Thank you. First of all, thank you very much for inviting me to speak at this seminar, which is so largely attended by so many number theorists around the world and hopefully not only number theorists. So today I'm going to talk about approximation by algebraic numbers and the main question for today would be to understand how well algebraic numbers of a bounded degree are distributed or more exactly given a real number of psi, we want to understand how small can we make the difference psi minus alpha, where alpha runs through algebraic numbers of bounded degrees or degree of alpha is at most n and bounded height of alpha is at most h. And here in this talk by height we mean the naïve height of the minimal polynomial of alpha and primitive minimal polynomial of alpha. So here's the naïve height of p alpha, basically the maximum absolute value of its coefficients. Right. Okay, let's firstly start with some heuristics. What can we expect from this difference? So we know that there are around h to the power n plus one different polynomials of height at most h. Okay. And then with a bit of work we can derive that there are approximately the same amount of algebraic numbers with bounded height and with bounded degree. So if we assume that all of them are equidistributed, are uniformly distributed, then we expect something like psi minus alpha to be smaller than h of alpha to the power minus n minus one, probably some constant. And that should happen for infinitely many algebraic numbers. So this is our expectation from very brief, very rough heuristics. Okay. If you look a bit deeper into the discussion, we will see that this heuristics does not always work. For example, it does not work for algebraic numbers. For example, let's take an algebraic number psi of degree d at most n, then the classical Luegel's inequality gives us that psi minus alpha is always at least h of alpha to the power minus d, which is, as you can see, this expression h of alpha to the power minus d is much bigger than h of alpha to the power minus n minus one. In some sense, it shows that algebraic numbers do not like each other. If we have an algebraic number of small height, then the neighbors will be quite far apart from it. Okay. And because of this issue, to be on the safe side, we usually assume that psi is transcendental. So we don't can see the algebraic numbers of psi. Okay. Right. Now let's make our problem more formal. Let's define the first, the finite exponent for today, the quantity w star of psi, which is a supremum of all numbers, positive numbers, double star, such that the following inequality, psi minus alpha is less than h to the power minus w star minus one, has solutions in algebraic numbers, alpha of bounded degree, degree at most n and bounded height, h of alpha at most h, for arbitrarily large values of h. So it should not necessarily have solutions for all large values of h, but it should have solutions for some sequence of h, which tends to infinity. Okay. Then if we translate our heuristics into this language, then we should get that the w n star of psi, it should be at most, at least n, at least n. And that's actually something posed quite long ago that was firstly posed by Verzing in 1961, and now it's called the conjecture Verzing. So the conjecture is that for any transcendental number of psi, w and star of psi is at least n. Right. Now, before we go into some proofs and some ideas, let's have a look what is already known about this conjecture. First of all, this conjecture is known for small values as well. For n equals one, that's basically the Dirichlet theorem, the classical Dirichlet theorem. So basically we have psi minus p over q is always smaller than one over q squared. So yeah, so w one star of psi is always at least one. So that's basically Dirichlet theorem. So nothing difficult, but when n becomes bigger, the problem becomes much harder. For n equals two, this conjecture is also verified by Davenport and Schmidt in 1967. However, for higher values, so then nothing is known. So for the case and the case n bigger than two is still open. Now, let's have a look what bounds, what estimates for w and star of psi we know for the moment. And his initial paper version in 1961 proved that w and star of psi is at least n plus one over two. So it is at least something. Well, it's quite far from n, but still it's at least n plus one over two. In 1969, Springjuke verified the conjecture for almost all real nonmask psi. So basically it means that if we have counter examples to this conjecture, the Lebeck's measure of those counter examples should be zero. So the set of counter examples is very small. Then later, Bernick and Tyschenko made some improvements to the law of bounds of raising. Namely, in 1993, they showed that w and star of psi is at least n over two plus two minus something which tends to zero as n tends to infinity. So they have precise formula, but it doesn't matter. So it's quite technical. But what does matter that we still have n over two here. So asymptotics is still n over two, but we win a little bit with a constant. And just for the reference, the number three star of psi in their work is at least two to two point five, two and a half. Actually not too good. I think the number three star is two point five exactly, but yeah, but it's not always rational. Later Tyschenko improved this bound again a little bit in 2007. He showed that w and star of psi is at least n over two plus three minus something which tends to zero. And again, for n equals three, that low bound gives us two points 73 and something. And