Welcome back everyone, and it's really a great pleasure to introduce the second speaker of today, Anieska Zelović, who will talk about inducing schemes and a role in thermodynamics. Thank you Anieska. Thank you to the organizers for the invitation. So I would like to talk about my joint work with Farouk Shahidi. Our results are not that new, I think the paper was published in 2019, so it's not the newest result, but I thought it was very appropriate for the conference, and maybe it's good to advertise our work because I didn't give that many talks about what we did. So our paper is partially a survey, so the idea was to put together all the known results that involve inducing schemes and towers, specifically in particular to study thermodynamic formalism. So this was our emphasis on studying thermodynamic formalism and equilibrium measures, but we go a little bit beyond that. So the idea was to put together all the known results and point out the relations in the intermediate systems that are used in the techniques of inducing towers, and also fill in the gaps. So find out what is not known and see if we can say something, like fill in some of the gaps. So this should be a rather easy talk to follow because a lot of it will repeat from what already appeared in other talks and also during the mini courses. So we start a little bit more abstractly. So we just start from a continuous map on a compact metric space. So we'll try to do the setup at least at first a little bit general, so not even the thermomorphism, no smooth structure for now, just a continuous map. And then we imagine that we have some inducing scheme on that map. So what is the inducing scheme? So we call it inducing scheme of hyperbolic type. I think this was introduced, at least we use the setting that was introduced by Pesin, Sentie and Zhang in their paper. So we imagine that we have some inducing domain, which is actually there, which is made out of a countable collection of this joint borrower sets J, right? So we take the inducing domain, which is also will be referred to as the base of the tower. This is still there is a countable union of this joint borrower sets, and then for each of those sets, we have inducing time. So we require that for every set J in this inducing domain, the appropriate image corresponding to this inducing time will return back to the base. So this is this condition I1, and then if I take all the appropriate images of all the sets in this union, then they will cover the whole inducing domain. So this is the first condition. And then the second one is that, okay, so then we can, once we have something like that, we can consider the induced map, which is F tilde, which is defined on the inducing domain, so only on the base. And the second condition that we want is we want this inducing map to be conjugate to a full shift in a countable set of states. However, we can weaken this condition a little bit so we don't need to require that it's conjugated to the full shift, but we require that there is some set, some shift invariant subset of the full shift on which we have this conjugation. And then I'm not stating it now, but later I will assume that this set is in a sense big, that the complement, I think I later I will assume that the complement of this set doesn't see any nice measures. But for now, let's just say that there is some subset of the full shift on which the induced map is conjugated to a shift, okay? So we have the important thing is that we have symbolic representation on the base of the tower, on the base of the tower, right? And then it will be also useful for us to study the tower map which is defined like this. So the tower map, what it is, it's a simplified abstract model of our original map. So the tower map is trying to mimic our original map, but it is a little bit more abstract and a little bit simpler in a way, right? So now what we are going to do, we are going to take our inducing domain and above every set J, we are going to stack a column, a corresponding column which is made out of copies of J and how many copies we put, exactly tower of J, right? So the tower of J is the return time. So above each J, we are going to put tower of J copies of itself and this will be our tower and then the corresponding tower map which I will denote by f hat is given by just going up by one, right? So from point X which was in J to a copy of X in the J, in the copy of J which is above, right? So in the tower, I will just keep going up until I reach the end of the column and then I go by, I do what the induced map tells me, right? So then I go f tilde of X and so I'm back in the base of the tower, right? So the tower map is like an abstract model for the original map, but it will be later useful to study the original map, okay? So we have really three dynamic systems here and so our goal was to study the relations between the three of them, all right? So okay, an example of course, this is a workshop on Young's Diffo-omorphisms. So it should immediately look similar that this abstract setup resembles a Young's Diffo-morphism. Yes, the Young's Diffo-morphism is definitely an example of what I just described. And so if we have a Young tower, then the base of the tower would be this countable horseshoe, right? So our sets J would be nice rectangles whose boundaries would be stable and unstable manifolds, right? So this is, and then we would have symbolic representation of course, because the base of the tower is a countable horseshoe, right? So this, we have this Markov property for the, for the Young, for the Young Diffo-morphisms and this property ensures that the base has symbolic representation. Okay, so that was an example, but our setting in principle is more general because we don't a priori need a smooth structure, okay? So now what I want to say is, okay, so now we want to study invariant measures and the relations between invariant measures for the three systems. So let's say that as a starting point, we have a measure which was invariant under the induced map. So here I will follow the convention that whenever I talk about the induced map, so the map which is on the base of the tower, I'm going to use notation with the, with the wave, right? So if I have mu with the wave, it means that it's a measure which is invariant under the induced map and if I have a hat, then it means that I'm talking about the tower and if I have nothing, then it means I'm talking about the original map. Okay, so let's say that we have a measure which is invariant under the induced map and then I integrate the return time with respect to this measure and it is important for our analysis that this integral is finite. Okay, so one thing that I should point out is that the induced time, we do not require that it, we do not require that the induced time is the first return time. This is kind of important generalization that it doesn't have to be the first return time, which makes the analysis a little bit more complicated. On the other hand, the way we defined the tower map, for the tower map, the induced map, the induced time is the first return time. So that may be a little bit helpful later. Okay, so anyway, so yeah, so we do, because we do not require that the first, that the return time is the first return time, we don't, apriori know that the induced time is integrable. So we have to assume that, okay, so we assume that the integral of the return time is finite and if we have that, then we can lift the measure from the base to the original space using this formula and we can do the same on the tower, on the tower, okay, so maybe the formula itself is a little bit more complicated, but it's very easy to see what we would, what would happen on the tower, how we would extend the measure from the induced base to the tower. We would just, because the tower is made out of copies of subsets of the base, right, so we would just move the measure, right, so we would take the measure restricted on J and put it in the copy of J, right, so we know exactly what the measure looks like on the tower, how we can lift it to the tower and then you would, you could see that you would get exactly the same formula if you tried to write it down, okay, so we can, we have this. Now the relation which is very easy to see is that if the measure that we started with the measure defined on the base was ergodic with respect to the induced map, then the lifted measures are also going to be ergodic. Of course they will be invariant for the corresponding maps and they will be also ergodic, but this is very easy to see. There is a little bit, there is a little bit of risk that our mechanism will not see all the measures, because for example on X, not all the measures which are invariant under our original map can be obtained as a measure lifted from the base, in particular because, okay, but here this relation which, so we will only restrict our attention to measures which can be obtained by this procedure, so we will only consider the class of lifted measures and those are all the measures which were lifted from the base and what this class is for the original map, maybe it's not so clear in particular if the return time is not the first return time, however, for the, if I look on the tower map, because on the tower map the return time is the first return time, then we can see that all the measures on the tower which were lifted from the base, those are all the measures for which the base of the tower has positive measure, so all the measures invariant under the tower map which give positive measure to the base, all of them can be lifted from the base and this is because on the tower the induced time is the first return time, okay, and then there is a relation, the tower map and the original map, though they can be related through the base, right, so if we have two measures which were both lifted from the base, we can relate them by, so if I take, if I have a measure for the original map which was lifted from the base, I can project it back to the base and then lift it in the tower, right, so that's how I can relate the measures on the original map and on the tower through this projections and lifting again, so I will actually call them, say that, that mu is a projection of some mu hat, if I can obtain mu hat by doing this, projecting and lifting again to the tower, okay, all right, okay, so yeah, so okay, so natural question to ask is since we have a way of obtaining measures, invariant measures for the original map and for the tower from measures on the, on the base, the natural question to ask is what kind of properties will also transfer from the, from the base to the tower and to original map and also since we can relate the measures, the measure, the original map and the tower map, they seem to be very closely related, what are, what are the relations, what are the properties of the measures on the tower and on the original map, so like this is exactly the kind of questions that I will be asking and we will see that beyond just ergodicity, so we can