So the last talk this morning will be by Barney Bramham from Borum and he will speak about Poincaré's Last Geometric Theorem, a 21st century proof. Okay thank you very much and it's an honor to be here this week especially to be able to actually give a talk so I thank the organizers very much for that. So as many speakers have said already the last day or so Poincaré spent a lot of time thinking about motions of planets especially three and so back in 1912, a hundred years ago, I suppose he'd been thinking about them for close to 30 years and I would like to talk about an interesting question it was very influential called that he asked shortly before he died and this question which he came to from considering the motion of planets is just a question about maps on a shape like this so we have a two-dimensional surface it looks like a plate with a smaller plate a sort of hole removed from the middle and instead of this motion which was just planets moving under the laws of gravity we now have a law on our disk on our sorry on our annulus which says that if I have a point like a then this law tells me that there's some other point I should move to such as B and no two points go to the same one and this is defined for all points and so on so this whole thing now is called a transformation and he was particularly interested in configurations of planets that after a certain amount of time come back to their original position because then these are ones that you can then understand you know trivially for all time and then maybe once nearby well anyway so he's particularly interested in fixed points of this transformation so before I won't really explain exactly how this this annulus map is arrived at but let me just say for a sort of simpler a similar example I believe he also thought about and and Birkov also is the following situation so you have a surface maybe looks like the surface of an egg sphere like this one and you have a point a particle I've made it look like a planet and it's attached to this and it's there's no friction it's free to move around but it won't fall off maybe there's a magnet or something and if you give it a nudge in any direction then there's a sort of a natural path that will follow and then this is called a geodesic but it will keep going forever let's say and he's interested in the analogous question in this situation for that he asked about for celestial mechanics would be is there a curve that is closes up so this is a difficult question and I'd like to just quickly explain an idea that you may use to approach this and it goes like this you say well supposing I can find one such close curve so I have my my egg and I managed to find one path then I say maybe I examine the other parts that start off from this one and I see where they go and maybe if I move around a lot I find one that closes up so I take a point and I take a direction I don't care about the length of this direction and I nudge my my my particle and it goes along and I see what the natural path is and if I'm lucky maybe it comes back and intersects the red curve let's assume it does then on the second time I intersect it I have a well-defined vector arrow based at this red curve pointing the same side of the red curve as the first vector so in some sense I now have a law which says if I start off with a vector like this one then I can produce another one and I sort of forget about what exactly goes on on the blue curve in between this and then if you think about it abstractly the space of all such vectors we don't care about the length of it well there's sort of a two-dimensional family of them I can move tangent to the curve and I only to the red curve and I only care about vectors pointing to one side and then there's 180 degrees as I sweep out from top to bottom and I could also change the base point as I go around a circle so if you think about it for a minute you actually have something where the natural notion of closeness between these vectors gives you something that looks like a closed annulus so this this space I mentioned a minute ago and now this rule that says I start off with a vector a and I get a vector b now turns into a rule on the annulus so I now if I'm given a point on the annulus such as a this corresponds to a vector on the left hand side I follow the blue path around it gives me another vector and that corresponds to another point on the annulus so now I have a law that says I do move from a to b on the annulus so now we have two points of view of the same same situation and Pongka Ray did analogously for celestial mechanics and for three bodies and he was interested in are there paths which close up and in this case this would correspond to a point on the annulus which is fixed by the transformation so he's particularly interested in these now what's common to both of these approaches is that what's going on is that there's some three-dimensional space with some arrows on it a vector field and you're interested in the motion if you start at a point and you follow these arrows where you do you ever come back to yourself and in all of these he's picked he's cleverly picked a two dimensional sort of slice of this which will call a surface of section which has the nice property that if you start off on a point on this surface and follow the arrows you come back to another point on the surface and this gives you a map on the surface and in fact in both those cases you end up with something that is in some sense an annulus and I just wanted to mention this now because later on in my talk will show that well these are quite hard to find in general there's actually ends up a way using a partial differential equation that allows you to in some sense naturally arrive at surfaces of section if you're lucky and this was where I'll come to so I just wanted to draw a link between what was going on a hundred years ago and what happens a long time later so back to the story so Pong Gray now has a map of the annulus he's interested does this have fixed points because this would correspond to some interesting properties of the of the planets he's studying now he asked himself what properties of this map do I know now and there are two two interesting properties so one is that if you instead of just considering where a single point goes you take a set of points you consider what happens under the transformation well the set of course gets distorted like this cat it turns out it'll have the same area and this is somehow a property or comes from the nature of the laws of motion and then the second property is that on the two different boundary circles the points are moving on one circle to say counterclockwise and on say the inner circle clockwise or the reverse but in nevertheless in opposite strictly opposite directions and then this is often referred to as a twist so given these assumptions he oh yeah so so if I now took a set like this this cat and applied this I would get a cat of the same area but now it gets distorted in this fashion and then by playing around with many examples he asked if maybe such a map must automatically forget about where it comes from in mechanics just with these two properties I should also say orientation preserving and so on does this map always have a thick two fixed points so that is like these two red points where the transformation doesn't move them if you remove either of these assumptions you can clearly see that this this doesn't have to be true if you ignore area preserving it's easy to find a counter example and if you don't have a twist at the same you could for example rotate in the same direction around so so this is the question he asked and I believe he managed to answer it in a number of cases and I like to explain a beautiful idea that sort of almost works because then something I'll show later there's some sort of resemblance to this and the idea is roughly as follows said supposing I take so first of all I use the fact that this is twisting the inner boundary one direction in the outer boundary another direction so supposing I take a straight line that goes from the inner circle to the outer circle and then I start walking along this line from the inner boundary so if I start on the inner boundary clearly the transformation moves me to the right and if I as I go further up it moves me to the left so the image maybe looks like this of course it could be a lot more complicated than this come back to that nevertheless there must be some point by continuity as I move up that doesn't move either to the to the right or the left of the line and therefore stays on the line so there must be some point like this red one that moves to some other point on the line such as this green one it could be of course closer to the center or the same point so okay so now I could play the same game with another radio line so let me take this one and again I start from from close to the center and move outwards and there must be some point that moves neither to the right nor the left such as this red one and it goes to another point and I can do the same with another line maybe this time the red point moves inwards and then more lines and more lines and if I do this for all of them maybe I end up with a picture like this where I have two circles that are enclosing the central boundary so I have these two circles the red one being taken to the to the green one and in this example they intersect they are of course for intersection points here and of course we think about it what what's special about these intersection points is these are points which stay on the same radio line and go from the red curve to the green curve so assuming they only intersect once on that radio line these have to be fixed points so in this case we were lucky we even got four fixed points he's conjecturing maybe two now why should we have any of these intersection points so if we can show two intersection points we're done so to summarize we've constructed a red circle and a green circle going around this central boundary and we would like to show the intersect in at least two points and then we've proven there are two fixed points so so far we've only used one of the assumptions that was a twist we haven't used area preserving and if we don't use it something's wrong because the statement is clearly false if you don't use this so this comes in now so supposing by bad luck we end up with the green circle and the red circle not intersecting and they must look probably something like this because they have to go around the curve the boundary but then of course this means that the area enclosed inside the red circle is getting mapped to the to the region of much larger area inside the green circle so this is a problem because this map had to be area preserving and so of course we think about it two regions two circles which enclose two regions which have the same area have to intersect in at least two points because somehow either they sit exactly on each other one of them kind of has to come in and then come out again so you end up with two to these intersection points and then these two fixed points so that's basically the argument and it's a beautiful argument because one problem with with it is right at the beginning is that there need not be these unique points that move neither to the right or the left and you could then end up with so actually this picture I drew of course is actually not not what could happen because the regions inside are not going to have the same area but I only realize this just I didn't have time to change this but nevertheless you can make up configurations that clearly you're not going to have to two intersection points was less so a year later nevertheless bookoff actually found a correct argument or argument that really works and it's funny but humans, mathematicians, scientists I guess everyone you know when a question is answered they're really satisfied where you just want to know does the answer to the question suggest new interesting possibilities and things like this and I don't know actually how bookoff's proof was was used in other directions but certainly what Poincare's ideas I