yeah, if you look at all this law of bounds, you can see that we always have n over two. So the asymptotics in all this law of bounds is n over two. And for a long time, nothing better was known. So no better estimates or asymptotic estimate than n over two were known. Okay, I will introduce our result mine and later where we beat this asymptotics. But for the moment, let's not do this. Let's leave it to the end of this talk. Right. Now I want to talk a little bit more about the ideas how to, what can be done? How can we attack this problem? How can we estimate the distance between the given number and given rational number? Usually it is relatively hard to to study the distribution of algebraic numbers themselves. And it is much easier to study the polynomials, the minimal polynomials. So we will introduce several more, several more different time exponents, which will be used later. So the first exponent describes how small can we make the values of polynomials at a given point? So that's namely wn of xi, or respectively, w hat n of xi is defined as the supremum of all w's, real w's, such that the following system of inequalities. So basically the main one is this, the value of the polynomial at xi is at most x to the power minus w. And all the coefficients of that polynomial accept possibly a zero are between one and x, capital X. So if this system of inequalities has solutions in integers a zero and one and so on, a n for arbitrarily large x, that gives us wn of xi. And if we require the system of inequalities to be true for all large x, then that gives us wn hat of xi. Right. And one, and we will need a dual version of this, of this exponents. So here we basically consider the dual body to do the previous one. And yeah, and we define the exponent lambda n of xi and respectively lambda hat n of xi as a supremum of all lambdas, such that the following inequalities x zero times xi to the power i minus xi, all of those are small or are not bigger than x to the power minus lambda. And x zero is between one and x. And again, if that happens for some arbitrarily large values of x, that gives us lambda n of xi. And if, if we require it to be true for all large values of x, that gives us lambda hat n of xi. Cool. So now we have five different definite exponents. Right. And now let's, let's, let's see what can be done with all of them. So we start with some basic ideas. Right. Right. The most basic idea is if, if alpha is, is very close to xi, that implies that immediately implies that the value of minimal polynomial of alpha at this point xi is very small is very close to zero. Right. And well, that's not, that's not something hard. Right. We can estimate the absolute value of pf of xi as xi minus alpha times the derivative of this, of this polynomial at some point between xi and alpha. That's, that's just the basic calculus. Right. And yeah, that can be estimated as h of alpha times xi minus alpha. Right. And if we write it down in terms of different exponents, that, that gives us this, this inequality. Wn of xi is always at least Wn star of xi. That's of course good, but we need low bounds for Wn star, not upper bounds. And so we need, we need to get, we want to get the inverse implication if, if the value of polynomial is small, does it imply that xi and alpha are close to each other? And that inverse implication is only true if somehow we can guarantee that the, the derivative of that polynomial is, is large. Otherwise we cannot guarantee that. So if you, if you have some play that then the inverse is also true. But for, for arbitrary polynomial we can't, there is no way for us to guarantee this. And then for in all, in all the methods, in all the, in the other works of various mathematicians who try to attack this problem, the biggest challenge was to construct or to show the existence of one or several polynomials p, which are very small at point xi and satisfy some other, some other conditions such that, well, that guarantees that one of the roots of that polynomial of one of those polynomials is close enough to xi. So that's like the biggest challenge. And that's just a very brief and vague idea what, what we want to achieve. So Dimitri, we have a question in the audience. Could you repeat the definition of Wn of xi? Wn. Wn of xi. It's here. So it's, it measures how, how small we can make the value of a polynomial. Is it, is it okay or I can, I can repeat. Is it okay? I just don't know who asked the question. Yes, that's good enough. Thank you. Where did we stop? Somewhere here, right? Yeah, right. So now let's, let's think about how can we make one polynomial small at, at a given real point xi. That's, that's not a hard problem, right? That's just a consequence of classical Minkowski's theorem. So for any, for an arbitrary capital H bigger than zero, bigger than zero, there exists a polynomial p such that its value with integer coefficients such that its value at xi is less than h to the power minus m and all its coefficients, the absolute value of all its coefficients are at most h. That's just a classical Minkowski's theorem, a convex boundary Minkowski's theorem, right? And in terms of, in terms of the, the afro tonic spoilers, that means that Wn hat of xi is at least m and also Wn of xi, which is also, which is always at least Wn hat of xi is also at least m. We can do the same for dual, dual body. We can apply Minkowski's theorem for dual body and show that the following system of inequalities, a zero xi to the power i minus ai, absolute value less than capital H to the power minus one over m for all i's between one