clearly see if we have, if we started with an invariant ergodic measure, we will obtain an invariant ergodic measure if we, after lifting it, but if you ask about any other properties, since turns out it's very difficult, so let me start with the first thing, which is the Bernoulli property, so we imagine that what we have, okay, so we start with the measure which was on the base and then we lifted, then we lifted to the tower and to our original space and now we are going to ask about the Bernoulli property, so the first thing is I'm going to ask if I can prove Bernoulli property for the tower map, does it imply Bernoulli property for the original map and this is one of the positive results that we obtain and I even included the proof because the proof is very easy, so here we can see the way that we define the tower map as I said, oh I froze, did I freeze? No, we can hear you, it's fine. Okay, I see my face is frozen, alright, okay so, so as I said the tower map is supposed to serve as an abstract model of the original map, in fact what we can show is that our original map is isometric to a factor of the tower map and why is it so metrically isometric, so why is it not actually isometric or isomorphic, sorry isomorphic, why is it not actually isomorphic to the tower map and the reason is because on the tower map we have the first return time which is the first, the induced time is the first return time but it's not necessarily a case for the original map, so what can happen is that when we take the tower and we stack copies of elements of the tower one above the other, we always obtain disjoint images this way but in actuality for the original map if we take, if I keep iterating sets j under my original map the images may not be disjoint, right, because the induced time is not necessarily the first return time, okay, so the original map and the tower are not necessarily isomorphic but if I account for this relation, right, so I can introduce, I can, I can introduce this relation that will say that two pairs on the tower xk and yl I identify them if they are actually, if you have this relation that fk of x is the same as fl of y on my space x, right, so if I do this identification then I definitely have isomorphism between the tower and the map after doing this identification, right, so, so then if the tower map was Bernoulli then the original space as a factor of it must also be Bernoulli, because every factor of Bernoulli is Bernoulli, can you hear me because something strange is going on, I think? On this side it seems everything fine, actually, although we cannot see you, okay, let me see if maybe I can, but we can hear you fine actually and we can see the slides, yeah, that's fine, I think I came back, all right, okay, so this was Bernoulli property but now also from this you see that it's not so clear if we can have the implication the other way around, right, because the original map is a factor of the tower, so that's why if the tower is Bernoulli then original map is Bernoulli, this doesn't necessarily seem to happen the other way around, right, okay, but this was very simple but now what we are really interested in is let's say that we have a measure which was Bernoulli on the base and now can we say that this is Bernoulli on the tower, because this is really the direction that we are interested in when we use the methods of inducing, right, we would be able to show that, yes, that the measure that on the inducing domain is Bernoulli and can we say that it's Bernoulli when we lift it and this is much more complicated and in general it is probably not necessarily true but we can prove that it's true if we have those two conditions B1 and B2 for the measure on the base and those conditions they look very strong and they're probably in general very hard to check but there are some situations in which I can imagine that they could be verified, so the condition B1 it should be rather easy, it just means that the measure on the base had a product structure and that should follow from product structure but condition B2 is much more restrictive but how can it be used? Well the only advantage of this condition is that I don't have to, I can stick to just analyzing the measure which was on the base, right, so if I am able to prove that the measure on the base is Bernoulli with respect to the induced map in order to show something like this I would probably have to show condition B2 with replacing F hat with F tilde, right, so if I had induced map so in order to show that the partition by cylinders is weak Bernoulli and so in order to show that the induced map is Bernoulli I would probably need a condition like this if I replaced F hat with F tilde, right, so if I am able to show that the induced map is Bernoulli most likely I am able to show this condition for the induced map and so our result says that if I can replace here the induced map with the tower map but still only analyze with respect to the induced measure then the tower map is Bernoulli, okay and I will show later when I will move to more concrete classes of measures how this can be verified, okay but in general we would have to check something like this, okay, all right, now another question that one could ask is what are the relations between mixing rates and maybe central limit theorem is it true if induced map satisfies central limit theorem is it true for the for the lifted measures as well and those aren't our results, I mean this proposition follows easily if we just put together results of Young and so this is one paper which was done for I think expanding maps and then there is another paper by Melbourne Therese that extended to hyperbolic maps so if we put together those results those two papers we obtain a result like this about decay of correlations so of course you always expect when once you know mixing rates for the induced map in order to say something about the the tower map you have to know something about the decay rate of the tail of the rate so you have to study tail of the measure with respect to the induced time and that's really the only way that you can claim something for the tower but this is itself not enough we also need to know something about the measure the measure has to have some nice properties too so the result that is known is that if we have a measure which has this nice property which is like the push forward Jacobian is held there continues pretty much this is what it says so we have this condition for the measure where the g of mu tilde it's just the push forward Jacobian of the measure so if a measure has this form then we have the following so for the tower map we have that if the induced measure had exponential has exponential tail then then the tower map has exponential decay of correlations right and the same with polynomial yeah okay and yeah and about the central limit theorem we can claim central limit theorem for the for the tower map for observables that have certain form that they don't go too far into too high into the tower so if they are supported kind of in this lower portion of the tower this finite portion of the tower then we can also show central limit theorem all right so this was for the tower map and then in order to claim the same for the original map we need a little bit more we need those two conditions f1 and f2 that pretty much f1 pretty much tells us that we have contraction and expansion respectively so here you would expect some kind of hyperbolic structure on the on the base of the tower so for example for young's the film morphine this will be satisfied and then there is another regularity condition f2 and so if we have those two conditions then we have the same result for the for the original map okay all right so this is as much as we can tell in general in order to verify those conditions and actually say something about particular measure we need to know something about the measure and then there is a big class of measures for which those results can be established and so now I will restrict my attention to just equilibrium measures and study equilibrium measures okay but for this we also need additional conditions so those conditions that we borrowed from the paper by passing sentience yang so passing sentience yang they wrote a paper in which they use those inducing schemes of hyperbolic type to establish existence of equilibrium measures for certain maps and so we are exactly going to use this and then establish some more properties so what we need is so I mentioned that at the beginning of my talk that we need on the base of the tower we want the base of the tower to be pretty much conjugated to the full shift right so I said that we assume that there is some set a which is a shift invariant subset of the full shift on which we have the conjugation and so now we add this condition that the set that the complement of this set supports no invariant measure which gives positive weight to any open set so basically the idea is that because we are aiming at we and our goal is now to find Gibbs measures for the induced map and so the idea is that no Gibbs measure can be supported on the complement of this good set a okay so this is the first condition and then we also need an existence of at least one periodic point in our inducing domain and the last one is arithmetic condition that says that gcd of the inducing times is equal to one and that will give us later that the tower is will be a topologically mixing mark of shift okay all right and so now we want to study equilibrium measures uh again for the three uh for the three maps so we start with the some potential which is defined on the original space and then we define two corresponding potentials one on the tower and one on the inducing domain right so on the on the base we uh we induce right so we sum up along the columns of the tower pretty much um okay and then we study equilibrium measures but we restrict our attention to only measures which can be lifted right so by equilibrium measure in this setting I will mean the measure that maximizes the sum of entropy and the integral in the space of all lifted measures right so this doesn't necessarily immediately give us equilibrium measure but in many cases we can show that those lifted pressures defined in this way they are actually the same as topological pressures okay so we have this and then on the inducing domain we actually have this will be the same as the Gurevich pressure later okay so this is it you should speed up okay and then we have collection of conditions for the potential and again this is just the list of conditions that guarantees that so this is going to guarantee two things it's going to guarantee that on the base of the tower where we have symbolic representation if we study thermodynamic formalism for the induced potential we can apply all the results of that were established by Sarig so we will have unique equilibrium measures and they will have really nice properties but also those conditions guarantee that we can lift those equilibrium measures