number normal derivative is also prescribed. For example, imagine your gamma is let us say in d equal to 3 gamma is x y plane. So, you are prescribing u on x y plane it means automatically u x and u y are determined on the x y plane.  So, if you give u z you have three derivatives. Now, same thing is true even if gamma is not x y plane gamma is a regular hyper surface. So, if in case of regular hyper surface you are given u on gamma therefore, all tangential derivatives can be determined keep in mind the example of the x y plane as gamma and r d is r 3.  So, you have d directional derivatives and important thing is the directions are independent directions.  So, let us review characteristics surfaces and classification as was done in the case of two independent variables. So, let us recall from lecture 3.1. We had a linear system when we are trying to compute the second order derivatives from the PDE and the Cauchy data alone. So, this is the system. F and G was the parameterization of the gamma. Gamma is f s x equal to f s y equal to g s. So, we are trying to determine the second order derivatives then it satisfies a linear system of linear equations non-homogeneous. Determinant of this matrix was what is called delta of s. This is the determinant. If you expand this determinant you get this formula. We did this in lecture 3.1. Now, if delta s equal to 0 then what are the implications? What will happen? So, in other words you have a system let us call this a x equal to b. We have a system a x equal to b and determinant of a equal to 0. What can you say about the solutions of the system a x equal to b? What we can say is there will be b for which there is no solution, there will be for which there will be solution, but the moment you have one solution you have infinitely many solutions. So, you will never have a unique solution either you have no solution or infinitely many solutions. So, if delta is equal to 0 then this system can have no solutions. When will that happen? When the data is incompatible with the PDE. It can have infinite number of solutions. This will happen when you have compatibility between the PDE and the Cauchy data. The next example illustrates these possibilities very clearly. It is a very simple partial differential equation. So, the Cauchy problem is u x y equal to 0 and u of x 0 is given to be f x, u y of x 0 is given to be g x that is u is prescribed and the normal derivative is prescribed on x axis here gamma is x axis. What about this problem? The general solution of the PDE u x y equal to 0 is given by a function of x plus a function of y because you integrate this u x y equal to 0 imagine it is d by dy of u x equal to 0 then u x becomes a function of x and you integrate you get this is a function of x plus function of y. This u satisfies the Cauchy data. What is the Cauchy data? These are the equations. So, when is u x 0 equal to f x substitute here put y equal to 0 you get f of x plus g of 0 must be equal to small f of x. This is the first condition. What about the second condition? You need to differentiate u with respect to y that will give you g prime y and when y equal to 0 that is g prime of 0 that will give you g x. So, these are the two condition that we get. So, if these equations hold then the function g must be constant because g prime 0 is a number that means g is a number. If g is not a constant function then the Cauchy problem does not have a solution that is very clear from this is not satisfied. If g is a constant function then Cauchy problem admits infinitely many solutions. Just convince yourself it is a very simple to show that you can have infinitely many solutions proving this assertion is left as an exercise for you very simple. Now, observe that the Cauchy data is prescribed on the line y equal to 0 that is the x axis which is a characteristic curve for the given PDE. Let us check that delta s this is a formula c f prime square minus 2 b f prime g prime plus a g prime square. What are a b c in our case? a and c are 0 our equation was u x y equal to 0 right. So, a and c are 0 and gamma is x axis therefore f s is s and g s is 0 when we plug in this into this what we get is delta s is 0. So, it is a characteristic curve and clearly u y y cannot be determined along x axis using the equation and the Cauchy data because Cauchy data gives you only u u x and u y anyway is given, but u y y you cannot get because it is not there in the equation. So, now we are ready to define what are characteristic surfaces in higher dimensions. So, the preceding discussion inspires us in generalizing the notion of a characteristic curve to the context of PDEs in more than two independent variables. So, let us define the notion of characteristic surfaces. What is that? A hyper surface in R D is said to be a characteristic surface for a second order linear PDE if at every point of gamma if at every point of gamma there exists at least one second order partial derivative of a function u which satisfies the PDE and that cannot be uniquely determined. That cannot be uniquely determined from the PDE and the Cauchy data that is from the PDE and the values of u and all its partial derivatives along gamma. From this knowledge of u and all its partial derivatives on gamma you cannot determine at least one second order partial derivative uniquely determined cannot be uniquely determined means either you have too many values or no values that is no solutions or infinitely many solutions. If you recall that is what is true right with in two dimensions when delta is equal to 0 we have the two possibilities which were seen in the last example. So, let gamma be a hyper surface now we are going to define a non-characteristic hyper surface. Gamma is said to be a non-characteristic hyper surface. Recall what we have defined in the previous slide what is a characteristic surface. Now we are defining what is called non-characteristic hyper surface. What is that? At every point of gamma all the second order partial derivatives of a solution to the PDE can be determined uniquely from the PDE and the knowledge of u along the gamma and partial derivatives of u along the gamma. Now I would like you to think over the following understand the difference between gamma is not a characteristic hyper surface on the previous slide we defined what is the meaning of gamma is a characteristic hyper surface. Therefore gamma is not a characteristic hyper surface and gamma is a non-characteristic hyper surface there is a difference. I just give you a hint understand the difference between delta S identically equal to 0 on I in fact this is what we called a characteristic curve if this happens and delta S is never 0 that means that curve was non-characteristic curve that is the difference one is not a negation of the other you may call one is a extreme negation of the other that is fine but you must understand the difference between not a characteristic hyper surface and non-characteristic hyper surface both are different. We have a theorem let you be a C1 function on a domain omega in RD let gamma be a regular hyper surface and you be C2 on omega minus gamma that means what we are thinking of is a situation like this you have a omega and you have a gamma then u is C2 here u is C2 here at all these points but u is C1 throughout and jumps across gamma for all secondary derivatives are defined that means that at points here at points on gamma look at any derivative that you think of u x1 x2 this is one partial derivative this jump is defined that means u x1 x2 coming from this domain let us call as omega 1 call this omega 2 at a point here the u x1 x2 this secondary derivative has a meaning that means it is continuous from this side so that means in other words u restricted to omega 1 is actually continuous function of up to closure so that the