believe well I know inspired many people later and in particular Arnold in the 60s he made a conjecture there's a number of conjectures that generalized this question about the annulus and so he managed to make a statement that would include the included spaces of higher than two dimensions and not just a shape like an annulus and so on personally if I had been around at the time I would have put my money on it being a two-dimensional thing I mean I'm clearly wrong but that's what I would have been my gut instinct from the idea that we just looked at it seems somehow that the twist and the air preserving are somehow accounting for the two of the dimensions and so I would have been very surprised that this holds in higher dimensions but Arnold actually finds a statement that turns out to be to be true so now his question is a question in symplectic geometry so it's a geometry of the equations of motion and there's a long story here and I'm not going to say much about this except how it relates to what I want to say in the next part of my talk so in the 80s Gromov then introduced a new tool to this this geometry of the equations of motion and he showed that solutions to certain elliptic partial differential equation called pseudomorphic curves in the context of a symplectic space have wonderful properties now then there's this somehow was crucial to answering Arnold's question so just before Gromov Ali Ashberg answered the Arnold's conjecture for all two-dimensional surfaces to which it would apply and then Conley and Zaynder managed to do all dimensions for this particular class so Torai or even dimensional Torai so and then Floor sort of combining Conley Zaynder's ideas and Gromov's managed to do a substantial chunk of all of all the spaces and then there are many other people who also contributed to this I mentioned just a few so important so relevant for the rest of my talk is that in the 90s Hoffa-Wazowski and Zaynder discovered that in a certain framework these these these these pseudomorphic curves actually naturally give you a surface of section if you for certain Hamiltonian certain certain three-dimensional spaces with a sort of Hamiltonian vector field on now in general you it's not at all clear that even today that you actually have a surface of section coming from this is not known for every contact three manifold for example but they showed that in many cases sort of how to construct them and this will be important for what I want to say in a minute and in fact using this technology a pseudomorphic curves and surface of section to come from these turns out you can go sort of historically backwards and return and actually prove Pankare's question again and this is what I like to explain because it has a particularly a geometric feel to it and and in some sense once you if you assume that you have the existence of these solutions to this equation and so on then you end up with a picture that's not dissimilar to the one I showed ten minutes ago so so to explain this I'd like to so so just recall what the statement is the statement was you have a transformation of the surface and annulus it rotates the boundaries in opposite directions and it preserves area so let me reformulate this as a statement for disk maps just just for convenience so now I've sort of essentially shrunk the inner boundary to a point and I'm saying okay I now have a map on the disk it preserves area it fixes the origin and it sends the points on the boundary in some sense to the opposite direction to the points infinitesimally close or the linearization at the at the origin and then now your conclusion would like to be two fixed points besides the origin of course so now to apply these pseudomorphic curve techniques I'd like to re-embed kind of go backwards and re-embed the disk in a three-dimensional space with a flow but now pick the flow to be kind of convenient and the space to be topologically simple so I'm going to make it look like a Torah a solid Torah so a donor so I have a three-dimensional space here and visiting putting this disk map in here and now for the moment forget that this is a twist map just keep it area preserving so we put it in here and now we reconstruct some sort of vector field on the three-dimensional space so that if I started a point on the disk call it P and I follow the vector field I go in a curve and I come back to some other point I'll call it tfp here on the on the disk and it's the same map so fixed points of the map on the disk of course correspond to periodical bits of this flow here that go once around so in this situation it turns out that let me first open this up this is kind of more convenient for the next pictures so I'm just slicing it here and opening it up turns out that you can actually fill up the whole space by surfaces of section now of course they're all they're originally it was filled by surface of section that look like you'll these disc slices are also surface of section but here's a ones that are different they're not topologically discs these are now annulises each of them so what do we have here so roughly we have a filling of the space by surfaces I've written a foliation of course it's really a singular the foliation and this consists of a typical leaf looks like this so it's topologically an annulus because the boundary here should be identified with the one here it won't in general I just drew in my picture I made it look exactly flat like this of course it's going to wiggle around a lot and then the rest of the leaves looking similar they're all looking like annually and the relation to the dynamics is that the vector field that we have on the interior of each of these surfaces is strictly is never tangent to it so it's points always in some direction that's the red arrows they in this case they point upwards and on the boundary they are tangent so a small caveat is that they don't have to be tangent to the boundary of these curves that lie in the boundary of the three manifold but sister so in particular the boundaries of these surfaces if they exist have to be on periodic orbits of this flow on the solid torus so correspond to fixed points of the original map and these surfaces come from these are not pseudomorphic curves these are in an odd dimensional space but these are the projection of pseudomorphic curves in a four-dimensional space down to this picture here so now to explain supposing we actually have a map that's a twist map so this thing exists generically I've a generic air preserving map then you can actually get this of course it still doesn't immediately imply necessarily a lot of periodic orbits because it could be a much simpler looking affiliation a priori so let me take a slice like this and say well we said that the flow is transverse to the leaves in the three-dimensional picture so lying a little bit intuitively at least in the two-dimensional slice the flow is somehow transverse to the leaves of course the leaves could be moving around as we as we walk around the solid torus but approximately this is this is the case so you end up with a picture like this these big bold dots are now corresponding to fixed points of my map and these other leaves you have the flow transverse to them here so so now I'd like to apply this to the situation that we actually have a twist so now we say supposing we have a map with it as I said that you're moving infinitesimally in a different direction around the origin which is a fixed point to on the boundary and now we say okay supposing we have one of these fillings by surface of section I just described and let me just draw the transverse slice of these fillings it's easier to draw so supposing that this this this this foliation actually contains this particular fixed point at the origin then I mean this is this is not rigorous but I'm saying supposing locally around there it the leaves are meeting in this fashion here this just coming in all directions and supposing on the boundary the leaves are coming out like this so we'd like to conclude somehow that the structure of this foliation is rich enough that we can conclude two more fixed points right so worst possible scenario is that it's just boring and the leaves do this they just go from the end to the out well then of course that means the flow has to be transverse to the leaves on the interior so in some sense the flow is either moving counterclockwise or clockwise whichever but then of course we're assuming that there's a twist so the flow is transverse in different directions near the boundary and near to the interior so we have a problem so this can't happen so clearly all the leaves that start off at the origin cannot connect to the boundary so there has to be something extra in the foliation that prevents this something getting in the way so we would like to conclude two fixed points so let me try and assume that we can get away with this was just one so maybe something like this we have one and we have a leaf a curve that closes around and then we haven't filled in the rest of the picture but somehow imagine that the rest of the curves are then prevented from going to the boundary by this other ring in the middle okay then I'm still not done because I've only got one fixed point besides the origin but then if we think about it of course this leaf is also a surface of section in the solid three and the solid torus so again the flow has to move strictly outwards or strictly inwards we don't know which let's say it's outwards and that would mean that the whole region enclosed by this circle would end up when I come back again in a region with strictly greater area so we have a problem so there has to be a little bit more in there and that has to be at least one more fixed point so there's now sort of two windows one of which the vectors can move out one on which the flow can move inwards and so we get our two fixed points and you can make that reverse this is what the rest of the foliation could look like I mean of course there could well be many more fixed points but that is how it could look like the rest of the leaves now of course this actually only works if you have one of these foliations and so it works which you do have generically so if you took a dense set there's a dense set in the smooth topology on the space of air-preserving dipimorphism from the disk and you can find set all this up and you can obtain this and you can get the two fixed points now Poincare's statement is not closed under limits right if you see you can't conclude from the truth if the statements true for a generic map that it's true for for all air-preserving maps because the two fixed points could collide nevertheless if you buy this argument and you keep track of this obstacle in the middle these two red curves then you can take a limit with those and then you can get any air-preserving dipimorphism and you get again still at least two fixed points so this is really using Gromov's compactness there so before then we really only use sort of topological properties of these sections of the vectors of treaty transverse eventually to do that take a limit then you really need there's a analysis behind that and actually use Gromov compactness to get the full story so everything I just said more or less did not I mean apart from when I actually tried to prove there are two fixed points the whole existence of these surfaces of section filling up the space that does not require there to be a twist at all so you could hope maybe if you can construct these maybe you can apply these to other situations and it turns out there are there are a great many of these foliations by surface of section as I said if you take a typical three manifold with a suit let's say a contact three manifold you don't know there even exists a single surface of section coming from a pseudomorphic curve but in the particular this particularly a nice case where the flow is really two-dimensional because of the way we constructed it and you can find them and in fact you can pick any homology class on the boundary and you can make sure your leaves meet that homology class you can pick any single one period of orbit and