to obtain equilibrium measures for the on the tower okay so those are conditions and then here is the first result which it's not ours so so the result is for the induced map so under those conditions on the induced map we can apply results of Sarig to obtain that there exists a unique equilibrium measure and in fact it's a Gibbs measure for the induced potential okay on the base and then since it's a Gibbs measure it's a well-known result classical result that this measure is going to have exponential decay of correlations and satisfied central limit theorem and also another result by Sarig is that this map has Bernoulli property so this map that this measure has Bernoulli property so we have all the nice properties on the base okay now in order to lift them to the tower well here's what happens yes we can lift them to the tower so if we lift the measure under those conditions we we obtain ergodic equilibrium measure for the potential on the tower and this is a yeah and now about the other properties we we have that if this lift that measure is mixing then it is Bernoulli so this is the result we would have to check mixing independently but if we can check that the lift that measure is mixing then it is Bernoulli and then we have decay of correlations but only but only under depending on the on the tail right so if the tail of the lift that measure decays exponentially then we have exponential decay of correlations if it decays polynomial then we have polynomial of correlations and we have the central limit theorem but with this if we restrict our attention to observables that only remain in this finite part of the tower so we have this and then for the original map so the existence of a of an equilibrium measure this was the main result in the paper by passing sentient shang and then we added to it several things so so we added the relation that that the measure on the on the original map is can be obtained as by using this relation between the map and the tower right so all the three measures they are related in this nice way and and then we also have the same that if if the measure is mixing then it is Bernoulli and under those conditions f1 and nf2 that I introduced earlier we have the same results about decay of correlations and central limit theorem okay and I wanted to talk a little bit more about how we obtained Bernoulli property because this was really our main contribution here so in order to obtain Bernoulli property we we actually prove a more general result in symbolic setting and then extend it so we use so on the tower we can we can have a symbolic representation so we we define the following mark of partition of the tower which says let me see if I can maybe what happened oh no I messed up everything's fine we can see you and here okay no I exited the full screen oh yeah now it should be better no I just wanted to be able to mark something okay so we have okay so we introduce the mark of partition on the on the tower in the following way we treat the whole we we treat the whole base of the tower as one element of the mark of partition and then other elements of the mark of partitions have this form so for k strictly positive we take each j k right so each copy of each j as a separate element of a of a mark of partition but then the whole base as as just one element of the mark of partition and then we have we obtain a countable mark of shift with the following allowed transitions so from base of the tower I can go to the copy of any j in the first level right so to any j but on the first level and then from from each j k I can go to j k plus one and then from j once I reach the the top of the tower the allowed transition is to go back to the base of the tower right so we have those allowed transitions so now this is a mark of shift okay and it's topologically mixing because we have this condition condition ify all right so now what we are going to do we are going to prove I mean in this talk I'm only going to state but what we prove the following result in the symbolic setting is that so imagine that we have a topologically mixing a countable mark of shift and we we choose one element right so one one letter right one state and then we are going to consider the induced shift on this on this one letter okay and we assume that we have a potential which is only defined on this on this one cylinder okay and we assume that this potential is locally held there with respect to the induced shift uh huh right so we have a potential which yeah so we assume that we have a potential which is induced which is induced on this one element and it's locally held there with respect to the induced shift and has finite garbage pressure and so then we have unique ergodic equilibrium measure for this potential and we can lift this measure to the full to the to the mark of shift that the countable mark of shift that we started with uh and then we have the following if we can prove uh that this lifted measure is mixing then it is burning okay so this extends the result of sarik so so if I assumed um that the original potential on the on the original countable mark of shift was locally held there continues that um it is a result of sarik that that the equilibrium measure is uh Bernoulli however so we extend it and we only uh so when we are on topological mark uh mixing mark of shift we now induce uh on one element and then we assume that the induced potential is locally held there and we can still approve that the lifted measure uh so I I do all the analysis for the induced shift and then I lift this measure and it is still going to be Bernoulli the lifted measure okay so this is uh this is what we prove which I thought maybe was interesting to see um and what else oh okay we also talk about phase transitions um so so so so now it's separate because we no longer talk about measures but since we we are talking about equilibrium measures it also makes sense to talk about pressure itself um so now we are going to study uh regularity of the pressure so we assume bunch of conditions on the potentials now we have two potentials uh and we require that they satisfy various conditions and then under those conditions uh we can show that the pressure on the tower uh which is the same as the pressure for the original map uh is a real analytic and so again um the fact that the pressure for the induced potential is is really analytic it follows from the results of Sarik and we extend it to uh to the tower and the original map um and do I explain how I do it I don't think it's oh no now I just apply to okay um okay so maybe it's worth mentioning how we can extend results about the analyticity of the pressure from the induced domain to the tower um we do a nice trick so um right so so Sarik proves analyticity of the pressure on the countable mark of shifts under certain conditions he proves that the Ruel operator has a spectral gap and it has all those nice properties and what we do is we obtain the pressure on the tower implicitly as the as the zero of a certain potential so we would have potential so we have an induced potential minus omega so the pressure is zero right and the and the omega will be pressure on the lifted our lifted pressure so we obtain our pressure on the tower implicitly as a zero of a certain equation which was set up for the pressure of the induced potential and then uh we obtain analyticity of our pressure using the implicit function theorem so we use this uh kind of this using the simple trick we can uh we can obtain that which by the way reminds me of how we actually prove those properties to obtain earlier the Bernoulli measure the Bernoulli property for the equilibrium measure we also use operator for the for the for the for the induced measure uh and verify this condition which I stated earlier okay um all right so now just uh applications of like maybe some I thought maybe would be good to actually give some concrete example of when our all results play out uh so let's go back to uh Young's defilomorphisms so now we have nice hyperbolic structure nice smooth structure defilomorphism and nice hyper with some hyperbolicity uh but so I I'm listing all the conditions here that I'm assuming and so some of them are standard conditions which are just part of the definition of a young defilomorphism but I also added the conditions that we need for for our results to play out so uh I think I I don't even remember which are which I think yeah condition y4 it doesn't always appear in the definition of a young defilomorphism but we need it for our results right so that you see this arithmetic condition so this is the first set but like the first two are just standard conditions for the young defilomorphism and then we have more right condition y7 is the standard condition for the for the distortion but it's also usually the most difficult one to verify um okay and we also need I think it's not usually a part of the definition of a young defilomorphism but we have this condition y8 which will help us establish the tail of the um yeah the decay of the of the tail of the measure with respect to the inducing time so we we do need this condition in our setting all right so we have all those conditions and then we consider a potential which is a geometric potential um and then under those conditions um it has been verified by passing sentient rank in their paper that a young defilomorphism admits an inducing scheme that satisfies our our conditions that abstract conditions that I introduced earlier um i2 and i4 which I forgot what they are but condition i3 has to be checked independently condition i3 was to check that um that the complements of of the set where we have conjugation to the full shift doesn't support any nice measures so under this condition we have unique srb and then this condition guarantees that the geometric potential satisfies the conditions that that were needed for the for the existence of equilibrium measures right um okay so what is actually the result so this is so this is just saying that the young defilomorphism satisfies all the conditions uh in that that we listed earlier for our results to hold and so what is the actually the result when we put everything together we have the following if we have a defilomorphism that satisfies all of the conditions that I gave for young defilomorphism um and in addition as satisfies this condition i3 uh then we have uh some interval in t uh so so we have some t0 and we have inter on the interval from t0 to 1 we have a unique equilibrium measure uh for the geometric potential um and uh the pressure is real analytic and then we have exponential decay of correlations and central limit theorem if we in addition verify uh this condition for the for our map and we have that the equilibrium measure has Bernoulli property property okay so we have all this um and I think that was it okay all right so this is all I had to say thank you very much but thank you very much and yes thank you um are there any questions so I have a question that I've always actually