values of second order partial derivatives make sense on gamma similarly u restricted to omega 2 is C of omega 2 bar not C in fact C2 because C we already assumed u is C1 there is no need of writing C of omega 1 bar or omega 2 bar what we want actually is about second order derivatives have values at points of gamma coming from the right hand side or left hand side I have written picture in R2 that is why I am using the word right hand side left hand side so in other words what I am assuming is that this hyper surface gamma cuts omega into two parts one part you call it omega 1 another part you call omega 2 u is C1 on the whole domain omega but on each part u is C2 of omega i bar when you restricted to omega i so that jumps these are well defined quantities so now I am going to talk about that in the next hypothesis assume that at each point of gamma some second order partial derivative has a non-zero jump and let u be a solution to the PDE in both the parts omega 1 and omega 2 as I have written them then conclusion is about gamma gamma must be a high characteristic surface the hyper surface gamma must be a characteristic hyper surface sometimes I am calling characteristic surface sometimes I am calling characteristic hyper surface does not matter because anyway gamma is a hyper surface to start with so it is a characteristic surface suppose it is not a characteristic surface so the proof is going to be like this I assume that the conclusion does not hold and I will show that one of them does not happen in fact I am going to show this does not happen all second order derivatives are continuous across gamma I am going to show that so that will prove this theorem so assume gamma is not a characteristic surface okay then there is a point of gamma at which all second order partial derivatives are determined uniquely call that point P there is at least one point so call that point P all the second order partial derivatives can be uniquely determined from the PDE and the knowledge of u and all its partial derivatives along gamma this is always there okay from this this is what we call Cauchy data in the Cauchy problem from there and the PDE we can determine all second order partial derivatives uniquely at that point now this is where you should compare with what we did in lecture 3.1 expression for them involves expression for what expression for the second order partial derivatives involves u and its partial derivatives along gamma apart from the coefficient functions in the PDE aij, bi, c and d we assumed u is c1 of omega and aij, bi, cd are continuous therefore at P we get the same values for all second order partial derivatives on gamma whether you come from the omega one side or omega two side you have the same value that means no jump across gamma thus all the second order partial derivatives are continuous across gamma and as we discussed at the beginning of the proof this finishes the proof of the theorem how to identify characteristic surfaces this is the next question because what we have defined characteristic surface it is a qualitative definition okay it just says that some partial second order partial derivative is not uniquely determined at each point of gamma such a gamma was called characteristic surface this is a qualitative definition now we would like to have a quantitative version of this so that we can go and find some characteristic surfaces so therefore it is useful to find a quantitative criteria the example which we discussed at the beginning of the lecture suggests the following if dou 2 u by dou x square dou x k square does not feature in the equation then x k equal to 0 would be a characteristic surface in that example what was the example it was u x y equal to 0 right and we have looked at u x 0 is given to be f and u y x 0 this is a normal derivative given to be g and we could not get what is u y y using this PDE and the Cauchy data u y y was missing so if some derivative is missing then that variable equal to 0 will be a characteristic surface this idea so this discussion gives rise to a necessary and sufficient condition for a regular hyper surface now we are going to look at hyper surfaces of this form phi x equal to 0 to be a characteristic surface this means set of all x in r d such that phi x equal to 0 so called level set of the function phi we are going to derive an extreme sufficient condition for regular hyper surface of this form to be a characteristic surface so let gamma be a regular hyper surface defined as the level set of a smooth function phi 1 from r d to r what is the definition set of all x in r d such that phi 1 x equal to 0 and such that gradient of phi 1 is not 0 for each x in gamma so this actually tells you that there is a clearly defined normal at every point of gamma so this is the regularity hypothesis for the hyper surface then the following statements are equivalent what are those gamma is a characteristic surface for d l that is same as saying that this phi 1 gamma is defined through the function phi 1 that phi 1 satisfies this PDE what is the PDE grad phi 1 dot a of x grad phi 1 equal to 0 what is a is the matrix aij which is appearing in the principal part of the equation d l so this is an equation for characteristic surface a level set phi 1 x equal to 0 is a characteristic hyper surface if and only if this equation is satisfied of course this is a first order PDE non-linear okay so consider a non-singular coordinate transformation given by x 1, x 2, x d going to eta 1, eta 2, eta d and eta i equal to phi i of x we were given only phi 1 of x therefore eta 1 is phi 1 x now you find phi 2 of x, phi 3 of x, phi d of x so that we have this coordinate transformation defined which is very easy so it can always be done that is an exercise in analysis essentially what we are asking is can you given a function phi 1 with grad phi 1 non-zero can you find phi 2, phi 3 up to phi d such that certain Jacobian is non-zero okay that is the question it is possible. Now under the change of coordinates we have a new function w related to u w of eta 1 eta eta d such that u at the point x is equal to w at phi 1 x, phi 2 x and phi d x now the given PDE will be transformed into the new coordinate system and then we find conditions under which dou 2 w by dou eta 1 square does not appear remember eta 1 equal to 0 is same as set of all x as that phi 1 x equal to 0 is a hyper surface and that is precisely our gamma. So we know that disappearance of this is a sufficient condition for gamma to be a characteristic surface so we ask the question is it also a necessary condition answer is yes when Cauchy data is prescribed on gamma which in the new coordinate system is eta 1 equal to 0 we will not be able to determine this derivative dou 2 w by dou eta 1 square from the PDE and the Cauchy data. As a consequence one of the second order partial derivatives dou 2 u by dou xi dou xj cannot be determined along gamma uniquely okay why because there should be some connection between these derivative this derivative and these derivatives imagine you can find out all of them then can I write this as a combination of that think about this think about chain rule okay. So since dou 2 w by dou eta 1 square will arise only from the principal part of the given PDE namely this part when you change your DL equation into the new coordinate system this one dou 2 w by dou eta 1 square which is a second order derivative it comes only through these terms therefore you will find principal part how this transforms into the new coordinate system this gives rise to this where each aij is this expression. So go back to lecture 3.3 I think where we have done this change of coordinates okay thus the analytic characterization of a characteristic surface gamma is obtained by setting the coefficient of dou 2 w by dou eta 1 square to 