ensure that that is a period of orbit in the boundary of one of your curves as an asymptotic orbit and you can also do this for sort of coverings of these these mapping Torah and so on so there's there's infinitely many of these that are not just trivially related so there's a pro a lot of information here so we construct if we if you have this then we just observe that it's very easy to go from there to say well if I happen to have a twist at the origin then there's also two fixed points but what about in general so there are a number of things you can do and I just mentioned one that just just because it relates to the notion of a twist so you might ask so okay if I have an error preserving map on the desk let's say generalize our notion of a twist map to be not just that there's the fixed point is at the origin and there's a little twist in some direction compared to the boundary but there are some fixed points somewhere on the interior such that infinitesimally you have this rotation in a different direction to the boundary and then of course if you took a typical map at random it would have a twist because this is you could just give a little perturbation to anything if it wasn't and you would have a twist or at least at least for some iterate so how about if you don't allow yourself to take these perturbations and you just say i'm just given any smooth error preserving this map is there any way to say which ones have a twist in some sense and which ones don't so clearly so what are the ones that clearly don't well clearly the identity map doesn't have a twist and and more generally any map which has a finite iterate is the identity clearly doesn't have a twist another another another class of maps of the disk error preserving maps of the disk that clearly don't have a twist of those that have only one fixed point and no other periodic points because if that one fixed point was a twist on craze theorem would tell you there were many more periodic points and we're just assuming those not and these do exist for example irrational rotations but they're also more interesting egodic examples and these maps clearly don't have a twist so there's two classes of maps here that clearly don't have a twist those that are roots of unity and those that have a single periodic point and it turns out all the others do have a twist if you allow yourself to take an iterate so the reason for this i won't explain but it comes down to the fact that we observed in the in the proof earlier that we found in our proof of Poincare's question we found that these two extra fixed points came from the fact that we had a foliation here which had this structure on the right hand side so on the left hand side all the leaves are kind of tree-like you could uh they don't have this sort of topology that you have on the right hand side we actually have a closed a closed chain of leaves so a twist kind of implies this picture and it turns out that actually the converse is also true if you have this picture you also have a twist so you can use this the cycles are equivalent to twists to prove the statement i just said which is that every smooth orientation preserving error preserving map of the disk is one of the following either has precisely one periodic point or it's a root of unity or there's some iterate that has an interior fixed point about which the motion is infinitesimally in a different direction to the boundary of course to me that rigorous you have to speak of covering maps and so on but intuitively that's clear so uh and then uh there are other things one can do and uh with with with this uh this structure that's there and i won't talk about those now um but uh i'll well uh stop there yeah thank you the questions remarks does this proof work for continuous map or do you assume smoothness uh i smooth smoothness yes okay yes yes yes right yeah yeah thank you yes so uh patrice la calva is and very interestingly in it from not using supermorphic curves at all comes up with um a picture very similar to this so he shows that there's a single or one-dimensional foliation if you have only a continuous error preserving or measure preserving map on a sphere or a disk and um uh this doesn't have a he doesn't associate it with a mapping torus instead he has a picture like this and he shows that given uh uh given a point and then the point that the transformation takes it to you can find an arc that is then connects these two that is transverse to every leaf in his single foliation and with this he was able to prove very strong results for continuous error preserving maps and he came through this not through considering pds but by a generalization of the brah uh plane trans translation theorem so that's very interesting he ends up with uh with these singular with these one-dimensional foliations with this transverse property from this point of view yeah thanks yeah just as there is some time maybe you could take five minutes to explain where where where the foliation comes from from this holomorphic disk is it possible so um right so so um so the foliations come from maybe i go back a second to this picture of the mapping torus so so here we are so here so really if you take a uh maybe this picture so here we have a three-dimensional space if you cross with this with the real line you have an uncompact four-dimensional space and you can equip this with a with an almost complex structure that is invariant in the art in this direction in the art coordinate in this four-dimensional space so now um where these leaves come from in here is these are the projection of surfaces that live in this four dimensional space you just project down into the three-dimensional space here and these surfaces if you can show that they are invaded upstairs and have the property that when you shift them up and down they don't intersect themselves then this corresponds downstairs into them having this transversality property there's also an energy condition that has to be the finite energy condition has to be satisfied and in some senses is very like uh i mean these curves are very much like negative gradient flows i mean so it's sort of i mean these come historically from the variational principle for which these periodical bits come from so in that in hindsight there's there's another natural links even though it's such a difficult you know amazing concept to have come up with and these come from that so then where do the leaves in the four dimensional space come from well these unlike the dynamics are actually very stable under perturbation so you can start off with a flow on the solid torus that is not the one you're interested in but as simple as possible for example in an irrational rotation and then you find by hand a foliation by uh by the by by these holomorphic curves and then you can homotope all the data so that means the vector field and there's the background symplectic structure from this model situation to the situation you're interested in and when you do this you can carry over all the information all the all these leaves that you started off with and at some point sort of in some sense at the last minute everything can kind of break up and you started off with a picture that's actually rather simple there's just a single binding orbit going through the center and just leaves going around it's really an an open book at that point but in the final picture you end up with is much richer and you end up with potentially a whole collection of these period of orbits and that's roughly where this comes from and this was a technique discovered by Hoffer-Vazosky and Zehnder like i said in the the 90s and they did this for the situation where instead of having a solid torus you have a three-dimensional sphere and you have a certain kind of this is sort of like an energy surface of a certain kind of Hamiltonian on an ambient symplectic manifold and they were constructed a filling of the three sphere by surfaces transverse to the vector field they were interested and they got marvelous results out of this in that situation where the flow is genuinely three-dimensional unlike here they could really only construct one foliation here because you really have something that's coming from a two-dimensional situation you can actually construct infinitely many and there's multiplayer around it so perhaps you can also in for the three sphere but that's presumably harder and so is that helpful maybe more questions remarks so if not we thank the speaker again


Professional appearance, gravitas, communication and position in a key prerequisite for greater career acceleration as it takes less than 30 seconds for people to determine whether or not they want to do business with you or not. This was the consensus of speakers at the Made in Edition of Executive Presence Conference held at the Cedar House of Grace Church, Lakey Lagos. Plus the corresponding love Ikuko Yedokun tells us more in this report. The Made in Edition of the Executive Presence Conference drew participants from different fields of professional career. It is designed to empower career professionals, executives, graduates and undergraduates alike with soft skills required to give them an edge as they ascend the corporate ladder. Ayon Fulua Wole Oju is a convener of the conference. She holds strongly that improving one's appearance, poise, communication skills and gravitas are all that's needed by anyone hoping to move up the career trajectory. How you show up and what I say every time is that forever men look at the outward appearance. There's only God that looks inward. Men look outward. So every time you need to look the part and you need to always anticipate this compliment from people that you look good as always. Not you look good today. Not oh you look good. No. They have to add as always. Because without that as always it means that you're not consistent in the way you show up. Marvie Isibo harped on professional appearance. She encouraged participants to always dress up as if opportunity is going to meet them on the way. Appearance informs the first impression that people have about you, your brand. How do you want to be known? What do you want to be known for? How do you want people to address you and interface with you? Appearance determines whether or not you have the sad to your name or the mad to your name or it is removed when people greet you. And it is not about stature. It is not about position. It is not about how much money you have in your bank accounts. Alasukome Adenuga is another speaker. He spoke on communication as an integral part of building executive presence and how it can really make to the friends in career acceleration. When we're talking about this gravitas executive presence, communication and appearance that's what it should be with us. We arrive somewhere and we acquire that right to win. That's what I say. Everybody, everyone in this room, every professional can indeed attain that level of executive presence once they win that game in their minds and know that they can get to that level. That mindset shift is really important. Executive presence may not get you the next job but if you don't have it, getting the next job will be very, very difficult. So it is something that you need, it is something that will help you, it is something that needs to be developed. You just have to have a voice that you can project, that people can hear you very clearly and with a powerful blend of passion and confidence to sound convincing, speak with absolute certainty that what you are saying is right. The panel of discussants in their different remarks re-echoed the benefits of a good look, physical appearance, poise and encouraged all to invest in themselves. Highlights of the conference is a launch of a 200-page book which delves into gravitas, communication and public speaking. It looks at the interplay between emotional intelligence, workplace etiquette, style, substance, public speaking, social graces, character and how it fuses into executive presence called pillars, its articulation. The book demystified how anyone can become someone with executive presence. Love yadukou, plus TV news.