been very intrigued by this last condition you mentioned about the cardinality of the sets that I have a certain return time right yes this s and yes this one yes um because so what do you is it is there a way to explain why this comes in or somehow what the role of this condition is because in some sense the cardinality of the partition element is not necessarily an intrinsic it's not necessarily intrinsic part of the tower like because you could well yeah it's not clear to me what that why that condition is used uh yeah I think this condition is supposed to use to verify uh the condition p4 for the potential which was I think yeah the hardest condition to check so let me maybe go back and see what the p4 is yeah so p4 is this condition uh this technical condition which is uh if I remember uh correctly in the language used by Sarik I think it's called um positive records or some more than a strongly positive record the Omri is here so maybe he can have us yeah so this is the condition that is usually the also I think the harder to start the hardest to establish uh that relates to strong positive records yeah so so this this uh bound on the cardinality is just a sufficient condition to prove this is this what I say I say so the might be so so is it do you think um it is possible to relax that condition you know to use different ways to verify this other than having that can you can are there examples where you do not satisfy the bound on the cardinality but you do satisfy this condition any examples like that I mean of course if you could verify this condition uh independently then uh then all the results should follow because I think other conditions can be verified without it but uh verifying this is not easy I mean there is another work I think by Ben Kohl where he does something I don't know which methods he uses but he obtains the whole so we have so we not only have that we need this strange condition to verify p4 but even with this condition we only can obtain that there exists this interval from t0 to 1 right and it's not clear like why this t0 appears if it's uh but like it appears in the estimate that we cannot do it for all the t's like less than 1 but there is this t0 which this is where we run out of good estimates but I think there is a work by Ben Kohl where he also studies geometric potential and he doesn't have this t0 so I think he has results for all the t's but I'm not sure what results about the methods he's using so maybe he found like a better way but yeah the short answer is I don't know okay okay okay thank you are there any other questions for Nieshka okay well then let's thank both of today's speakers on Nieshka and Omri thank you very much and thank you to all the participants for being here today it's very nice to it I recognize the names every day so it is a little bit of feeling of the of a regular conference in some way of seeing the same people every day and so we will be here again as Yuli said same time same place tomorrow for the last day and the last day of talks okay so very best wishes for the rest of the day everyone bye bye everyone thank you


This is stock number 11098A. We are here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used. Light duty truck headquarters. Today we are checking out this super clean 2017 Chevy Silverado 1500 double cab six and a half foot box. This truck has the 5.3 liter V8 motor. It has been fully safety and inspected by our service shop has a fresh oil and filter change. All the fluids have been checked and topped off. And this truck is 100% ready to go. Summit white is the color. We shoot all of our videos in 1080p, 60 frames per second. So if you have HD capabilities on your computer, tablet, or smartphone device, turn them on right now because it is definitely your best way to check out the quality and condition of the vehicle before seeing it in person. And if you'd like to check out all the photos on this truck in the upper right-hand part of your screen is a link to our website. Click that and check us out there. This one comes with the 20 inch chrome dalloway rims. Goodyear Wrangler 275 55R 20 tires. And these tires have probably about, I'd say 60 to 70% of the tread left on them. So a good tread left on those tires. And the front fender is in absolutely perfect condition. This one does have the HID headlamps, LED running lights, and LED fog lamps. The front bumper is in really nice shape. No major dents or dings on that. Headlight lenses are nice and clear and we'll turn those lights on at the end of the video so you can see just how bright those HIDs are. The hood is in excellent shape. I didn't see any dents or dings on that and it does come with that chrome trim, the grill on there. Passenger side front fender, very clean as well. And the passenger side rim, no scuffs or scrapes. As you go down this side of the vehicle, take note of how clean the body is, how reflective and mirror-like that paint is. We take these HD videos, so if you are far away or even if you're close by, you just cannot make the trip down but you're still interested in purchasing the vehicle. You can see the truck, hear the truck, and have confidence in what you're looking at before you even get here. So when you do get here, there's absolutely no surprises and that is why we offer the Summit Auto FastPass option in the upper right-hand part of your screen. I link right to our website where you can apply for financing, get pre-approved, see a payment quote, even appraise the trade, all from the company or your own home. So when you get here, all you gotta do is drive the truck, love it, you can be all set to go.  Has nice factory chrome step bars, bed rail covers and as we come around to the back of the vehicle, the rear bumper is absolutely perfect, no dents or dings on that. Those have the rear bumper steps and the tailgate is very clean as well at Insini Dents or dings on there. Does have a Truxedo soft roll-up tonneau cover at Insini rips or tears on there. Truxedo's usually the best tonneau cover that you can find. Has a bed mat in it and LED bed lighting up there. The bed itself is in really nice condition and the tailgate shuts nice and solidly. Does have that backup camera there and the locking tailgate. As you go down the driver's side just as clean as that passenger's side. Insini Dents or dings in the box and for full disclosure this back rim, nice shape as well. Down the rest of the side of the truck looks really good.   No rips, no tears on the seats. They are in really nice shape. Both of these are power, factory all-weather floor mats, auto headlamps, turned-out four-wheel drive and factory brake controller. Does have the power windows, power locks and power mirrors and it does have the power fold-in mirror option. I always like showing that both sides are working so that you know that everything's working on the truck. Bose sound system as well as we hop inside the vehicle. You can see that this one has 49,563 miles. Instrument cluster is very nice and clean. That leather-wrapped steering wheel is in excellent shape. I didn't see any scuffs or scrapes on that. You get Bluetooth and information center controls on the right, cruise controls on the left. This one does have audio controls on the back. Comes with the six-speed automatic transmission with the optional tap shift. Down here you get your heated seat buttons. This one has AM, FM and Sirius XM radio capabilities. You can get your Sirius XM capabilities there.  You get two USBs, two 12-volt power points and then a 110-volt, 150-volt plug-in. Passengers side, floor mat and seat are in excellent condition as well. No rips or tears on them. And the headliner is in nice shape. Didn't see any rips or tears up there. You do get your homelink buttons for your garage door security systems and lighting systems. On-star and SOS buttons in that rear view mirror. And this is also where your backup camera shows up. Right there. And you can also see there's no check engine lights or warning lights on the instrument cluster other than the seat belt light. We'll start it back up in just a second. We'll check out the back seats and then we'll check out under the hood. Back seats are just as clean as the front seats. No rips or tears back here. You do get the latch child safety system for any child car seats you may need to put back here. Power sliding rear window with the built-in rear defrost. These seats do fold up. It does have all-weather floor mats back here and they are in nice shape. And bottoms of the doors all look really good as well. And we'll start it up and take a quick look under the hood. I would personally like to thank you for checking out the video today and hopefully from this HD video you will have been able to tell just how clean this truck is all the way around inside and out. Under the hood we have the 5.3 liter V8 motor. Engine bay is very clean, runs very smooth. This truck has been fully safety and inspected by our service shop has a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100% ready to go. I would highly recommend it from a quality and condition standpoint. There are those HID headlamps, LED running lights and LED fog lamps. And to see more pictures of this truck or one of our other 450 new and used cars, trucks, SUVs, minivans, wranglers, you name it, we got it, go to our website. Right there, www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summitauto.com. And if you'd like to check out more HD videos you can go to youtube.com slash summit auto. Remember to like, subscribe and share on this video and all the videos that you see there. In fact, any second you'll see a link to subscribe to our YouTube channel on your left, a link to more Chevy half ton truck videos like this one on your right if you have not been to our website. On the bottom link to this vehicle on our website, click those, check us out. And we really look forward to helping with this super clean 2017 Chevy Silverado 1500 double cab short box, LTZ in Summit White. Thanks again for checking out the video.