and m and a zero is at most h, that this system of inequalities also has a non-zero integer solution in values a zero and one and so on a m for all values of h and that gives us that lambda and hat of xi is always at least one over m and lambda n of xi is at least lambda hat of xi. So at least if we, if we just want to estimate the value of polynomial or if you want to estimate lambdas or like for, for dual body, that's not, that's not a hard problem. The hardest problem is then to estimate or to somehow derive the information about Wn star. Okay, now I want to discuss several ideas of, from the, from the words of Wrensing and then other mathematicians. Actually, in his paper, Wrensing has many, had many ideas, many relations between different different exponents. I will discuss only two of them, which will in some way be used later. So the, the first idea is, as, as I also already mentioned in the previous slide, we can always get sequence of polynomials, p of xi, which are smaller than h to the power minus Wn of xi. Yeah, that's just by definition, oh, plus epsilon, plus epsilon, that's just by definition of double of xi, of xi. And by, by some easy tricks, we can, we can guarantee that p of xi is irreducible. And then by, by working with this discriminant, we can, we can derive, we can derive that it's closest, it's, it's closest root to xi. It has, it's, for it's closest root to xi, xi minus alpha is always at most the value of the polynomial times the height of the polynomial to the power n minus two. So here I skip all the details, I just, I just provide the idea, right? Actually, this, this number alpha is not necessarily real, it's, it's a complex number, right? And then from, from this inequality, p of xi is less than h of p to the power minus W, we derive that xi minus alpha is smaller than h of p to the power minus W plus n minus two, right? After that, we use some tricks to replace a complex number by a real number. So if, if, if alpha is, is not real, then we have two conjugate roots, which are very close to xi, and then we can replace p of xi by its derivative and its derivative again has a, has a root which is very close to xi. So it's some trick, some trick, which, which ensures that we can find a real algebraic number alpha with all, with all the same properties. So xi minus alpha is smaller than h of p to the power minus W plus n minus two. Yeah. And finally, the conclusion from, from, from this idea is that we have W and star of xi is at least W, Wn of xi minus n plus one. In principle, this, this low bound usually does not give us a good low bound, right? For example, if, well, we, we, we know that Wn of xi is at least n, and if it is n, then we just get Wn star of xi is at least one, which is, which is rather weak low bound. But if Wn of xi appears to be very high, then it could give some theories about what is reasonable. And also this method shows what can we do, what, what result we can derive if we can see that only one polynomial, we, which is small at xi. So possibly this, this, this factor can be improved, but not too much. Now the next idea, again, YouTubersing was instead considering one polynomial, which is small at xi. He considered two polynomials. It's one polynomial p1 comes from the definition of Wn of xi. So we can always find such a polynomial that p1 of xi is smaller than h to the power minus Wn plus epsilon. And then by reducing h a little bit, a little bit, a little bit, and applying Minkowski theorem, we can find another polynomial p2 of xi, which is, which is also small at xi, right? p2 of xi is at most h to the power minus m. And we can, we can guarantee, again, by doing some tricks that they are co-prime. They don't share any, any root. And after we have two polynomials of this form, and considering some careful consideration of the resultant, we, we can, we can derive that they, there exists the alpha of their product, or basically the root of one of those polynomials, which gives the following lower bound for Wn star of xi. So I don't want to give all the details, because they're technical, and I just want to give an idea. We get Wn star of xi is at least the minimum of these two numbers, and, and Wn of xi plus one over two. And, yeah, and, and this gives our lower bound n plus one over two, and that is the result of verzing. Okay. Yeah, and the conclusion from, from here is that Wn star of xi is at least, yeah, n plus one over two. Right. Now, since verzing, various people tried to make some improvements into this idea. The first improvement I want to discuss is due to Peugeot and Schleschitz. That's in, that was written in 2016, but the, the improvement in self is not too deep, I would say. So if you, if you look closer to, to the initial idea of, of, of verzing, we can find two prime polynomials. And for the first one, we have the same estimators before P1 of xi is at most h to the minus double n plus epsilon. That's because of the definition of double n of xi of xi but for the second polynomial, we can, we can do a little bit better. We can guarantee that it's smaller than h to the power minus W hat of n, n plus epsilon. And that's due to the definition of double n hat. So if double n hat of xi is n, then we don't have any improvement. But in some cases we can, we can, yeah, if double n hat is bigger, strictly bigger than n, we do have an improvement. And then again, if we apply all the same, all the same arguments of verzing, we have an improved low bound for double n star of xi in terms of double n hat. So it's, it's now bigger than the minimum of these two numbers. W hat