0 that means this equal to 0 the above equation is nothing but what we want because this is grad phi 1 dot a grad phi 1 equal to 0 please ignore this number 26 this refers to the equation grad phi 1 dot a grad phi 1 equal to 0 okay. The previous lemma asserts that a hyper surface phi 1 x equal 0 is a characteristic surface if the equation grad phi 1 dot a grad phi 1 is 0 is satisfied. We are interested in knowing whether the equation has any characteristic surfaces a partial answer is provided by the previous lemma it also tells that characteristic surface exists when the equation does not feature the second order derivative with respect to one of the independent variables if the missing variable is xk that is dou 2 u by dou x square is missing then xk equal to 0 is a characteristic surface. Let us look at an example which is wave equation so we will try to determine characteristic surfaces for wave equation. So let gamma be a regular hyper surface defined as the level set of a smooth function phi. Now we have to be careful that wave equation we have x comma t so therefore x in rd and t in r so we write this so gamma is phi of x t equal to 0 and gradient should be non-zero here gradient is not with respect to x and t just to clear any confusion we write this gradient of x comma t of phi x t is non-zero for each x t in gamma. When will this gamma be a characteristic surface for wave equation? Answer the function phi must satisfy this equation grad x t phi dot a grad x t phi equal to 0 and what is a? a is a diagonal matrix minus c square minus c square minus c square in the end 1. So this is like ut t equal to c square u x 1 x 1 plus c square into u x 2 x 2 and so on up to c square u x d x d. So these are d number these 1 so this is a d plus 1 by d plus 1 diagonal matrix. So this equation grad phi dot a grad phi reduces to this equation. This we can write because this is the Euclidean norm is nothing but this whole thing phi x 1 square plus phi x 2 square plus phi x d square is precisely norm grad x phi square Euclidean norm. So this equation exactly this. Now I can get rid of the squares and I get this equation phi t equal to plus or minus c norm grad x phi. Recall from lecture 3.2 that when one of the independent variables is time which is true in the wave equation we will be interested in there the curves of the form t equal to psi of x. Now here we will be interested in surfaces t equal to psi of x. So we are not interested in arbitrary phi of x t equal to 0 but we are interested in t equal to psi of x. We explain the reason why why so because this is going to give the location of the discontinuity that that is what discussed in lecture 3.2. Please go back there and understand again. So in other words we are interested in the level sets of functions of this type t minus psi x what how the equation changes this can equation for a hyper surface to be a characteristic surface will now in terms of psi becomes this norm grad psi grad x psi equal to 1 by c. So when d is equal to 1 this equation is simply this equation. Now we can factorize them like this phi t square plus c square phi x square minus c square phi x square it is there then you have phi t c phi x minus c phi x phi t which gets cancelled. So this is exactly same as this factorization. So two important families of solutions they are the characteristic lines x minus ct equal to constant and x plus ct equal to constant. They come through solutions of these two equations phi t minus c phi x equal to 0 and phi t plus c phi x equal to 0. So now we are going to classify linear equations in more than two variables based on characteristic surfaces. So linear second order PDE is called elliptic if it has no characteristic surfaces. Parabolic if there exists a coordinate system such that one of the independent variables does not appear at all in the principle part when the equation is written in that coordinate system and the principle part is elliptic with respect to all the variables that appear in it hyperbolic if it is neither elliptic nor parabolic. So now we finished this lecture with a comment on the regular hyper surfaces that we started discussing at the beginning of the lecture when we introduced the Cauchy problem. So Cauchy problem is posed on any hyper surface gamma. We did not even define what it is meant right. We went with the understanding of what we know in two dimensions or it is a curve tangent is defined at every point of gamma like that. So naturally we understood by a hyper surface as geometric object in RD which is parameterized by D minus 1 parameters this is correct but we need to add regularity assumptions as was done in two dimensions. In our analysis we assumed that gamma is a level set. So when we looked at the theorem and the lemma we assumed it is a level set of a smooth function with gradient being non-zero. Now is every regular hyper surface defined like this with D minus 1 parametric hyper surface is it level set because we are not if it is not so we are not proved a theorem for a general hyper surface. So are we missing something by analyzing only maybe possibly a special case. So regular surface may be defined in many different but locally equivalent ways. There is no need to worry whether what we did is fine or not do not worry due to the equivalence. For equivalent notions of regular surface there is a wonderful treatment in this book by Wister, Matt and Koch multidimensional real analysis part 2 integration. They have two books on multidimensional real analysis part 1 is differentiation part 2 is integration. Of course if you want to study the part 2 they often refer to part 1 also very beautifully written books. Now let us look at some examples. This equation uxx plus uy plus uzz is of elliptic type. Since there are no associated characteristic surfaces how do I say it is elliptic? I have to ask whether there are characteristic surfaces if there are none it is elliptic. There are none why? Let us look at the equation said to be satisfied by a hyper surface to be a characteristic surface. So assume this gamma given by a level set be a regular surface. Gamma is a characteristic surface if and only if phi 1 satisfies this equation grad phi 1 dot grad phi 1 because the a is identity here. The matrix A that you get out of this equation is identity because only uxx, uy and uzz appear no mixed partial derivatives appear. So half diagonal terms are 0 in the matrix A and diagonal terms are 1. So you have this but what is this? This is mod grad phi 1 square equal to 0. So this will be satisfied if only if grad phi 1 is 0 but we are assuming the set gamma is a regular hyper surface that means grad phi 1 is never 0. So this tells us that there are no characteristic surfaces. Therefore the equation is elliptic type. Look at this equation ut equal to uxx plus uy y. This is a parabolic type. Check the definition. I will not discuss this. Please check that by the definition that is not it is a parabolic equation. Now this equation ut equal to uxx plus uy y it is a hyperbolic type. It is actually a wave equation in two space dimensions. It is a hyperbolic type. Check that it is not elliptic. This is what we have to do. It is not elliptic, it is not parabolic and by definition it is going to be hyperbolic. So let us summarize inspired by discussions of lectures to 3.1, 3.2, 3.3 we defined the notion of a characteristic surface in more independent variables, PDE in more independent variables. Derived a necessary and sufficient condition for a regular hyper surface which are level sets to be characteristic surfaces. And characteristic surfaces for a wave equation are analyzed. That is what we did towards the end. Using the notion of characteristic surfaces we have classified linear partial differential equations in more than two independent variables. Thank you.