Hello and welcome to NewsClick. Today we have with us Poranjay Guhatakurtha, eminent journalist and also one of the petitioners in the 2G case in front of the Supreme Court. It has been argued for quite some time that the Finance Ministry was really not involved in fixing the issue of the license fee and it did not give its concurrence to Raja's position that they should be given on a first come first serve basis under 2001 prices. It's been argued that Mr. Chidambaram and Raja had met but no concurrence was really given and no minutes were kept out of this. Though Raja has argued in different places and made statements that Chidambaram was fully involved, he had concurred with the prices, he had concurred with the 2001 prices being accepted and there is really no final difference between Chidambaram and Raja on this. What does the current report indicate? I think we have to take a little more nuanced view of the issue because clearly what has now happened in the 2G scam case is that the spotlight is on Mr. Chidambaram. We have to first look at the circumstances that led to the award of licenses on the 10th of January 2008 and then look at what happened thereafter. Moreover, it's also very important to in this case at least distinguish between the ministry and the minister. In the weeks and the months before the award of the licenses or the letters of intent I should say on the 10th of January 2008, there is evidence that Mr. D. Subarao who was the then finance secretary who is currently the governor of the Reserve Bank of India, Dr. Subarao had written a series of letters to his counterpart in the Department of Telecommunication that is Siddharth Bhikkura before him Mr. Mathur. So, Mr. Subarao was writing to his counterpart in the devotee and what he had clearly indicated that the manner in which each license was sought to be valued because it's not just a piece of paper, it's not just a license because bundled with that license was spectrum electromagnetic spectrum which was very very precious which was very very scarce. To price it at 2001 rates when it was discovered by an auction was in the opinion of Mr. Subarao and the officials of the Ministry of Finance clearly not on. He says that either you have public auction or you have some sort of an indexation of market mechanism to derive its true market value. Now, what happened thereafter was the duty under Mr. Raja overruled every objection of the Ministry of Finance and went ahead and gave its awarded those letters of intent. Now, this is what happened. Now, what happened after that? It now subsequently transpires that there were meetings that took place between Mr. Raja and Mr. Chidambaram in the presence of Mr. Bhikkura who's in jail and Mr. Subarao their secretaries wherein it was mentioned in the minutes the same meeting which was supposed to be not minute but now those minutes indicate that the Finance Minister said in that note that he is not seeking to revisit the situation that prevailed. Even at that stage it was just letters of intent. The government could theoretically have stalled that process but it did not because the Finance Minister chose not to revisit the process. The issue that really comes out is the fact that not only Mr. Chidambaram overruled his secretary which is of course he is well within his powers to do but he also publicly at least his colleagues in parliament said that no notes were kept of the meeting and no formal ministeration did not transpire that is not the case. Now, it transpires that is not the case. There were indeed records of the meeting that took place. It's not that meetings on all meetings are necessarily minuted but in this case this meeting was minuted because we also have the Prime Minister's office involved in this and we have Mr. Pulok Chatterjee's meetings also. Yes, you know, what is coming out is something very, very curious. It also explains why the government went out of its way to ensure that the public accounts committee, the first draft report that was prepared by Dr. Munlu Manohar Joshi was not adopted by the committee and by a very thin margin. There were 21 members, 11 members opposed it, 10 members supported it and the same Mr. Munlu Manohar Joshi is now trying to have another report but in that report he was critical of Mr. Chidambaram's role saying that he tacitly approved, he may not have explicitly approved. Now, what happened thereafter? The Prime Minister himself has acknowledged in his media interviews that initially there was divergence of views between the Department of Telecommunications and North Block which is the headquarters of the Ministry of Finance. Thereafter he says there was a concurrence of views. Now, how exactly was there a concurrence of views when the secretaries of the two departments clearly differ and here you have the Minister eventually overruling his secretary. This is one of the interesting sort of sub-theme of this whole thing. In an interview Mr. Chidambaram had said that they were waiting for a meeting of the telecom commission to take place and in that telecom commission meeting his secretary, Mr. Subar Rao would have participated but before that telecom commission meeting took place, the letters of intent were issued on the 10th of January 2008, almost preempting that process. So, once again we are finding a big question mark. Mr. Chidambaram said he didn't know that this would happen. Then after and this is very interesting, the Prime Minister's office says that an arms-length distance should be maintained and we have an interview given by Dr. Montek Singh Aluwali, the Deputy Chairman of the Planning Commission to Mr. Karanth Harper saying that you know when there are two ministries of disagreements, eventually the view of the ministry which has mooted the proposal prevails. Now this is strange logic. All along we have been told that actually the Ministry of Finance is the big boss, the Minister of Finance is the big boss and he can actually overrule and there are hundreds of instances where the Ministry of Finance has overruled proposals of other ministries. Even aside the correct rules of procedure is if the ministers have a disagreement they have to either go to the full cabinet or to an empowered group of ministers. Absolutely correct. And in this case the law ministry headed by Mr. Hans Raj Bharadwaj at that point of time had suggested that since there was a difference of view between the Ministry of Finance and the Department of Telecommunications there should be an empowered group of ministers. The point is it was not only not referred to an EGOM, it was not even taken up by the Cabinet Committee on Economic Affairs and thereafter Dr. Aluvalia in his interview to Karanth Harper said that this must not be construed as the Prime Minister Dr. Manmohan Singh turning a blind eye to what was happening. But if this is not Nelson's eye what is it? But leaving that aside for the time being let's calm down. I mean somebody is being economical with the truth. Absolutely. I mean let's be very clear about that. Let's be very clear that the economist in this case Dr. Bontek Singh and Aluvalia is being economical with the truth. But coming back to the issue which you have raised earlier the issue of mergers and acquisition. This is an issue on which actually finance ministry has even better locus than on the issue of license fee. And obviously again these terms were also modified and agreed to it appears in the same cabinet in the same meeting between Chidambaram and Raja. Basically what Mr. Raja did was that after the letters of intent were issued on the 10th of January 2008 roughly three months later in April that year Mr. Raja issued an order sumoto without taking anybody's consent changing the rules relating to mergers and acquisitions. And one crucial element of the rule was there should be a lock in period of three years before the license fee holder could sell its license. Now once again here again is a very very clever interpretation of the law. One thing is to sell a license and the other is to dilute the equity of the company which has bought the license. In this case what we found is that the unit a company in the unit a group and another company in which was earlier called SWAN and then became DB etysalat these companies what they did was that they roped in foreign partners. In the case of Unitec it was Tele-Nor of Norway in the case of the Balva DB reality group it was etysalat of the United Arab Emirates. What is interesting? I mean subsequently of course there was another similar deal involving the Tata Tele services at Dokomo of Japan but just sticking for that matter to SWAN stroke DB etysalat and also the unit a group what clearly the change in the merger and acquisition rules enables them to do was to rope in the foreign partners and what was very interesting the price at which the foreign partners purchased equity clearly indicated that the value of the spectrum behind that license was 7 to 10 times higher than what had been paid and what is worse is that you're indulging in semantic jugglery by trying to justify what happened by saying this is not sale of a license but dilution of equity you know it's a bit like the way in which even the first come first serve system was manipulated you know whether it should be the date of applying for a letter of intent or whether it should be the date on which you pay the amount of the letter of intent or the license fee it's almost like you shouldn't be selling a resource that belongs to the people of this country a scarce resource a national resource a natural resource in the way in which cinema tickets are sold that's the first point but even if you assume that they are selling it and you are standing in the queue and you're about to reach that box office and you said oh it's now my turn to get the ticket suddenly a bunch of goons from the back pull you back from that queue and said no the guy behind you will get the ticket but that's how the system was grossly abused and there is again proof to some proof to show that people are sitting in Mr. Rajah's anti-chamber and became number one on the in the queue but really now what we are seeing are really what shall I say the more sophisticated nuances being expressed and what is selling what is dilution of equity and also the issue what is an associate what is not an associate company that swan was really a part of ADAG group just as also loop telecom was a part of SR the Rui see once again we are seeing a desperate government trying to use the letter of the law to justify what happened I think what is also a rattle the government is the defense that that Mr. Raja has taken and and Kanimo he has taken I mean their lawyers have clearly said firstly they're saying please bring the Prime Minister summon the Prime Minister that's certainly not a particularly edifying situation to be in what is more their lawyers arguing in court that if what Mr. Kapil Sible the telecom minister is arguing that there was zero loss then why the hell are we in jail if there was no loss to the exchequer why was there any reason to put them behind bars and and the way in which this is all playing out and I think the court will take a very very proactive role one is the CBI in who who is it going to now investigate is it really going to close its investigation that this juncture you know and this whole issue of the associate companies the definition of who is really an associate company I'll give you a classic example on how this whole tiger cheetah leopard zebra was done you know suppose you have three companies a b and c a was 50% of b b owns 50% of c c owns 50% of a so a b and c claim they are independent corporate entities not associates why because neither owns more than 51% of the other and therefore has a controlling interest but you know if you if you see the larger picture mr. Chidambam lawyer we have mr. Kapil Sible lawyer both arguing in different mr. Salman Khurshid lawyer mr. Virappa Moilli law minister okay so you know you have this entire argument that the government is giving which is to defend what has happened that license have been given at very low costs really a true of a prices by companies have made a killing by reselling the license dilution yeah they would call it reselling dilution equity as a colleague and then what is it that they are willing to accept has been the problem for which mr. Raja is in jail that actually procedural lapses took place the poor man is in jail only for having done procedural lapses well all the money that has been made apparently been done all in good faith because there has been zero loss to the next checker this is really the government's argument and the government's argument as you rightly pointed out is sounding so weak so specious so hollow that I do not think that we've heard the last about this 2g spectrum scam and in a way in a strange way it's coming back again and again and again to haunt those who are holding very very important positions the the most important positions in the current government we have a brazen scam followed by brazen defense thank you for enjoying the coming down here