Hi, welcome to the session. I am Deepika here. Let's discuss the question. Question says, find the nature of the roots of the following quadratic equation. If the real roots exist, find them. Quadraty equation is 3x square minus 4 root 3x plus 4 is equal to 0. We know that the roots of the equation Ax square plus Bx plus C is equal to 0 or given by x is equal to minus B plus minus B square minus 4 is equal to 2A. If B square minus 4 is greater than 0, two distinct real roots we get. If B square minus 4 is equal to 0, two equal real roots we get. And if B square minus 4 is less than 0, no real roots exist. So let's start the solution. Our given quadratic equation is 3x square minus 4 root 3x plus 4 is equal to 0. Compare this quadratic equation with Ax square plus Bx plus C is equal to 0. We get A is equal to 3, B is equal to minus 4 root 3 and C is equal to 4. Therefore the discriminant is that is B square minus 4ac is equal to minus 4 root 3 whole square minus 4 into A that is 3 into 4. Which is equal to 48 minus 48. Hence our discriminant is equal to 0 because B square minus 4ac is equal to 0. Therefore two equal real roots will exist. Now we will find the roots of this quadratic equation. Let alpha and beta are the roots of the given quadratic equation. Therefore alpha is equal to minus B plus discriminant that is B square minus 4ac upon 2A. And beta is equal to minus B minus B square minus 4ac upon 2A. Therefore alpha is equal to minus of minus 4 root 3 plus 0 upon 2 into 3. And beta is equal to minus of minus 4 root 3 minus 0 upon 2 into 3. Therefore alpha is equal to 4 root 3 upon 6 and beta is equal to 4 root 3 upon 6. Again on cancellation we have alpha is equal to 2 root 3 upon 3 and beta is equal to 2 root 3 upon 3. Which is again equal to 2 upon root 3 and beta is equal to 2 upon root 3. Hence for the above quadratic equation we have equal roots which are 2 by root 3 and 2 by root 3. This is our answer. I hope you understood the question. Bye and have a good day.


This CIO Minute is sponsored by Tejial Systems. The CIO role itself is changing quite a bit. Universities are looking to CIOs for just general strategic advice and support and increasingly CIOs are part of a general strategic conversation. Any more, as a CIO, you really do deeply understand the university and you're just valued as a sort of thinker and strategist, you deal with a lot of change. I was a CIO in 2000 for the first time and so this is my 14th year in the business. I think back then we were at the dawn of the internet age and we were really building out the internet rapidly. I mean the web browser was only a couple years old and the internet was growing very rapidly and so at that time it was a lot about provisioning services and provisioning resources and building infrastructure. Then it went to a phase where it was more about building applications and dealing with information. And now we're in a phase where I think it is dominantly about transforming the institution because the core business underneath is transforming. And so we're spending a lot more time in teaching and learning spaces and research IT support spaces but not to do infrastructure building that's been there for years. It's now about their business model is changing and we have to help them change it. I think that is something that's been on my mind a little bit is what is this role really becoming. It's becoming something that just doesn't solely have to do with technology doesn't solely have to do with supporting the university and technology spaces. It's becoming a general strategist role. This CIO minute is sponsored by Tegile providing flash driven enterprise storage arrays for virtualization file services and database applications. Visit www.tegile.com


What's going on guys got Kyle here relating sports cards, and we are ripping 2022 select football team all 10 box break number 10 We did a randomized for the break guys. I'll show you guys results again Ronald T with the bangles down to Noel with the Titans Good luck guys. Let's do it three green dragons to 89 in each box here first up is Gino wrote me off didn't write back Seahawks to 89 Miramar high school Miramar high school. That's correct. Same as Shawnee right here God Justin Fields 89 bears and Terrell Bernard rookie bills to 89 Keem Hicks base and silver Malik Willis die cut rookie Titans box two nice to 89 we got breeze hall green dragon We've got Rashad Bateman for the Ravens And Andrew boot junior green dragon to 89 There's a JK Dobbins base And mac jones die cut silver Patriots a strength London there for the Falcons rookie to 89 We've got rookie Trayvon Walker for the Jags also to 89 and rookie Zion Johnson chargers Three rookies there on the greens Got a enig bar a rookie and silver die cut givante Williams I like Givante as well man. I hope he's uh back when the season starts He had a knee injury at the end of the year Good luck here guys box number four. Um, we've got a Zidoo on the rookie for the Giants Got seikwan for the Giants to 89 And Kenyan green rookie This is Andrew boot junior rookie base and silver die cut rookie Martin Emerson the Browns green digs We've got red nick bonotto broncos rookie to 89 and we've got josh allen for the bills to 89 to a base And die cut david montgomery club level die cut. These are interesting looking guards club level die cut montgomery box six You clark grabbing three spots and star wars anthony grabbing a spot And no well grabbing some personals here Righty guys appreciate it box six Let's see what that first star wars is like Williams green to 89 We've got two uh two on the green dragon And we've got dak to 89 three to go first star wars guys nice do that after one football next Um, there's christian watson die cut rookie pack Seven it still gets me when I look up and I see that camera there Every time I look at the camera. I'm not looking at my like I'm usually I'm used to looking right at it Yeah, I don't want to like look over there either to be looking at the camera It's 89 davante adams.  Um As in conma rookie for the fins Read left box number eight get some one football full case after this one guys We're on to star wars first one has three left No, no nicely on star wars.   Let's get it filled up Breaking after a um one football case next Derrick stingley to 89 rookie Texans. We've got christian harris also rookie for the Texans And logan hall rookie for the um bucks luicine base rookie and silver die cut is herby or the chargers Alrighty there guys that does do it for select team all 10 box break number 10 Quick one there. Appreciate you guys. We'll get these cards right out to you


How it's volleyball from Saturday Beavers hosting Sioux Falls second set ESU attacking Sammy Leach sets up Maddie Philippiac for the kill and the early point there but the Cougars controlled the match Avery Axish sets up the outside and she hammers it home Sioux Falls wins in three Beavers back on the court Friday at Augustana if you've enjoyed this segment of Lakeland news please consider making a tax deductible contribution to Lakeland public television.