Patriot Prime Reviews is a channel for adult collectors and may not be suitable for children under 13 years of age viewer discretion is advised Hey, what's going on guys? Patriot Prime here once again with another Transformers review, but before I get started I need you guys to do me a favor if you're watching this video right here and are not a subscriber of Patriot Prime Reviews Please hit that subscribe button right now. It won't cost you a thing Will help me and my channel out tremendously. Also, make sure and visit my sponsor toyhacks.com Toyhacks provides reproduction and upgrade decal sets for transformer toys from generation one to the latest modern figures Make sure and stop by the toyhacks armory where they can equip your figures with new weaponry in multiple colors and toy stages provides backdrops for figure displays and photography Each purchase with toyhacks earns you RoboSense that can be used for future purchases. You can check your balance anytime in your cart Toyhacks is a company run by collectors for collectors So check out toyhacks.com and make your collection stand out from the rest and tell them Patriot Prime sent you now onto the review The featured button this video is Transformers war for Cybertron Kingdom Scorponok now This is one figure that I really had my reservations on getting because the online images of him Just really didn't look that good and then once I picked up the near perfect Transform element Stinger warrior. I was really debating on deleting my pre-order from entertainment Earth But I'm glad I didn't because he arrived in the mail yesterday really took me by surprise and The reviewer and me really wanted to check out the Hasbro offering Compared to the third party. So now let's take a quick look at the packaging We've got Scorponok here in robot mode Transformers war for Cybertron Kingdom and more of that fantastic Kingdom artwork You got Scorponok in Scorpion mode and robot mode back in the packaging You've got more images of the toy in that horrible image that I was talking about them We'll go over a little bit more in the review and there he is in Scorpion mode once again You also see his little cyber B on the side of the packaging is the Outstanding Kingdom artwork So let's go ahead and get this Scorponok out of the packaging and see if this bot has some sting and welcome to Patriot Prime reviews Now once you get Scorponok all opened up and out of his packaging You'll see he does come with a sheet of instructions that as usual are very well illustrated and very easy to follow He also comes with a trading card. This one is black arachnia and when you peel back the Sticker you've got another image of black arachnia holding a spear I don't think I have that one yet. So like that looks pretty cool and you have weapons for Scorponok including his Mega missiles and you have two missiles right here Fused together with a five millimeter peg here on the end so you can actually take these missiles open up Scorponok's claw And put them in there like so and he also comes with his little Cyber B and the cyber B doesn't look too bad. It's got some really good sculpting some nice paint applications But I wish it had a five millimeter peg Right there on the chest You can see the molded in wings to not wings the molded in legs That looks really good But the peg is here on the butt and that's so you can plug it into Scorponok's claws But I wish he had a peg there like I said on the bug chest so he could plug into other bots Because in the show the cyber B was used to inject venom to you know Effect maximal so this one if you're gonna peg him into some other bot It's gonna be sticking out and looking weird, but it does look good if you peg it into Scorponok's claws like this So now you have Scorponok all armed and ready for battle with his mega missiles in one claw and His cyber B in the other so now let's take a closer look at Scorponok himself Now when I first opened Scorponok up out of his packaging my first thought was wow He looks so much better than his images online And that's because the images online have him mist transformed with his beast legs all Splayed out all over the place for Packeting he was in the package like this the legs were all folded up and Stuck in the cardboard insert and that looks so much better much more show accurate than the legs all over the place also another issue that I noticed once getting hit this guy in hand was some of the other stock photos show the Scorpion mode head up over the robot head. It's actually tucked in here We'll get to that later in transformation But this image right here who shows the scorpion head over top of the robot head So I don't know what it is with Hasbro if you're going to be promoting your product At least have your people transform the figure right for photos. So enough of complaining about that. Let's look at Scorponok He's not bad looking, but he's not great. He's got a very blocky torso I think really detracts from the character or the figure kind of gives you a dad bod but he does have a lot of nice sculpted detail and Texture hopefully the lights catching is just right But you can see the texture on the claws and the chest there. I mean it looks really good It's like a insect exoskeleton think a closer look at the face sculpt The face sculpt is kind of a hit-and-miss well one the head sculpt looks great But the face sculpt itself. I do not like that. I mean, I think the mouth is way too big He looks like a bulldog Just the lips are too much. He's got his little pointed purple goatee the yellow visor Once again great paint applications the yellow there on the tusks and the crest a little yellow right there for the center display Her center emblem now due to transformation. He does have this big crack down his chest and if it would Pig in a little tighter It wouldn't look bad because he has all these other molded details on the chest as well But it is what it is legs look really good to lots of great molded details and paint applications now the tail The tail could be better. It's got a lot of hollowness Right there.  It's really bad with this hollow section But that's due to transformation So I'm not too worried about the hollowness right here because when he's displayed on the shelf You're not going to see that but this right here that sucks So somebody needs to get on that and make some filler pieces now a lot of people are wondering how the Hasbro version of Scorponok Compares to the transform element stinger warrior and as you can see stinger warrior is much more Cartoon accurate and actually surprisingly. They're almost the same size now another drawback that Hasbro has the Stinger warrior has the tail attached to his upper back where the Hasbro version has the tail attached to his butt in the Cartoon show Scorponok had the tail attached just like that what gave him a lot more range of motion now This is not too bad, but he can't really strike overhead like the transform element version Let's go ahead and get him out of the way. I've already reviewed this guy. Let's focus on Hasbro So let's do the articulation now and we'll start with the tail the tail can go way back here and Has a joint there and this stinger tip is on a ball joint But like I said, it really doesn't have the range of motion like in the show The arms can do a complete 360 they can go up and they can go down There is a bicep Rotation right there and as you saw a bicep bend and that is really tight Of course, I prefer to have my tight joints with my figures not going to complain The claws as you saw earlier can open and close and there is a wrist rotation He also has a waist rotation here legs can go out and in forward and back There is a knee bend and ankle tilt So he does have a lot of nice articulation Which is really really good for your more modern figures now if you don't like the Missiles or cyber be inside his claws go ahead and remove these I do wish these missiles Were separate, but at least they can come out the transform element The missiles actually flipped up inside the claw so you could hide them out of the way until you flip them out For battle, but with this Scorponok you just pop them right out and you have the option To use a blast effect if you like so blast effect plugs in there and I do like that I think that looks really cool. So now let's get Scorponok transformed into beast mode Now before we get into transforming Scorponok into his beast mode I want you guys to take a look at his claws. I Just find these Claws the way they have these molded they look so weird in his robot mode they got this weird angle and With the spikes it makes it look like teeth These claws remind me of Audrey to from little shop of horrors or a piranha plant from Mario I just they look like they could be a hand puppet.  