Welcome to Access to Trader, the number one community for those who are committed to taking control of their trading in order to achieve success, profitability, and longevity. Thank you for joining us. Here's Dan Shapiro to help you find your edge, master your process, and own your future. From those days, you didn't have to be that particular. You sat next to someone that knew something. You watched TV. You heard my conference call. You heard Dan talk. He had enough to deal with. We would trade a million, two million shares a day then. Sure. And even with the commissions, what were you paying? Three cents, Dan? The owner. I was paying three cents and I was a poacher. And you still did. I still was. 30,000 a month for commissions. It was a great time. You didn't fight for commissions. It wasn't like you were making one percent a day. Sure. You were making 10% on five stocks a day. 50 in one day we're talking about. Hey guys, good morning everybody and happy Memorial Day weekend. Hope everybody is having a fabulous start to their long Memorial Day weekend. God bless all the people who made this weekend. I guess possible. That's maybe some port sorts of words. We thank you again for all your services. Obviously, we're not here if it wasn't for the people to make the ultimate sacrifices. So God bless you. God bless all your families. Hopefully everybody is doing well. If you are brand new to the channel, please like, share, subscribe. We would love to share our journey, our thoughts on this wonderful journey of longevity through unbiased technical analysis. So let's get into today, right? So for all of you guys who are watching this video for the first time, again, welcome aboard. Thank you for your viewership. I started trading all the way back in 1999 in a place called generic trading. And I was very, very fortunate enough to be sitting near, right next to within five feet away. I could pretty much touch the top of his yarmulke. Myer Offmann, one of the greatest traders of all time. You can Google him, just a phenomenal trader. His partner, Ron Scheer, getting a lot of mentorship back then when I was 24, 25 years old. I'm going to be 49 in about 10 days. And the greatest part about that time was not only the great camaraderie that everybody shared being on the desk, creating bonds, creating less life relationships. It was a great time to grow up in the most incredible, most aggressive era. And at that time, it was the dot-com era. If you guys remember, a lot of people think of the dot-com era as being around for years and years and years. The dot-com era was basically from 1999 to the middle of 2001. That's it. It was about 15, 18 months with very, very huge aggression. But during that time, we saw what we thought was once in a lifetime type of market. Stocks going from $7 to $600, splitting six times within that year and a half. I mean, look at any charts like Amazon, anything during that time. Just split like three, four times within two years. And it was just phenomenal. And we believed at that time that it was us. We were doing something special and I've never hid the fact. I got very, very lucky. Nobody that I knew knew how to trade. You could convince yourself you traded that time. You can convince yourself that you knew what you were doing. You could convince others that how smart you are. But the moral of the story was stocks were on steroids. There was a performance enhancing drug test. Every single company that was trading at that time would get violated. Some sort of penalty against their performance in nature because stocks are just going out of their minds. Generational moves, real generational moves. And if you watch this interview, one of the best things that ever happened to me was being at the right place at the right time. When I was with Generic Trading in 1999, we had the temporary offices in Park Avenue South that we moved downtown to one seaport plaza. Then we finally moved back to Midtown to the Radio City musical building. And we started with 10 people. There was 10 people there. And by the time Generic was sold to, Generic Carlin was sold to the Royal Bank of Canada, 3,000 traders, 2,500, 3,000 traders. So I watched the whole business grow up. And if you remember that time, for all you guys that did trade, anything you bought, the market was forgiving. Absolutely forgiving. You didn't need to have the greatest entry to be right because that's how strong the market is. And if you watch this clip, Kyler is going to post, it's the only video interview that Meyer Hoffman had. We were very, very fortunate. Me and Meyer connected years and years ago once again. And unfortunately, he passed away a few years ago. But we sat down with the guys from this Lucci group, shout out to St. Lucci. And he basically told the story of what happened during that time. The reason why I bring it up, it's very, very similar. Very, very similar to what we've seen in the last two weeks. What we've seen now in the last two weeks is abnormal. Stocks that usually would put in a $2, $3 range on a very specific interval are putting in 5, 10, 15, $20 moves within the course of 12 hours. That's not us. There's nothing that I have done different in the last two weeks that I've done in the last 12 years that I've done in the last 24 years, more or less, that I'm doing something different to making these extraordinary moves in these stocks. It's the stock market, guys. And I see a lot of people pumping out their chest and they're talking like they just invented fire. It's not us. I guarantee it. If you've been trading Tesla, like I've been trading Tesla, especially Gressel in the last eight years, you know that Tesla doesn't put in these great, great moves every single day.   Split is like $240 move in two days. It just doesn't happen. And I think a lot of times going into this weekend, people are making a very, very big mistake without subconsciously even knowing it. They're putting themselves on a pedestal that they think they can't do wrong. Eventually, like all markets, this type of aggressive nature is going to end. I hope not. I hope we still are talking about this on Monday, on Tuesday, next Thursday, next Groundhog's Day. I hope this lasts as long as possible. But I have a history of stock markets just stopping and just going into full contraction mode. I don't care about they go down, but full contraction mode. And what we're seeing now is the ultimate, the absolute ultimate of exaggeration of average to range. It's absolutely phenomenal. I don't think anybody is going to be really upset with what's going on when we're seeing this action. But calm down. Take a breath. It's not us. I give you my word. It's not us. The same channel that you could identify for Tesla two weeks ago was the same channel you could identify Tesla on Friday. Friday's results are probably going to be four times, five times bigger than it were two, three weeks ago because that's the kind of the market is. So this weekend, yes, if you did great over the last couple of weeks, enjoy it. Right. Enjoy it. Feel good about it. Okay. Because what we have as traders, the only thing we have is our confidence in our process. And when they mesh, usually good things are going to happen. So this is a wonderful thing. But just keep in mind, take off the rose colored glasses, you know, remove the blinders and just realize that this is where that right now the byproducts of an extraordinary market. Okay. When it's going to end, again, I hope it doesn't. Right. But I know the truth. Okay. And for a long, long time, we know the ramification of what happens when it stops and when it does, you're not going to be very, very happy. It's like a drug addict. Right. It's like that drug addict, a heroin addict chasing that next high chasing that next high. Let me come back from before. They, they can't find that next high. Right. And then ultimately they start burning and crashing. We don't want that anybody to do that. Okay.  Right. Like might might the constant message I've always talked about was having a game plan, having a game plan on both sides. Don't guess. Don't have an opinion. See which side confirms and usually good things are going to happen. Well, this type of market, great things are happening and it's fantastic. But again, check your ego at the door.  You didn't solve the cure for flying for cancer. Check yourself at the door. Be humble. Stay humble.  When the market gods turn on you, you don't want to be that guy. Okay. Enjoy it while it lasts, but more important guys just take it one day at a time, one trade at a time. So let's talk about the tape. Ridiculous. Right. End of message, end of video.  Everything is ripping. The hardest part going into this week is, you know, not chasing the stocks up, up $27. Right. The hardest part is finding setups and we'll get to some setups that are coming off the bottom.  I know people are holding runners on, you know, different things this week, NVIDIA, Amazon, Tesla, whatever the case may be. The point is again, always remember it will end, right? Just always remember that it will end. And the last thing you want to do is start chasing stocks up three weeks above their pivot points, three weeks above their breakout levels.  