Thanks very much. Maybe just first of all to say who Ergurt is, we are the state-owned company. We operate and manage and control the power system across the entire island and we also plan for its future development in terms of the transmission system and what's needed. So what we like to say is that we make sure that the lights stay on today, tomorrow and every day. I think that just to pick up on what Mario's saying, the energy system needs to change and it's undergoing a paradigm shift. The imperative towards sustainability is driving a paradigm shift in terms of how power systems are constituted and managed. And what we're seeing as well is that increasingly ICT is playing a role in how we deliver on those challenges and you can even see that in terms of the panel that's here today and the various collaborations that are going on around the industry that I'll talk about. Maybe just to first of all take the European perspective on, does this click the sign? Oh no, pointer. So just to look at the European energy roadmap to 2050 that was recently published and to take two dimensions of it, the first thing is to say that electricity is going to double in terms of its share of the energy mix. And part of the reason for that is that in terms of the electricity mix itself and depending on what scenario you pick in that roadmap, but the percentage of renewables within that is going to rise to between 25% and over 90%. And that is a staggering transition in terms of the electricity system that we have today. And I suppose that's why electricity is being used to bring renewables and sustainability into the wider energy mix in a European context. And it's how do we manage that? And what I want to maybe talk about this morning is the great work that's going on in Ireland here and the opportunity we have through the presidency to showcase that and to leverage the experience that we have here of Ireland as a world leader in integrating renewables and how that can be exported internationally. So to put that in context in terms of where we are in Ireland, on an all-island basis energy from renewable resources last year was about 17%, slightly higher in the Republic, slightly less in Northern Ireland, but both jurisdictions are on a clear path to deliver 40% of energy of electricity from renewable resources by 2020. The vast majority of that will be delivered by onshore wind farms in Ireland and Northern Ireland. And that is a huge shift in terms of how we're going to do it. It's also because we are an isolated energy island, it is far ahead of what any other synchronous power system is doing right around the world. And if you just compare Ireland and Northern Ireland on the left over here with what the other synchronous power systems are doing in terms of penetration of wind onto the system, you can see that we're massively ahead of them. And the challenge to doing this is that because wind only blows some of the time, if you want to get to 40% on average, you're going to have periods when you have zero during the year. So therefore at other times you need to manage significantly more than 40%. And what we see is that you need to get to by 2020, you need to get to 75%. You need to be able to manage your power system for 75% of your electricity demand has been served by renewable and wind resources. Nowhere else in the world is doing that. Today we operate the system up to 50% of it being served by wind and that happens regularly on the system today. And we have a programme of work and I'll talk about that later to transition that from 50% to 75%. Nowhere else in the world was even doing 50% much less thinking about how they get to 75%. So here's the opportunity for Ireland to solve those challenges, to be pioneers in this and to leverage that and export it effectively to the rest of Europe. But in order to do this, and both the Minister and Murray touched on this in their presentation, you need energy infrastructure. We need to develop the transmission system. This resource tends to be in places where the transmission infrastructure is not strong, along the West Coast and the Southwest and up in Donegal. Terrific wind resource. We need to harness that and we need to get it to where the demand is typically on the East Coast and that involves significant transmission infrastructure. I noticed in the forwards this conference, the words of the t-shirt, he talked about wanting the presidency to focus on delivery. I think that resonates with what we need to do in terms of energy infrastructure here. We need to move forward and start delivering some of the major infrastructure projects. And through the early parts of next year you'll see Ireland coming out with several of those projects and moving them through the next stages, progressing them along. Our program, it is about 3.2 billion over the next number of years out to 2025 in terms of upgrading transmission links and new transmission lines. We've also just completed the construction of the East-West Inter-Connector, a high-voltage connection to Wales, and that's going to transition into commercial operation in the next while. And that was very, very gratefully that was supported by the European Commission through a grant which enabled an awful lot of other funding to be unlocked. And it was a great example of how a European grant can unlock a whole suite of commercial funding to allow a project like that go ahead. You can see just in the context of European energy networks that 200 billion is an estimate of the cost of infrastructure that's necessary between now and 2020. A lot of concern that that won't, it won't be possible to deliver that for reasons of access to finance, for reasons of public procurement, but that's an estimate of the scale of infrastructure that's actually necessary in order to deliver on this. But infrastructure alone is not going to be enough. It's only part of the answer. We need to do, we need to deliver this infrastructure in a smart way, and we need to integrate it into a smart grid and make the systems that we have better, more intelligent, and get the most out of them. Because as the level of renewables increases, we see complexity on the system increasing. And we also see user participation increasing, and we talked a little bit about heating systems and things like that and smart meters. All of this will see the user, the person in their home able to participate more actively in the energy system. In all likelihood, they won't do this in a very active way. They'll set it up via an app on their iPhone and set it there to maximize their utility, be it low carbon, be it low price or whatever. But with the introduction of smart meters, with the introduction of EVs, we'll see that dynamic coming into a power system, which to date has largely had passive users who just click a switch to use the power. Just want to maybe just mention some of the elements of the program, the smart grid program that we have underway at the moment. And in the conference brochure, there's a pack explaining our DS3 program. And that is focused around what are the things operationally that we need to do to manage a power system with 75% of your power coming from a variable resource like wind? How does that change from one where it's all, where it's largely based around large conventional power stations? Changing and evolving the operation of the power system. That's what that DS3 program is all about. The second bit is around technology and infrastructure. We need to ensure that the infrastructure that we do build that we get the most out of it and the infrastructure that's there already that we get the most out of it. So this is things like deploying advanced technologies on transmission lines to enable you to get more power down them to advance sensing on power lines such that in real time you can see what the sag on a line is and what the temperature of it is so that you can optimize in real time how much power you put down a transmission line. And that has already seen significant savings in terms of the grid development program over the next number of years. The third element is demonstration projects. And we launched this about four months ago. And there's been a huge interest in it right across the industry, not only the energy industry but wider field. And what we're looking to do there is to partner with industry to trial out new and innovative solutions that either exist in other markets or exist in other fields or industries and see can they solve real problems on the Irish power system in a very effective way. And we've two of them up and running now. One of them looks at control systems on a wind turbine. And the second one, Mari, we're delighted to hear is all about heating in homes. It's in conjunction with the Greenway project looking at to the extent that you deploy sophisticated advanced electric storage heaters, the extent to which they can also provide services to the power system itself. So work is underway on that. The fourth aspect to it is the smart grid innovation hub. And this is something we launched with the National Digital Research Center. And this is about trying to foster innovation and entrepreneurship in the smart grid space. There's huge barriers to entry in the energy industry. It's capably intense if it's highly complicated. So what we're trying to do is to break down some of those barriers, to get those nuggets of good ideas, to put them into a sandbox where they can be tested, they can be trialed. We can see if they can solve problems and to nurture them through the commercial expertise and incubator type facilities that exist at the NBRC. And around that, to help it, we've put an industry advisory council to make sure that it's all joined up with people like ESB, SCAI, but also people like Invest, NI, Enterprise Ireland, the International Energy Agency, just to make sure that the right people are looking at these projects that they get developed in the right way going forward. Through all of this research and innovation is absolutely critical in order to transform in the power system. This is a schematic of one of the research initiatives that's underway in Dublin. It's the strategic research cluster run out of UCD. And what I just wanted to show here is the extent to which it's not just academia anymore, it's academia and industry. And it's all about research and innovation, solving those problems that are core to the industry today and to moving forward. One of the unique benefits we have in Ireland is that we are a relatively small industry, we're a relatively small country, so you can get everyone around the table and solve problems. That doesn't exist in continental Europe, it doesn't exist in any other big economies. So there's an opportunity to do and to get trial trials and innovative solutions up and running and in place here much quicker than anywhere else and much more effectively. So that's why there's a huge potential for Ireland to be an exemplar to take the solutions that we're developing here to problems that we see because we have a huge natural resource and because we have an ambition to harness that for the benefit of the country, it means that we need to solve these problems that aren't yet visible on other power systems but will come in the next years and decades ahead. So there's an opportunity to leverage that. We had Nancy Pelosi, Congresswoman Nancy Pelosi over recently in our control centre with a delegation of congressmen and women from the US and what they remarked was that Ireland is small enough to trial something at scale and sorry, it is possible to trial something at scale and it's large enough to be relevant and yet you can do it before rolling it out in some economy like the US or something like that. So there's a huge interest in doing something and seeing solutions deployed on a power system like Ireland and then rolled out across Europe or the US or like that. So I think in terms of sustainable power system and moving forward, there's an imperative to get this right to underpin the economy because there is a transformation undergoing, there is a paradigm shift in terms of the move to sustainability and we need to do it in a way that one, we ensure we have secure energy supplies to underpin the economy but also in a way that drives sustainability going forward as well. So with the natural resource that we have and with the work that we're doing across the industry and the collaboration that's happening, I think there's a huge opportunity for Ireland to be an exemplar of how to build a sustainable power system and then export that around the world. So with that, thank you very much.