So the first thing we're gonna do is let's rotate the arms All the way up like so now what we're gonna do is split apart Scorponok's chest now it doesn't open all the way it only goes about this far and then you're gonna take his head and Fold down Just to right there and that is it now what we're gonna do is bring the tail down and Now take the scorpion legs and just manipulate these around Probably have to move the shoulders up slightly just like that and now you're gonna get these legs down and out of the way and rotating the middle section around and Just bringing those down there on kind of a soft clicking ratchet joint. Let me show you if we'll pick it up So see how that kind of locks in place that comes into play later on so just get these legs wrapped around and in Position now you're gonna lift the back section up and this is where the robot head is hid and This is kind of a pain to get a hold of I Just I don't have the fingernails to do it. Let me see up.  So the scorpion head goes over Scorponok's robot head now take these shoulders and turn these around so you have these little spike sections facing in Now once they're in like that, you're gonna bring the shoulders even closer together So they'll actually finish hiding the robot head of Scorponok and this part is really cool I love his leg transformation Flip the tail out and you're gonna bring the waist section Extended out further now what you want to do is pay attention to Scorponok's heels He has one heel that's purple and one heel that's gray So you want to rotate the legs around so they heal with the gray Section here is now towards the tail.  To face Toward the scorpion tail so you can actually fold the leg up then you go rotate once again Right there. So you've got the pointy heel facing toward the scorpion tail and now you're going to fold the foot forward and just Put the leg in the scorpion tail and there's this little hole right here that that heel is going to fit into And there you go. That fills up that big hollow spot on the tail now for the front of the scorpion just turn the leg once again, you're gonna bring the foot forward and You just fold it in on itself like so make sure Everything's lined up right the best way to know is these blue sections here are Facing down. Let's get this angle just right and There you go now. Unfortunately That's what that's going to look like. It's kind of sloppy looking But once you get these legs back in place and make sure and snap them down like I showed earlier He should stand up fairly well so The legs kind of balance him out. Otherwise, he's gonna be flopping around on this I hate that that sucks, but there's really no way I guess you can angle it up Let me see if the leg will fit Into that slot on the knee It does not so you just kind of angle that like so Get the arms position just right get the claws open here And there we go. We have Scorponok in Scorpion mode and I like Scorponok's Scorpion mode. It actually looks Like a realistic scorpion and as I said earlier the claws work more for Scorpion mode Then they did for robot mode. If you actually compare a picture of a real scorpion it works even with the red tip of the tail and Scorpion mode it's pretty long and I dig it. I really like this He's got red eyes right here on top. He's got the red fangs The way the spikes on the shoulder pads look kind of like looks like mandibles. Maybe it's got all the same Articulation and the arms that was in the robot mode and of course you can put in the missiles and the cyberbee Lot of articulation here with these legs now the front legs and the back. There is a ball joint here Near the connecting point of the body and that's it There's no extra ball joints for the knees Which is disappointing and the middle legs you got two legs hooked together on One ball joint and these legs are also Very very hollow. I hate how his robot face is just right there I wish I could have tucked more into the chest along with this whole leg section here in Genius transformation with the leg in the tail. I just wish they could done something with the leg underneath Now articulation with the tail is kind of limited now because of the leg I mean it just doesn't have much movement at all except for up here on top And the little stinger tip which is on a ball joint. So now let's compare Kingdom Scorponok To the transform element Stinger warrior So you can see where kingdom goes for the more realistic approach Where the transform element stinger warrior has that more cartoon look So there you go guys transformers war for cybertron kingdom scorponok in beast mode And now for some quick size comparisons here is transformers war for cybertron kingdom scorponok With kingdom beast megatron Kingdom black arachnia Once again with transform element stinger warrior And earth rise titan class scorponok Transformers war for cybertron kingdom scorponok Is all right. He's just not at all what I was expecting to be honest I haven't really been impressed with this third wave of the kingdom line I got ryan ox wasn't really impressed with him and now Scorponok here has left me wanting. I was just really expecting a lot more Especially after wave one and two just totally knocked it out of the park Now I do find his transformation pretty ingenious But there's just a lot of sculpting issues and design flaws that I think hasbro really should have passed on Though I do like his beast mode. I like the realistic scorpion Opposed to the cartoon version Of the stinger warrior. So there you go guys transformers war for cybertron kingdom scorponok So does a transformers war for cybertron kingdom scorponok belong in your collection? Well, this one was a little underwhelming for me for one I wish he was a little bit bigger two I find that they really had some odd design choices with him I mean, I'm not a big fan of the dad bod that he has and these claws just suck I don't understand why they went for this look Now it does look bad in robot mode, but scorpion mode actually looks pretty good I like the realistic approach to his beast mode But all in all I just think this guy could have been a lot better And he's more recommended for those of you who want to complete your line of kingdom figures So you have your predacon lineup, but if you want something a little bit more show accurate for us adult collectors I would go with the stinger warrior But this guy he's good Not great. So maybe wait for him on clearance Now guys, if you enjoyed the video, don't forget to like don't forget to subscribe and don't forget to click that bell icon To get notified when I upload new reviews Also, if you're in any position to help out the channel, I have channel memberships here on youtube and I also have a patreon page I also want to give a huge shout out to my newest channel member Benjamin G. Whitcomb Benjamin, thank you so much for your support. Once again guys. This is patriot prime signing out