So going into this week, again, you know, you want it, hopefully the gravy train keeps on going. Again, it's very, very hard for me to, you know, to talk about, you know, how many more, how many more cryptocurrencies can I use about this market? I can sit there for four hours talking about this. But the point is it's an aggressive market. Let's hope it continues. Any week openings, obviously, we're looking for the strongest stocks to buy on dips than the NVIDIAs of the world, the Teslas of the world. Marvel had an absolutely phenomenal run. Workday had a huge earnings quarter. You have Tesla that's, you know, ready, you know, maybe a day or two away from ready. Again, we just need to get above this whole thing, man. If this market just continues, and we've had some phenomenal pivots on Tesla, but if this market continues, we could just get above this whole channel here. You see this, this whole channel here, a close above 205. I think it might get a little bit of resistance here around 200, 202 area. But man, oh man, if this week, if Tesla could finally be, you know, just completely sprung loose above this 205 close with this type of environment, God knows, man, we could have some epic, epic events in our near future. So hopefully that continues. Other than that, OK, other than that, what's going on, right? So we have the debt ceiling, McCarthy, Biden. I've been saying this now for two weeks. Now that the focus is pretty much off earnings, we're going to debt ceiling talk. Look, I've been hearing about this debt ceiling talk ever since I started trading. The debt ceiling has always been has always been raised. Nobody wants a default. That's number one.  That's what he's going to run on for 2024. I'm the president to let the country default. So a deal is going to get done. The fact that they're talking about, well, you know, there's some sticking points. The deal is going to get done. OK, nobody wants this. Nobody sees it happening, especially it's not good for business. If you are running for reelection next November. So it's not going to be a pretty thing if we do default. And this is going to be the guy who finally makes everything cave in. We'll see, you know, we'll see what happens that other than that. Earnings are pretty much done deal. You know, the moves that we're seeing are just supernova, NVIDIA, just absolutely monster, absolutely monster, maybe one or two more consolidation. I think it started getting above the earnings high this week. You could see a push to four, you know, four 10s, four 20s. They're coming with massive, massive option flow all the way all the way through. Amazon has just been an absolute rock star. Apple is broken out.  Microsoft is just going absolutely insane. Anything with the word AI is going absolutely insane. You could see AI is getting close to its, close to its January, February, April, April 3 highs for a massive breakout there. Even a stock like Oracle. Well, is the last time we talked about Oracle. Look what Oracle did on NVIDIA's AI, right? Everybody's into AI just the same way everybody was into COVID testing. Everybody was into Bitcoin mining. Now everybody's into AI. God bless. Anything to make life easier is a wonderful, wonderful thing. I think the most important part of going into this week is, and I know there's some always data coming out. I think watch the tendency of the stocks the same way that we recognize stocks were getting tired. Remember a couple of days ago last week we were talking about an exhaustion cycle that we potentially had a potential pullback, which we finally did, right? An exhaustion cycle. The biggest clues this week is the leaders. If they start stalling out and we start putting in lower highs in consecutive days, it's not that the stock is going to go down. It just wants to rest a little bit no matter how aggressive or not aggressive it gets pulled. So keep an eye on that as well. We do have data coming out this week. We also have the Fed coming out sooner than later.  But the point is, again, guys, just trust me. I've been there where the euphoria ends and the bubble pops and the champagne has been drunk and there's nothing left, right? And it's a horrible, horrible feeling if you're not prepared for it. So the most important part is put yourself in a situation and just taking it one trade at a time, one day at a time and not long anything that is overextended. One bit piece of news before we go on to some ideas that I like for this week and the pivots from Friday. This three days, the Memorial Day weekend, guys, we are running our special trial. It's only 47 bucks. The whole 30, you could test drive, kick the tires for the PS60 theory and the pivots and all that great stuff that comes with it in the live webinar. And again, I really do think every trader needs to find their sweet spot. It could be the common form of pivots. It could be common form crypto, small caps, make up whatever the case may be. But again, I think you deserve to at least get yourself exposed to everything. And these three days through, I think through Monday, it's a special sale here. So if you are interested, it's only 47 bucks, guys, come check it out, see if it's the right fit for you. I promise it's not a fit for everybody. But if you are a patient trader and you are very attention detail, it could be something really, really cool and you'll really enjoy the ramifications when it gets started. So that's that. So let's talk about some pivots from Friday. Again, as you can imagine, just everything went bananas. Tesla 187 needs to build. Tesla went bananas, right? So it took out the 187, took out the 87 to reclaim the five day. Not only did it reclaim the 187 to five day, it reclaimed last week's highs of 193 and went all the way up to 9860s. Again, I think it needs to clear out. I think it needs to close above 20 for this thing to really get going. I mean, super and over-esque. I think this thing needs to close around 204, 205 to really get this done. Let's see if we can get there. But fantastic move on Friday. Apple again, when nuts 174 needs to build. Funny thing is Apple hasn't even taken out the previous week's highs. I actually like Apple going into this week. But again, it took out that 74 traded up to almost 76. I love that, you know, watch the last week's highs on Apple. If it goes, it could get stretched out.  Nvidia, this was awesome. 8350 rejected twice for experienced traders. Needs to build a couple of ways to play it.  I wanted to bounce it off the 373 level, got the 375. But this 8350, 84 was great. And here was the 60 minute view. And this is what we talk about part of this PS60 theory, the sneaky pivots, right? So you see this whole area here, right? You see this candle here, pre-market, 383.45. The next candle here, 383.49. That's where I got the 383.50, got rejected twice. So once it got above the 83.50, just absolutely exploded. And the video went all the way up to almost 92. Huge, huge move on the video. Just phenomenal action. Coinbase, we were watching through the downside, never got there. Marvel went absolutely nuts talking about a gap and go in this environment on earnings. Earnings gap, 59.40 and 60 needs to confirm for the next leg up. Here is Marvel. So let me show you the 60 minute chart, right? So here is the 59.40. You see these two candles here, right? Here is the 59.40, the pre-market highs. Here was 60, the after hours highs. It cleared out everything. And well, you see what happened to the stocks went absolutely nuts. I get everything went nuts. Workday 217 needs to confirm. Only ran up about a couple of bucks, but I still like Workday. Good consolidation. But you can see here, it took out this whole channel here. Only ran up a couple of bucks, but I still like it. Keep an eye on this thing above the earnings highs going into this week. And Amazon was phenomenal. Amazon was great. We saw a huge call buying coming in for the 18, 19, 20s weeklies. And Amazon did not disappoint. Definitely for one of the best moves of the day. Definitely one of the best trades of the day. The 1734 took out the 1860 and traded all the way up to the Bollinger Band of roughly 122. Huge, huge move on Amazon. And I believe that's it. I mean, listen, everything popped. You know what I mean? Nobody's a genius. Nobody's taking credit for this, you know, picking out these phenomenal moves. Everything is ripping, guys. Everything is ripping. Look at these moves. And by the way, did you see, what was that stock? What was that stock? It was the semiconductor. I don't trade the name often. What was the semiconductor? It went from like 700 bucks. A vago, a vago, a vago, right? This is the market we're in, folks. Okay, this is the market we're in. So when stocks go up 100 points, just because, again, this is not something that we're doing different. It's just the market rewarding us for our process, our patience, and give us the ability to thrive in a very, very small vacuum. So guys, again, if you are planning to join us, you have three days to take advantage of the really, really small investment in your life, man. Again, if you fall in love with technical analysis via the PS60 theory, the technical analysis is going to fall in love with you. It's just a phenomenal, wonderful process that so many people are enjoying. If you have an opportunity to spend some time with us, kick the tires in the next 30 days, I think you can make up your mind for yourself. Guys, God bless. Have a wonderful, wonderful Memorial Day weekend. Get some rest. Do something nice for yourself. Get healthy, right? It's all about health. It's all about happiness, and it's all about love. I'll talk to you guys all on Tuesday. Take care.


Lutrinos are one of the three very basic components of physics at the most elemental level that we know right now. But at the time we started, we didn't even know if they had a mass that was greater than zero or if they had no rest mass at all and traveled at the speed of light the way photons of light do. 60 billion Lutrinos per square centimeter per second passing through you all the time. So so many Lutrinos, but you can't see it. Lutrinos have very weak interaction. Therefore, very difficult to detect Lutrinos. We want to know whether Lutrinos has a mass or not. This is a really big, big question. When we started the Kamiokanda experiment, we found that the event rate of these Lutrinos was not as expected. Therefore, we started to think that maybe something interesting is going on with Lutrinos. We are two kilometers underground in order to avoid bursts of light that take place from cosmic rays. They're shielded out by the rock that is above us. There's an array of 10,000 light sensors that are extremely sensitive and capable of registering even the faintest burst of light. The most interesting thing in Lutrinos is keep producing unexpected result. That's probably a new one coming through the detector. We were able to show that Lutrinos changed from one type to the other, which is referred to as neutrino oscillation and therefore had a finite mass. We were also able to verify with great accuracy the calculations of how many Lutrinos are produced in the core of the Sun. So we now understand how the Sun burns with tremendous accuracy. The IAP experiment is designed to study a new kind of neutrino oscillation. When we designed it, we thought we are not going to see this oscillation, but in the end we got it. And also the value is so large that it surprised almost everybody. Knowing about the neutrino will help us to understand the beginning of the universe, how they evolve, and how the properties of the neutrino affect the formation of matter. That subsequently led to the formation of stars, galaxies, and so on. And of course, our existence.