Okay, here we go guys. This is gonna be a very common objection.  Let's move quick. This is gonna be pretty simple. How many times have you guys ever heard I need to talk to my wife? Man, come on, man. They always saying that. Gotta talk to my wife. They ain't even married, right? There is a way to handle this. There is a way to handle this that is very smooth. It makes sense. It's not like offensive. Cause I know some of you guys, guys I gotta talk to my wife. You're like, dude, let's just do it. Yeah, just do this and you ain't gonna do it, okay? Listen, here's the deal. You gotta handle this one with glass egg shells. Dude, it's the person he chose to die with. It's his wife. And by the way, she's important. Very. If you handle it just right, there's a way to get around this. There's a way to handle it most of the time. Let me explain the word most to everybody.  I told you guys to have an arsenal of closes to have on your heart. So when someone says something, you got multiple ways to go. Everybody in this room has something that they say when someone says, I need to talk to my wife. Let me give you another one. Does that make sense? And by the way, what you say the question is, does it work? I hear people all the time like, oh man, what would I say? I'm like, dude, you made 60 grand last year. I mean, come on, bro. Listen, let's talk about what works, okay? This works. I used it all the time. It's a brand new word track that we didn't release for a long time because honestly, it's a little bit longer and you have to learn how to memorize stuff. But that's not hard cause you memorize your address. When you move, you memorize that, okay? Cause you got to get your mail. Well, guess what? You got to get your paycheck up and memorize this one. Cool. You're on, you're going to get 30 push-ups, right? I'm going to start with you, okay? Okay. All right, here we go. All right, so listen, this is going to be simple. See this worksheet guys? This worksheet, it's right here. We're going to go to the pencil. Is that cool? We're going to the pencil. Me and you are sitting down. We're on the pencil. You've given me all the numbers and I'm like, hey man, look, it looks great. I really appreciate it. Kind of like I told you before, I've got to talk to my wife. Yeah, listen, Andy, I can totally understand why it's important to you and your family as it is to me. Listen, at the end of the day, you like the vehicle, if I could save you some time, save your wife the headache from coming down here and spending the next few hours with us and having to repeat this process. Wouldn't it be great if you could seem like to hear at the end of the day, save your family the time and get the car at the right deal? Would that be fair? That's my boy. Good job. That's my boy. That's my boy. All right, all right. We got the worksheet right here, right? I said, hey, thanks so much. But look, remember how we talked a little bit earlier? Same thing I served him with. I'm gonna talk to my wife and then I'll get back with you. I completely understand. Buying a car is a big decision. It's not like buying a pair of pants. You're gonna have it for a while. When you left your laneway this morning, your new wife probably had a discussion about what would look right for you and your family. Let me ask you this. Based on what you told me, this is the perfect fit for you. What if you were to save your wife the trouble of coming down here and going through this whole process again? You'd be the hero and you get a new car. I don't always sign a deal and do it today. Good job. Good job. Now listen, number one, hey, that's good. Come on, Canada. Let me tell you why I'm really massively proud of both. Number one, obviously I can tell that they're training, but number two, what they didn't say was this, which is this. This is what everybody goes to first. Hey, why don't we do this? We'll put a tag on it, right? Let's go show it to her. And then what does he say? Well, now she's at work. And you're like, okay. Well, then why don't we call her where she's busy? And you're like, well, okay. Why don't, you see what I'm saying? Do you want a yes or a no? What I do, a guy's understanding about odds, odds and sells is choosing your best odds. Does that make sense? If I ask him to take it to go show it to his wife, what's the chance he's going to say? Yes, it's pretty slim. Okay, now I know sometimes I know when it's good to take it to somebody's wife. Does that make sense? Like maybe the guy said like, hey, you know, if we work this out, like I'm going to need to go show it to her, right? Like I hear those things. If I don't hear that, I'm not thinking that that's something that they're planning on doing. So the goal is, is that what I heard are some key words. Understand the concept of the deal. Is anybody in here married? Raise your hand if you're married. We have a lot of single people here. That's crazy, all right? I'll tell you about people who are married. Normally when they buy a car, it's a planned event. It's generally a planned event. Let me explain what that means. Husband doesn't drive on the way home. He's going to get food for the family and he pulls off into a car lot and then he gets talked into buying a car. That didn't normally happen, okay? They have been premeditating about purchasing something coming up. Does that make sense? Okay, when they did, they probably spoke and discussed like married people do about what the deal would need to look like in order them to make a decision to do a deal. That's the truth. Why don't we repeat that? Why don't we really tell people how they're feeling? And then lastly, do you think wives want to come down to a car dealership and hang out? It's the last place they want to be. So the idea of it is we could call the customer who's in front of us a hero and tell them that he actually has the ability to pull all the headache out of the deal. Times have changed, things have changed and there's a better way to buy a vehicle without having your wife come all the way down here. Maybe last time, the different salesperson that you bought your car from didn't give you that option, okay? But I'm not him, okay? I'm married myself, right? And there is a better way. I'm gonna go over it with you. Does that make sense? Now, you're actually guiding them to a better way that they weren't thinking about.  Are you making them think, you know what, man? You know, this might be a better way. I like this. Does it sound like it should be done that way when you're describing it to them? Or are you kind of just merely stating the facts that this is how it goes at a house? Your job is to persuade people. Am I right or right? If you're not persuading anybody to do what you wanted to do, you're not gonna sell anything, okay?  So you're taking out a very small percentage of the market. I want the whole pie. Persuading and influencing are probably the two strongest things in the world. Guys, do you know what an influencer is? An influencer is somebody who influences. That's a person who wants to get somebody to want to follow them. Am I right? Are you worth following? That's a question. I'm asking you a question. Are you worth following? Then talk like it. Communicate like it. You're not a car salesman. You guys are business people. Start acting like it. That's the problem.  You're not.    Make them remember you for life. Let's go, baby. All right, all right, let's go. Let's go, Jacob. Let's keep going. Hey, so this one's too super easy. It's guys, hey listen, I totally understand. As busy as life is for most people when it comes to purchasing a vehicle, especially with the family, it's generally a planned event. When you left your driveway this morning, I am almost certain you and your wife had a conversation on what the deal needed to look like in order for you to feel completely comfortable making a decision. You said you love the vehicle that you would be extremely happy with the safety and the fuel economy and we're well within your budget. So let me ask you this.  In any way if I can do that for you? Guys, that's it. Come on, baby. That's it. Come on. Come on. Listen.