Hello there. This is the family doctor. Just got to pick up my medicine bag. Oh there, Judge Windsor. So you're driving home, thought I'd just go out of my way a couple of blocks to see you for a minute. Well, that's mighty nice of you, Sam. Yes, you see, Doc, you're about five days behind on this month's payment on your note. What? Well, gosh to Friday. I'd plum forgot all about it. Say, thanks, Sam. I'll be right down in the morning. All right, Doc. Didn't want to have to foreclose on you. Junior, why don't you speak to Dr. Adams? Now that's no way to greet an old friend like Dr. Adams. Say, how do you do, Dr. Adams? How to do, Dr. Adams. Hello, Junior. Now what you got there? Looks as though you were mighty interested in that book you've got. The book on chemistry. Got it from the library. Oh, well. You going in for science now, Junior? Yep. Yes, sir. Glad to see him keep his mind busy with something. Anything to keep him out of mischief. And this seems to be it. He's rigging up a shop out in the old stables. Oh, hello, honey. I've seen you once before. Now, dinner's getting cold. Good evening, John. Good evening, Mrs. Adams. Well, our dinner will probably be waiting for us, too. Good night, Doc. See you in the morning. Say good night to Dr. Adams Junior. Good night, Junior. Good night, Dr. Adams. Good night. Good night. Easy. Have I got everything out of the car? Grand! Huh? Oh, yes, honey. Coming right away. Right away. Be there in just a minute. Now, honey, you see? What? What do I see? The dinner didn't get cold. No, of course it didn't get cold. Why? Because I kept it in the oven so it would keep nice and warm. That's why it didn't get cold. If I told you it is in the oven, keeping warm, I'd like to have never got you in the house. So I told you it was getting cold. And the prospect of a cold dinner certainly isn't very appetizing to any man.  You never realize that a woman likes to serve a meal when it's ready. Yes, I do.  Oh, now, Lou, Costa Friday. Well, that's right. You know it is. Well, tonight's post bugle is in on the sofa. Go on in and leave it. I'll let you know when I'm ready to have you drive the dish. All right, honey. Oh, the post bugle. Never any news in the sheet. I don't know why I keep on taking it. Grant? Yes? Don't you hear that? Hear what, Lou? What do you mean? Well, that's tiring. There's a fire somewhere in town. Hmm? Wait. Yeah, you're right. There is a fire. Well, I'll call up and find out where it is. No, Lou. I'm the member of the Cedars and Volunteer Fire Department. Not you. I'll call up. Well, all right, Grant. Go ahead. Hello? Oh, Mabel. Where's the... Oh, over... Yes, I see. Well, I... Yeah, yeah, all right. All right, Mabel. Yeah. No, no, I haven't. Grant, Adam, where's the fire? Be quiet, Lou. What's that, Mabel? Oh, all right. Yeah, thanks. Yeah. All right. Yeah, goodbye, Mabel. Where is the fire? Oh, over at the Windsor's. It's just a barn or one of the outbuildings, though. Not the house. Well, I guess I'd better get on over there anyway, because it's... Get on over there? Well, I should say you will. You hop right in that car and drive as fast as you can. Sam, how did this happen? Gosh, I don't have any idea, Doc. Isn't this terrible? It cost me a pretty penny to replace that stable. Replace it? Why, you haven't any use for a stable now, Sam? Yes, I have. I have two fine horses coming from the east next week. Three-year-olds. Going to train them for racing. Well, maybe the boys will be able to save enough of it so that you can rebuild. Oh, I don't know, Doc. It's going pretty fast. The wind's in the wrong direction, too. Half the force is playing a stream on the house. So that won't catch fire, too. Sam? Where are you? Sam? Yes, I'm there. Oh, good evening, Mrs. Wynn. Good evening, Dr. Adams. Sam, I can't find Junior. What? Why, he was at the dinner table when Abraham came and told us about the fire. I know it, but he just isn't anywhere in the house now. I've called upstairs and down. He just doesn't answer me. Sam, do you suppose that he... That he's in the barn? Nonsense. He's got more sense than that. He wouldn't deliver it. Listen. Oh, it's Junior! Junior! Junior! Junior, where are you? Junior, near. Hello, Sam, he's at the table. Hey, Doc. Where are you going? Doc, don't go in that stable. You'll be killed. Dr. Adams. Has Dr. Adams gone into that? Yes, he's gone in that inferno. Where is Faith, Edna? She's down at the church at the young people's club dinner. Thank heaven she isn't here. How does that happen, Judge Wynn? Oh, hello, Bill. Edna, you know Chief of Police, Benson, of course? Yes, how do you do, Mr. Benson? get to the bottom of this what happened was a lot of no no of course not you know I don't know how it happened and I'm going to find out right now and that's what I think it is but what do you mean and I ain't saying much right now judge but I've been watching some mighty suspicious looking characters that have been hanging around to buy you theater of late and I don't like to look up no hush up feel right but they're nothing but actors actors what do you mean I mean Abe Myers is putting on a special show next week and those people are just actors he's had she well you can't be too cautious as a fellow says no I wish the doctor would come out of there doctor Adam where is he he went into the stable what yes we thought we heard Julia calling for help and Dr. Adams apparently thought he was in there so he went in after the boy oh I wish that my boy he's gone just wait maybe come out of the house we can't win him or out here come along he judge look what in the look is Dr. Adams in the hands of you with him thank you doctor we thought you were kidding you're safe oh darling my boy I'll come to mother oh I'm all right why you're soaking wet your clothes are stopping and shows Dr. Adams where you been doc well what happened to let's have the details oh well junior and I went swimming swimming we thought it was a good idea at the time didn't we junior yeah I'm gonna tell him Dr. Adams tell him tell him what when Dr. Adams found me I was out my laboratory and well my clothes were on fire and Dr. Adams he grabbed me up in the sister oh Dr. now now junior I thought we decided you know what's in my heart right now we can never thank you oh well I I brought Sam junior into this world guess I couldn't let him leave it so soon come into the house Dr. Adams we'll get you something dry to put on oh no thanks I'm all right I'll just drive home well I guess there's nothing more I can do here a good night all the night Dr. Adams and well thanks good night Dr. Adams there goes a real man Grant Adams indeed oh he's a hero that's what he is a hero yeah be sure it well I got to get started on my investigation gotta find out how this fire started why can't tell you how it started well I was working with my chemistry that's all chemistry young man you come into the house with me this instant well I guess I cleared up that mystery quick enough they're without my hearing why I didn't hear you come in Grant no came in the back way putting the car in the garage why you changed your clothes oh oh yes yes the others sort of smelled of smoke see well tell me about the fire fire oh it wasn't much the winds are stable burned down oh the judge is going to rebuild it right away soon though he's got a couple of horses coming from the east hmm well I guess I'll read the post bugle here it is Grant I was reading it there isn't a thing in it though hmm just seems like nothing exciting ever happens in Cedarton doesn't it hmm oh yes honey yes it does I like it though I like it nice and peaceful don't you yeah I would you would I mean yes Lou nice and peaceful yes that's it Cedarton's a great town all right nice and peaceful family doctor I'll be in to see you again right soon oh bye


Top Spanish-speaking country for teaching English abroad, Spain. Even though the economy in Spain has been a little rocky recently, it is still an attractive destination for many people wanting to teach English in a Spanish-speaking country. Spain is actually one of the most popular places for English teachers in Europe, as it has so much to offer, including a long and interesting history, a vibrant culture, delicious food, and a variety of landscapes. The big cities like Madrid, Barcelona, and Seville, offer the most opportunities for qualified teachers. A TEFL certificate is almost always required and also gets you a higher salary. While European citizens will not need a work visa to work in Spain, teachers from outside the Europe often work on a tourist visa, which is technically not legal but still very common. Alternatively you can easily obtain a student visa if you enroll in a Spanish-language course. This visa allows you to work 20 teaching hours per week. American and Canadian teachers can also apply for the Cultural Ambassadors Program, where 2,500 North Americans every year are placed into elementary or secondary schools across the country to work as assistant-language teachers. Thanks so much for watching. We are ITTT, the leading provider for TEFL and TESOL training courses. If you like this video, please subscribe by clicking the button down here and click on any of the videos here on the left for more interesting teaching tips for getting certified to teach English abroad and online.