it's been a day already and this video has just started a while back I made a video because my dog Kermit loves soap and we determined what his favorite soap was by having him do a little soap test. Oh I like that one. It was incredibly stupid but like a lot of people like that video because Kermit is a weird dog and he's very charming and we discovered that he likes Irish spraying soap and ever since that video someone all it takes is one somebody commented please make a bed of Irish spring for Kermit out of soap so he can lay in it and roll around in it. I've wracked my brain I'm trying to figure out how to do this I'm at the point where like if you want me to make a video I'm just gonna make it like okay what are we doing anyways? I haven't made it yet because I logistically could not figure out how to do it and second of all I really think those of you out there that won't stop commenting this are overestimating Kermit's reaction which I imagine is gonna be very like hmm okay that's some soap and then walk away like I really don't think he's gonna lay down and roll in it but because this has been requested so much I've been working literally all day to try and figure out how to make this work I need to explain some things before we start doing this I still don't even know if it's gonna work but let me tell you what happened so we went to the store we bought all this Irish spring the problem was soap even if you liquefy it and you pour it into something hard you can't like just tap it out like it's gonna be stuck in there so a lot of people use like silicone cake molds and like silicone form so you can just pop it out but they don't make anything like the shape of a bed like even the cake molds are like this big so what am I gonna do fabricate something out of silicone I don't know how to do that the mold was the first barrier so what we came up with was we bought these litter boxes for cats and I honestly think like this is the best I'm gonna do okay I'm gonna be able to fill this with soap and hopefully shape it to be like a bed that's it though like I'm not gonna be able to pop it out probably we'll see but I don't think so the second hurdle was the problem with Irish spring soap is that it's apparently not a melted pour soap it's like a we we tried a couple different ways so this way we put it in the microwave and it gets like the air bubbles expand so it sort of expands and like you can work with it a little bit but it's nasty and this this is one bar of soap and it took a while to melt this the second way to do it is to make almost like a soap soup where you add a little water again this is one bar of soap we cook this for like over an hour and it got only that melted so like it may be two hours like to take this many bars of soap and melt it down is like it's never gonna happen but even still when you melt it with water it like it I don't know it's like slippery and slimy like I don't think he's gonna like that anyways so these were our two options make a really gross bed out of soap or make a really slimy bed that's like got giant chunks in it and they take like who knows how long to harden so what I found out there's a specific type of soap called melts and pour that's made for like soap making which is a hobby I went and got finally three tubs of said soap and here's my plan I know you guys want me to make a bed entirely out of Irish spring but as you can see that ain't gonna fucking happen I'm gonna take this I'm gonna melt it down I'm gonna throw a bunch of Irish spring in my food processor chop it all up and then like sprinkle the pieces in here so that it doesn't actually have to get melted down since this is a different type of soap than this I can't just throw in the microwave or like put it on a pot and have it melt it doesn't work trust me I've been doing it all day it doesn't work it's just gonna be Irish spring pieces inside of this unscented like soap that you can actually melt down again I really think that Kermit is just gonna look at this and be so underwhelmed and everyone's gonna be disappointed and we're all gonna learn a lesson here today which is the internet is full of good ideas but they are very mediocre in practice some of you may be asking yourselves why why oh oh this is a fun thing oh yeah it feels real good June is their birthday month all of the dogs have a birthday in June Marbles just had his 10th birthday yesterday Kermit's birthday is on the 20th Peaches is on the 15th Peach honestly just like food Julian made a video for Marbles birthday that's on his channel now but like Kermit just like soap so I wanted to do something special for him for his birthday because we're probably just gonna feed Peach and Marvel got like a t-shirt and he's very happy about that so Kermit needs something special and he's a special boy so he deserves it I can't describe to you how much it smells like soap in here it's like nauseating like it almost makes your throat hurt but cut them all up at once baby Aries will die oh my god it's like breaking the processor we go baby come on does it feel cool it does it feels so cool I didn't really realize like I knew people did it but I didn't really realize how many people like made soap as a hobby it's pretty cool soap is 10 out of 10 fun to cut it's like hard cheese almost Kermit you better like this bed boy it's your birthday bed I love that dog I love that dog I love him no other reason for some dumb shit like this you know I haven't done something this out of control since everyone was like please fill a bald cap full of eyelashes and I'm like I don't understand it but I'll make it let's see what happens it's just one person starts it then everyone's like please make a bed full of Irish spring and here we are I swear to God if we do all this and I spent so much time figuring out how to do this with my brain and Kermit doesn't like it it's gonna break me I'll video it when that happens I already failed last week it giving myself beautiful extensions on eyelashes I can't take another failure I need him to like it this is what we're working with so far we can sprinkle this in as we go and see if we need more Irish spring we're certainly not gonna run out oh it's coming out I think so this does come out of something hard maybe we can do this it's cuz it's not that kind of soap like if we just melted the Irish spring it would never come out and be in there forever it's like so glycerin you got the soap coloring too right so we can try and fool him into thinking it's all green damn it so we just might lose and it melts yeah I don't know that lady on YouTube did a minute so let's do that following directions be like nothing fucking nothing happened so lot of stuff the videos you watched didn't have that much soap in the bowl well no one was making a bed out of soap no one was ever making a bed out of soap yeah you know that's liquidy enough I mean we're just throwing a bunch of other soap in it cuz I need to be completely like we could really be tedious about this but honestly bucket is a bed of soap for a dog pour in our soap you they're just gonna be chunks as Irish spring no one can even tell the difference what what are you seeing what I'm seeing what have we done I don't know this is the best I could come up with I want to see what it looks like after it goes over this layer God this is disgusting and it smells like so much like Irish spring look at all this up we cut we have so much so I love you Kermit can you smell the soap already couldn't you have like a less time consuming hobby bud how later was nice yeah this was a nice layer I can't fucking believe this is like actually happening it's so weird the internet requested it so I don't have control over what they asked me to do this was their fault Julian not mine it was theirs we're doing pretty good it's taking a very long time it's a lot of soap in between layers we're putting it in the fridge to try and help make it so it doesn't take forever to cool my back hurts from doing this honestly so unfortunately we just had a thought what if we put whole bars of Irish spring in here then when we pour the soap it'll just like encapsulate them and we I swear to God this this soap bed is gonna be the death of me like a brick oh yeah let's make a brick pattern we should have done this in the beginning why don't we bother cutting it up actually don't right I know I don't I shouldn't have to say this but this is not sponsored at all but honestly Irish spring where you are you're my dog's favorite so I've lost track of how many bars we've used yeah me too oh Kermit look how much your mom loves you it actually looks dope hi my name is Jenna I'm 31 I don't know what I'm doing my life alright so my plan is to use this silicone mold to spell out Kermit with yellow letters of all the like arts and crafts type videos you've done this is up there with the most fun it's just really fun to melt soap and then mold it oh good you did good it looks really good I'm sure it's gonna be very nice wait I have what that looks so cool I have a problem whoa that did come out good I feel like I'm losing my mind just a little bit doing this is that too much it's like a soap cake for him last layer my arms hurt my back hurts my legs hurt oh let's let it solidify do you think we can get it out of here we can try oh my god it's gonna come out of here oh there we go oh it's oh my god it works all right I don't think that's gonna work try it on the perfect tool a pizza cutter this is so difficult please don't leave your comments in the comments that are like you you're dumb you should have done it this way I will feel really bad I feel like I'm digging for treasure this is so stupid it's like Curse of Oak Island we're not gonna find anything just like Curse of Oak Island this isn't all like nice and pleasing like those soap carving videos on YouTube this is violent this is real life I don't want to sit in this ain't nobody want to sit in this this is uncomfortable for Samus or anybody why did I do this I don't know if you've ever tried to carve soap before but like this is probably a smooth it's gonna get it in here my arms are exhausted from doing that but I hope that's like enough of a little divot for the internet to agree that I did in fact make a dog bed out of Irish spring I don't think Kermit's gonna sit in it I don't think he's gonna land it but I think he will smell it it looks so cool though look at all the layers it's pretty rad just break the whole thing before we get it all for him Kermit, mommy made you a birthday surprise yeah mommy made you a birthday surprise there you go honey happy birthday please come back please come back please come back oh my god I swear to god what's your favorite soap shaped like a bed just for you wow places Kermit would rather roll around on the carpet Kermit please here bud this is what the internet wanted hates it hates it Kermit this was 13 hours of work please just look at it get in your bed it's a soap bed are you nervous cause everyone knows you have a soap fetish everyone knows it's okay we're not judging you you know you like soap it honestly might just be like so much smell it's like overwhelming it's overwhelming to me you know like the texture Kermit, do you like it he hates it I'm so upset I blame this on the internet this is why when you guys are like do this do this and I'm like I don't know man I don't think that's gonna work out right and you guys insist let this be the example to remember this does not work this is a mess this amount of soap is probably just making him want to like leave me I want to leave it smells so much like soap I feel like I'm gonna bomb honestly though it's so beautiful can you imagine if you had this in your shower like this like you could just rub on it and then you're clean yeah I can imagine slipping on that in the shower and hurting myself what no no it's safe to stand on okay when can you burn this thing I don't know what to do with it we've created ourselves quite the pickle we coat it in plastic we can sell it to in our gallery for $500,000 no less that's a nice place to lay but you know where else is a nice place to lay this fucking soap bed that I've been sleeping over for hours he literally doesn't even care Kermit is it too much soap see the internet thinks that if I made this for you that you would lay in it and roll around in it I don't think that's true you know what babe I think we just kind of chopped this one up too just a big old big old well you can't say I didn't do it and that I didn't try I'm sorry you didn't like your birthday gift sometimes people get you things and you just pretend to like them which I appreciate you doing right now he's like an avocado thanks I hope you enjoyed watching us at least make this it's very cool like I think it's really awesome I like it a lot it just it smells like so much soap that I want to die but this is what you guys wanted I'm sorry that this wasn't quite as exciting as you all thought it was going to be but let this be a lesson to you your ideas suck I just feel like we wasted so much time it's weird that you feel like that no it's actually not because we did yeah make sure you subscribe to my channel I'm over here melting soap every day this is my channel now hi my name is Jenna I'm 31 I need to go to bed