Bemidji State University's Hague-Sauer Hall may be upgrading in the future. Hady Clotter shows us how a tour could get the ball rolling for a new building. After 47 years, what is known as Hague-Sauer Hall at Bemidji State University may be no more. Faculty, staff, state representatives and the House Capital Investment Committee took a tour to learn more about a proposed bonding project that could replace the building. Hague-Sauer just did not fit into the bonding, into the budget this past round. Now, for that reason, now it's at the top of the Minskyu to-do list. The demolition and new construction of the outdated facility would also erase $9.3 million in deferred maintenance such as water damage in the basement. There's momentum in the legislature behind the project. And I'm on the bonding committee and talking directly with the chair, and so we'll keep things moving the best we can. The proposed Hague-Sauer Academic Learning Center is 27,700 square feet, or less than one-third the size of the current building. 10 state-of-the-art teaching spaces and an auditorium to seat 320 students are some of the proposed additions. The project would also signify campus-wide improvements. This will allow us to build classrooms that are on one level. They'll have ADA accessibility, and all the students will be able to have the same access to the faculty member in a really active learning environment. The tour allows the committee to see the building firsthand and understand the needs for it. A face lift for Hague-Sauer could enhance campus life at BSU. If we can make it a more modern builder and downsize it a little bit, it'll help the school as a whole save some money and they can then roll that into the student. BSU is seeking $22.5 million to finish their design and complete the construction. In Bemidji, Haiti-Claudier, Lakeland News. If approved, the completion of Hague-Sauer Hall would be in the fall of 2020. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


Welcome folks, we have the Dow. Dow industrials are up 33, Nasdaq's down 69, S&Ps are up one and a half, and the weak link in here folks is still the NDX100, and it's going to get intriguing of course because after the closeout here, you're going to have a couple of the big dogs inside that NDX100 come out with their numbers, Google of course will be the monster, and the way Google trades folks, okay? The bottom line is that they will come out in a split second after four o'clock. They're going to be looking for 32 million to their top line, they're going to be looking for 1035 to their bottom line, and the kicker of course is going to be what do they say going forward. Gold, gold contract rejected the lower price out here today, gold's down a buck and a half, trading 17.22, you got silver down 6 cents, $15.15 a bar, an ounce, light sweet crude, that baby's flat, $12.70 a barrel, notes and bonds, you got the 10 year, right now up 11 ticks, trading 139 to 30 year, up a full point, plus 9 ticks at 181.27 and King dollar, King dollar's down 164 ticks, trading 99, 877, the euro's at 108, the yen is at 106.86 and the British pound is at 124. We get over and take a look at these S&Ps, S&Ps bottom line, I've been having a hard time giving it up. Right now you're up 35 cents, the number to keep your eye on in the S&Ps, the spy is 287.30, we're at 287.41 right now, and the X100 as I said earlier, this is the lead dog on the way down and bottom line, I doubt this thing is going to get up until the 216.51 area once again. We had a failure in price, failure in volume yesterday, now what you do have, you have an expansion of volume as we're hitting the lower. We did 36 million shares, that was going into the 62 million, well we're already at 36 million now, so you can expect that inside the queues we're going to be doing maybe 36, that'll bang out like 42, 43 million, and then of course right at the four o'clock time frame, you'll get quite an expansion in volume. We go take a look at the N queues, the futures, and you can see the futures basically gave it up in spades. The N queues got to 89.45 and right now you're 220 points lower than that, we're down 95 for the day, but bottom line is that this baby continues to want lower price. To recap out here, we have the Dow industrials right now trading up 59, Nasdaq is down 62, S&Ps are up 4.5, we'll come right back.


This is a really big box from NRG Innovations It's extremely large What's up guys so before we get to unboxing that big box that I got from NRG Innovations I want to talk to you guys about something real quick. NRG Innovations getting into gaming. It's true NRG Innovations is going to be getting into the gaming industry I know this for a fact because I've been going back and forth with a member of the NRG Innovations team Talking about my wheel setter if you guys know I do work in the Logitech G920 and I used a 350 millimeter NRG Innovations wheel With you know an adapter hub and all that which I got offline now NRG Innovations is going back and forth with me talking to me about my wheel set up They actually have a wheel set up the individual that I'm going back and forth with he has one He has a logitech and all that and he's basically building the setup based off the tutorial video that I made on how I You know wired in my handbrake and mounted the energy innovations wheel Which is pretty cool to you know know that a major company like NRG Innovations is looking at my video and using as a reference point So that is why I'm talking to you guys right now about energy innovations getting into gaming They're in the process of designing hub adapters for gaming systems So you can take like a G920 and buy a wheel off energy innovations and a hub adapter and bolt it right to Your rate, you know, which is a pretty cool thing that you can get it all in one place I'm super excited about it and guarantee you nobody else around here talking about this because I've been going back and forth with them And I know I was going to you nobody else is talking about this So I want to bring this to you guys and let you guys know energy innovations is in the process of you know Researching and development of making hub adapters for gaming, which is a pretty cool idea I'm super excited to see how this comes out and you know what they're doing You know how they're gonna make the adapters, you know because it'd be pretty cool that they can you know Be able to take your wheel from your car put it on your sim rig and you know use the same wheel And then take it off your sim ring and put it back in your car and go get lunch or something on those lines I don't know exactly all the details on how they're doing it, but I know they are getting into the gaming industry That's why you know Right now they they're sponsoring me as a gamer Which is pretty awesome to you know for me that energy innovations is sponsoring me and the channel You know as a video gamer and you know, you know my love of cars So that's what that big box is that big box is a package from energy innovations You know it's a sponsored sponsorship part from energy innovations super excited to open it up So but I want to talk to you guys first about energy innovations And the fact that they are going to be getting into the gaming industry with you know hub adapters for their wheels For people that run sim rigs, which has become a very big thing now in you know Gaming is people running, you know full wheel setups and sim rig set up So, you know, I'm super excited that they're gonna be doing this. It's really awesome. So We're gonna get on packing this big box that energy innovation sent me, you know I kind of know what it is, but you guys don't I'm super excited to show you guys I haven't opened it yet. It is actually still sealed So like I said, you know stay tuned to the channel for I'll give you guys as much information I can when I get it, you know from energy innovations about you know The hub adapters that they're designing and such like that. So let's get over there and unbox this box So I know you guys are here to see and I'm super excited to open up So let's go unbox this thing and you know, see what it's in there All right, now it's time to do what you guys came to see unboxing of this giant box with this handy-dandy Box opener that somehow I ended up in my house. There's about seven other ones from a Person that we're not going to talk about from an old work We're gonna rip this open carefully because I don't really want to destroy it Probably use it how it's meant to be used This thing's actually pretty awesome. Come on so much tape Okay Almost there There's more tape they really did not want this to Come apart. That's a really big sticker energy innovations. That's pretty awesome actually That's definitely going up on the wall. That's a really awesome sticker actually So what do we got in here? I already knew it was but you guys didn't other stuff in here. There's more stickers. I like stickers energy innovation stickers, of course We have here the energy innovations bucket seat We get this box out of the way. We have the black energy innovations bucket seat with padding I'm super excited to actually have a bucket seat on my ring Other than that leather boats, so I can see that I've been using All right, so in the box. We have the energy innovations geo black Seat with removable pads and such the embroidered energy suede's on the sides. Definitely a beautiful looking seat glossy black back as well as Adjustable base, which is gonna be really good because it has a flat bottom so I can monitor directly to it It's got the spot on the bottom for Seat belts on the sides and everything so I guess time we get this thing set up and Get rid of that Volkswagen teeth that I have in there You get this thing to go on the rig because it's definitely gonna look good with my all-black rig and my minty green NRG wheel. It's time to get rid of the old and in with the new for this big heavy folks so I can see Time to move in the NRG seat Which already looks ten times better sitting there with it all so we're gonna have a seat here See I may have to build a base Because this sits a little bit lower than my other seat does. Yeah, I definitely have to build a base I feel like a midget right now so we have to go a little bit of a base which Not not a big deal a little since I don't run a full like set up like a full stand I had built my own just build a little square base, you know on the wood just to raise the seat up a little bit So but I still feel like we need to give this a shot. So we're gonna swap over to the game cam All right, so we're here in the game now with game cam and another external cam out now This seat is sitting a little bit lower than I would normally like right now That's because I still have to build a little bit of a base on it, but I still wanted to you know Give it a rip here It's definitely a comfortable seat hands down the seats so much more comfortable than my other one It it feels a lot nicer feels kind of more like an actual sim rig big shout-out to energy innovation It's a huge. Thank you to you guys for sponsoring me and sponsoring the channel and you know a huge Thank you for this seat this seats gonna be a great addition to my wheel setup here makes it look more of a sim rig You know makes it definitely look more You know legit then with just a random gray leather wrapped seat You know like I said, I'm gonna build a base for it I'll definitely show you guys the base that I build when I build it So stay tuned to the channel for more updates on energy innovations in their gaming aspect as well as for my you know setup Because uh, I got some big things coming in with the setup not only is the seat make my setup a lot more epic I am in the process of building my sequential shifter mod So if you guys want to see how I built the sequential shifter mod with the logic to unite 20 stay tuned to the channel That's gonna be coming here very soon as well as you know the regular game content We'll be coming out to you guys just ribbon assess 13 around the parking lot here So once again, I wanted to give a big shout out to energy innovations a huge Thank you to to them for sponsoring me and the channel.  