Everybody for a syrup in 2022. I'm at football hobby six box full case number three pick your team style Andrew a Vikings Andrew C has the Bears Anthony s Broncos Armando chargers Brett T Saints Brian s Falcons Brian P Seahawks Carla with the Jets Charles K Washington Chiharu Rams Daniel K Colts Ed D Bucks Edward P Cowboys and Ravens goo H with the Jags Hilton T Packers Joel B with the Dolphins Jonathan B. Bills Jordan H chiefs Casper P Giants Costa with the Texans Matt M. Lyons Matthias with the Browns Michelle K Raiders Nicholas P with the Cardinals Nixie Bengels Oren W Steelers Sean M. Niners Titans Thanks for grabbing the last team there Sean Steven H Eagles Taylor with the Panthers and Zach has the pads. Good luck everybody. Oh good orange line. Yeah, I've had dude. I've only I've only been a boss in a handful of times I've had some interesting experience on the orange line I can only imagine how it is daily. They've been on the subway. They're just like any other subway but I mean oh no I had the remote so it happens quick too it's like one minute and if you don't look up it's like channel five or something. Here we go y'all best of luck. Yeah, well who's it's been it's been very good today so far first case was crazy second case was very good too. It's been a good day. Shield right here. All right Jake calling a shield. I was wrong. All I all I pulled was a Nike swoosh of Joe Burrow but it wasn't a shield right? It wasn't a shield. All right Tyler Lockett number to 25 for the Seahawks. Clearly immaculate rookie jersey for the Ravens Kyle Hamilton 78 of 99. Seen card type this time for the Jets Sausgarden or 49 of 99. That's actually the first Saus we pulled today. Someone earlier called Saus Shield. Numbers RPA goes to the Chargers Isaiah Spiller 11 of 28. Three colors there. Oh Wahoo that's right it was you. Chargers. Prime patch auto for the Packers is Brett Favre 2 out of 10. Player worn patch on the Favre. Thought it looks a bit different. It looks like scrunched together. And redemption goes to the 49ers. Tyrion Davis Price, iMac signature patches rookie gold to 10. Niners Tyrion Davis Price. This is Hobby. We're still behind a little bit. Hobby Boxer. I don't even know if we have any photo. My knowledge we didn't get any but maybe we just haven't gotten it yet. Cardinals based parallel Hollywood Brown 28 of 99. Three color patch card Dolphins Mike Gisicki numbered 58 of 99. The standard jersey card 13 of 49. Jonathan Taylor Colts. Let's take a look at the next one. Dude. What's up smack? That might dude. Vaughn's gonna get jealous of this one. I know a few Jaguars fans are gonna get jealous of this next one if it's not theirs. Jaguars so goo has a Jaguars. One of 10 logo patch Trevor Lawrence. Jaguar logo patch Trevor Lawrence one of 10. What a card man. What a gray looking card. Nope. That was a one time thing. Also isn't the eye. No eye. That's disgusting. That's disgusting. This is cool too. Steelers on the three color patch Otto Heinz Ward 8 of 49. On card Ward too. Player worn patch and prime patch rookie Otto Johan Dotson 45 of 99 commanders. That's a nice Johan three color patch. Now you're one of the crazy people on the orange line Vaughn. Now you're one of those people. People making weird noises on the subway. This stuff is great you guys. I want to grab your spots for later. I want to get your spots for later. Looks like there's still some teams available on cases five and six tonight. There's random teams K7 has 21 to go and some divisions cases as well. I know who's stuff is awesome. Bengels T Higgins number two 99. Four color patch chargers Keenan Allen 81 of 99. Allen could have a ding on the bottom of this one right here. I'm going to send a Boxer wrapper that's not the biggest ding in the world for like a patch card but it is noticeable. It's bugging me so I'll get the next one. I'll put it down at the bottom. Rookie clearly Immaculate Jersey Johan Dotson to 99 commanders. There's always one person Zach. For the most part I mean no one else has said anything negative but yeah the one person that says something negative just kept saying the same thing. It's like okay like you can criticize that's totally fair. Like we don't just have to say oh yes everything is good but like if you're watching the stream like you know gotta have something that isn't criticism right. Immaculate Numbers Auto for the Jets Mark Gaston 91 of 99. Like I'll never ban you guys for saying something critical of something like that's fine. Be fair. Say something good. They're nice cards. Just speed ran about the Jets. He wants another one of those patches. He's Gaston. Jets Eye Black RPA Garrett Wilson 50 of 99. Nice. Congrats Jets. Back to back hits. This one's great. Offensive Rookie of the year. Could be getting a new QP soon. Nice card for you Karla. We'll get that magged. And RPA Sam Howell 64 of 99. True RPA this time. There you go Marks. You're asking. Yeah yeah there was one. There was one in case one but this is a true it was a double. This is a true RPA though so this is a more sought after I would think. Congrats on the Howell. As of right now it seems like I mean I think he should get the chance. Like Heineke's cool and all but I feel like if you're not gonna be like a very like a great quarterback you may as well go to the younger guy and see what you got. We'll see man. Draft's coming up quick too. We've got free agency next week. A lot of trade dominoes is