I can maybe try and get in contact with them, you know and get those questions The answer as well. So I hope you guys enjoy this episode in the sun boxing Uh, and you know my announcement to sponsoring with energy innovations So until next time guys, you know, you can follow me on facebook twitter and instagram All of it's are found in the description box below as well as links for energy innovations We're getting all of your, you know, automotive accessory needs whether it be wheels seats harnesses and such It's all down there in the description box. So until next time guys, I'd like to thank you guys for watching I'm evil rabbit I'm out


everyone Shaber 1000 here today we're going to be reviewing this boar scope that I ordered and I'll tell you how much it was and we're going to check it out together so stick around everybody I bought a boar scope I thought it would come in handy so let's go ahead and open this up I got this online I can't remember if it was eBay or Amazon but I'll tell you here in a minute and if you want one I'll put a link in the description box below so go ahead and open this up I could have used this the other day instead of pulling the head off of the boat motor but I didn't have it yet so but we're gonna we're gonna check it out and try it out so while it works you can apparently hook it up to a phone or a laptop like that so here it is Android camera boar scope for Android and it comes with a mirror a hook and a magnet see what you can see and touch HD camera they always say that but a lot of times it's really not HD but we'll we'll find that out when we open it up and check it out okay so it is a newest Android camera built-in six white LED lights with LED and photo control switch focal distance for CM waterproof IP67 through the distribution can used the PC with a mirror hook magnet I guess it's supposed to be can be used here's the Apple need for that so let's go ahead and open this up also can be used in medical treatment and there's no space in between in medical say so let's see something get out here oh we have a disk cool this is our user manual Android and PC and scope so powerful and smart well I don't know we'll we'll have to see now this thing only cost like $12.75 and was free shipping but I thought well you know it ought to be worth that here's the extra little there's the mirror right there there's the hook and here's the magnet okay so cool alright now I'm gonna open this up I forget how long is this it's like three feet 1.4 meters or something so there's the little and this will plug into here and then you plug it into your your laptop or whatever I don't know I don't think this is gonna work with my phone I may have to get an adapter to use this with my phone I'll have to check that out I do have an Android phone but it's got the C type and this is not the C type but so I'm gonna have I'm gonna read up on this and see what all gonna take to hook it up to my phone I do have a I do have a laptop in there so but let me check this out only works with Android system phone does not support iOS system your Android phone must support OTG function and must support to connect external camera why can I can I don't know I may have an adapter for that we'll have to see let me read up on this and then we'll check it out okay guys so I got it to work on my old phone I can't believe it still kicks on the batteries bad and you can't change it that's why I got a new phone but it'll work already for this and I got her dead's a laptop in there and it works on that it will not work on my phone because this is not the C type and when I used my adapter it just it didn't the light would come on but work so that's alright cuz and if I drop this one when I'm out you know working on a car or something I won't you know it's not so bad you know what I mean so it'll work all right for that so we're going to take it outside and put it down into a cylinder and see what we can see okay guys we're going to put it down in into this cylinder on the old Scott at water and see what the cylinder looks like so I'll get this here now we're just going to stick it down in here that looks like the top of the piston you know what I'll tell you what I think I can record this let's record okay alright we should be recording but then I'll throw that clip in here looks like the top of the piston there's the cylinder wall so let's um let's pull this a little bit alright now let's stick it down in there there's the cylinder there's again the piston here's the cylinder wall whoops and that cylinder wall looks pretty good let's go a little further with I'm trying to oops trying to move it around there a little bit also I can turn the the light down on it so yeah that's pretty decent I don't know what that is there I think it's reflecting so there we go yeah alright so let's go in I'm gonna go in and pause it and I'm gonna bring this footage up and we'll see and we'll see see what it looks like and then I'll be back with you okay guys I did get this working on my phone I do have an adapter that works on it so we're going to go ahead and try this and then we'll check and see which one one's better for this camera okay so let's go ahead and take this this out okay so that's pretty cool see what's up in here I mean you know it can tell me stuff so yeah that's pretty awesome looks a little used but I think that'll clean up once it's run sounds pretty good okay so alright guys so there I can't believe it records audio but that's pretty cool so yeah it's supposed to be high definition it's not you know it's only six what is it 680 or whatever the hell it is so anyway guys alright so let's see which footage is better okay guys so as you saw I did get it to work on my phone and I'll tell you I did get this on eBay it was $12 and 50 cents came out to be 13 something so there must have been tax but I know there was free free shipping so there it is right there I'll put a link to it in the description if you want one but the trouble I was having see it comes with this okay and this is for your laptop like I said I you know worked on her dad's laptop I couldn't get it working on my phone but because you know mine my phone takes this you know the C takes that style and this takes that style so what I did was I had an adapter but it wasn't working with it so I was like okay well then I remembered I had this adapter so what I do is I can plug this into here and it comes with this one so I'll plug this into here okay now I can plug this into here just like I would if I was going to use the PC and now I can plug this in to the bottom of my phone and that's that's how I made it work so that's that's pretty good to where my old phone I can just plug the camera directly into it with that now I don't know what do you think's better let me know in the comments below I've got to use it more you know and I mean I can see that'd be nice because I've got her dad's old laptop so it'll be nice so like I said I can use my old phone I can use my new phone or I can use her dad's laptop which which is kind of cool because then it'll be bigger for me to see and I can record it and go back over and look at it later but which one do you think's better the the first one was my old phone and the second one was with my new phone so but the new phone is two different apps now because the app that you scan on here that app no longer works with this phone okay so I had to download the old app or that app on my on my old phone worked but on this phone I have to use this one which is what I use like when I want to go live with this camera let me tell you what it is here in just a second it is called USB camera pro okay so it's free but I think I paid for pro or paid extra a little extra get more functions with it now that's the one I had to use with my new phone because the one this one here just just won't work with it and it tells you if it doesn't work it tells you any instructions if it doesn't work to go download this and of course it didn't work either and so let me know in the comments which one of you thinks better and but like I said I'll have to use it more and I'll use different or use my different phones or use the laptop and stuff when I when I do use this that way you know I've got a good assortment you know of different ways that I can look at it but what do you think looks best so there you go guys $12 and 50 cents I think there was a little tax on it because it came out to 13 something but it is free shipping so I mean they've got them you can spend a lot of money on them but like I said just just for what you know if I was gonna be doing this every day again I would definitely have a good one a real good one but I think I think it's as good as now I've never used one but the green one that them guys was reviewing a couple years ago everybody was reviewing them I forget what it was called but I think it's as good as that and it was 40 bucks almost bought one but I was like no I didn't want to pay $40 for all the more I use one but you know anyway there you go that's the review on that and it's just it's just it's called an Android camera like I said it says HD it's not you can tell it's not an HD camera it won't go into HD like when I try to change it it won't it it's like 320 or 640 or whatever you know that's it so it's not HD and I knew it that's why I said it before I even opened it I know I knew it but that's okay so you know I mean see what you can't see in touch but yeah just it's made in China but it just says Android camera HD camera but it's boar scope for Android now remember this won't work on your iPhone guys so alright guys I'm gonna get off here now hot haven't eaten yet so I won't say shit I barely met the man legend gone for now thanks for watching guys appreciate it and hope you had a great weekend or having a great weekend so today today's my daughter's 32nd birthday so happy birthday Bambi we love you daddy loves you we'll see you guys we'll see you guys in the next one and that being said bye guys have a good one