gonna fall. I wonder if it'll be anywhere near as crazy as it has been the past few years. It doesn't seem like it. All the quarterbacks are getting deals already. You know what I mean. Like all the quarterbacks are getting off the market. It's like as Roger will get traded if not basically. Seahawks to 99. DK Metcalf. Three color patch card. Broncos Cortland Sutton 82 of 99. They were saying he's on the trade block too. Interesting piece. Two color patch card. Cowboys Ezekiel Elliott 78 of 99. I feel like if Broncos could be a team that's like quietly very active and like changing their team around because they have new coach. They got a lot of pressure to do well because got the expensive quarterback. Cowboys on the Zeke. Clearly immaculate jersey card. A.J. Brown four of 10. Two color patch for the Eagles. Brady Shield will be cool. No, no Brady Autos in this. Oh that's pretty cool. That's an older design I believe. No, yeah it is. This is from 2021. Patch auto Panthers Christian McCaffrey 29 to 49. Nice. Congrats Panthers. Yeah John. Sneaky Panthers hit here. Are these cards on the checklist? Taylor with the Panthers. Very nice. Let me see. I would think they're on the checklist. It should be right. Yeah but this is a 2021 card so I'm like I wonder if those are on there. He does have 2022 Panthers stuff for sure because a lot of the on-card stuff will be Panthers. A lot of this. I think mostly I think McCaffrey is all Panthers in this actually. Maybe not base but his base is Niners. Everything else is Panthers from McCaffrey. Just FYI guys. And true RPA Bailey Zappi 77 of 99. True RPA QB for the Pats. There you go. Let me double that one just for charters right. It's been awesome smack. It's been great. Every case has had at least a few like really big hits. Rich was saying he's pretty sure it's there's less production on it this year so it seems like the hits are a little more streamlined and there's not as much. How do I say this nicely? Not as much like just like filler autos? Like there's less autos. There's more like RPAs and things like that so that's pretty cool. Bucking Ears Mike Evans 33 of 99. What's the jersey? Is it Wander today? It's Blasnow. Blasnow? Jersey Card Paul Warfield Dolphins 23 of 49. Jake has like the whole roster. Yeah and then guys keep getting cut or treated so I have to buy new ones. Get a FireEisen. He's on the Dover's.  Get a Josh FireEisen. I can't name anyone in the race bullpen. Jason Haddon. He's on the Team USA. Matthew Stafford clearly Immaculate Jersey Card Rams to 49. Dual patch for the Cowboys to Marcus Ware, Micah Parsons to 99. Not more not more junk. I think it's just like we've seen a lot more like RPA stuff in it this year for sure. Like that's the one noticeable thing. I don't know exactly why that is but that's what I'm seeing. For the most part. Ware and Parsons, that's a cool one. Dual patch for Kiyoto Titans. Malik Willis 79 of 99. So Sean, I forget what's Sean, but Sean bought the Titans in the last couple of cases and is hitting very well with them I'd say. Get them Malik Magged and Ravens Inc. Jonathan Ogden to 49. All right last box of Case 3. Case 4 is the last one. Daytime up next. This case has been a little quieter than the others so maybe we got something big coming in this box. Matt Jude on to 99 Patriots. Cowboys Jersey number patch card to 88 CD lamb. Steelers patch card Brett Kiesel with a ball in his hand. Eight to ten. Hey what's up Jeremy? How's it going man? Steelers Brett Kiesel. Got a Shadow Box Sanitures Giants. Tiki Barber one of 99. Tiki. 2021 as well right there. Tiki Barber. It's a clean signature man. That's a good looking card. I Black RPA Ravens Kyle Hamilton 69 of 99. And on the back we put a lot. We've hit one of these guys's autos every single case so far. Prime Patch Rookie Auto 3 of 25. George Pickens. I believe that is a Rookie Premier Jersey right there. That is awesome. Rookie Prime Patch Auto 3 of 25. George Pickens Steelers. Got a Pickens Auto in every single case. Steelers doing well today. Oh yeah we've had some big hits today. We had Palo Auto to 25. You know Nightmove Sohan. The J and Ivy Basketball Parallel. Jobarro Nike Swoosh one of one. Jobarro Auto to 10. Some nice stuff in here too. Let's recap. Relics first we had DeMarcus Ware, Michael Parsons. Ezekiel Elliott, Cortland Sutton, Keenan Allen, Mike Gesicchi. A Sauce Gardener. Kyle Hamilton. Quarter of five tomorrow. Johan Dotson. That's right. You're already here anyway. So just. CD Land. We're leaving a quarter of five. Okay. Taylor. That's right. Warfield. Matthew Stafford. AJ Brown. And Brett Kiesel. What is this?  Sam Gull? Yeah, we split it. That's awesome. Is everybody going? No, it's just me. Davis Price, RPA Gold for the Niners Redemption. Rookie Sanitur Patches Auto Gold. Rookie Sanitur Patches Gold. Not true RPA. Gaston Oates, 99 Jets. Tiki Barber Giants. I've like RPA. Kyle Hamilton. Johan Dotson on the Prime Patch Rookie Auto. Heinz Ward Prime Patch Auto. McCaffrey Prime Patch Auto. Panthers McCaffrey. Jonathan Ogden Ravens. Isaiah Spiller. Numbers RPA to 28 for the Chargers. And Brett Farr Packers to have 10 Patch Auto. Dual Patch Rookie Auto. Titans Malik Willis to 99. RPA 77 to 99. Bailey Zappi Patriots. Sam Howell. RPA Commanders. Garrett Wilson. Rookie Eye Black Auto to 99. Jets. Prime Patch Auto Rookie. George Pickens Steelers to 25. And Trevor Lawrence, 1 of 10. Logo Patch. That'll do it. One more Case Day time.