n of xi and W hat n of xi minus n plus what we had before, double n xi plus one over two, right? Or this can be written as the following formula. So I probably have it, oh no, I don't have it. Okay, so it's three halves double hat and xi minus n plus one half, right? And yeah, and later we will use this low bound. So let's, let's have it here. So also Bernick and Titian in 1993 and 2007 also use similar ideas, which I'm not going to reproduce. I just want to say that they chose polynomials p i of x in more delicate way and considered various cases for the absolute values and for absolute values of their derivatives and that, well, and all of those helped them to reach, to reach this, this low bound, which is still, yeah, which is still n over two plus plus something bounded. So compared to the initial bound of verzing, we improve by basically two and a half, by the constant two and a half. Okay, so that's these other ideas of verzing. Now I also want to, to talk about the ideas of Darin Potenshmid. The first idea of Darin Potenshmid, so they also tried to, to, to attack verzing, verzing conjunction. And yeah, the first idea was to construct polynomials p such that p of xi is much smaller than the derivative p dash of xi. And this idea worked for n equals two. So they, they, they proved the following theorem that L and M be two nearly linearly independent linear forms of three variables. Then, and actually they can be arbitrary linearly dependent forms. Then they exist infinitely many non-zero integer vectors a such that absolute value of L of a is at most with some absolute constant, then the absolute value of M of a times the length of a to the power minus three. Now, if we, if it's in substitute in place of L of a, we substitute the value of a polynomial, which is, which can be considered as a linear form in terms of its coefficients. And for M of a, we consider, we take the value of its, its derivative at xi. Then this inequality basically implies that w two star of xi is at least two. Okay. And of course, after, after you get this theorem, it's tempting to, to generalize it to not be true again. And of course, Darwin potentially tried to do that. And unfortunately, for, unfortunately, they, they, they realized that it cannot be generalized to high velocity. So basically, they proved the following result in the next year, in 1968, they proved that for any n, at least three, one can construct linear forms L of a M of a, such that the inverse inequality is true. L of a is at least with some absolute constant M of a absolute value of M of a times the length of a to the power minus three. So yeah, so for this, this result, the required result is not, is not true anymore for arbitrary linear forms L and M. Of course, maybe if one uses the specific linear forms and we have specific linear forms, one is a failure polynomial, another one is a value of derivative maybe if we use specific linear forms, maybe something can be done, but the, the, the general result is not true. And yeah, and, and, and, and since then this idea, well, I, I, I, I, at least I didn't, I didn't see that anyone pursued this idea any further. Right. That they have another idea, idea two. They, instead of dealing with polynomials to P of psi themselves, they looked at the dual case. So they consider two convex body dual to each other. So the first one is, is, is this, so it consists of points of real points such that x zero plus psi x one plus and so on, plus psi to the power n x n is at most y to the power minus n. And, yeah, and all x i's are at most y. That's the first, the first convex body and it's dual, dual to that convex body is, is this one. So that's the, the set of all points x and plus one dimensional points, points x such that x zero times psi to the power i minus x i is at most y to the power minus one over n and the absolute value of x zero is at most y. So we have these two dual convex bodies and what is good for them about them, we have, we can relate the successive minima. We have the smaller duality theorem. So if we, for us, two successive minima are important. The first successive minima for the first body convex body lambda one of y and n plus first successive minima for the dual, for the dual convex body for c star of y, which is lambda n plus one star of y. And by model duality theorem, they are related by the following equation. So that product is, is bounded from above and from below by some absolute constants. So it's comparable with one. And what does it give us? So what we can do by the definition of lambda and head of psi, the following system of inequalities.  This system does not have solutions for some arbitrary large values of x and that gives us the upper bound, right? The upper bound for lambda one of, sorry, lower bound for lambda one of y. So from there, we can derive the lower bound on lambda one of y for some values, for some large values of y. And then that will, through this duality theorem, that will give us some upper bounds on the lambda n plus one star of y for some values of y. And now, now we need to, we need to understand what's, what does this mean? It means that we have n plus one linearly independent polynomials, p i, such that their values are rather small. So we can, we can derive, yes, their values p i of psi all, for all of those, for all of those independent polynomials, the values are at most h to the power minus one over lambda head n of psi and the heights are at most stage. So we have n plus one linearly independent polynomials, p. And the, yeah, are there any questions? And after that, because we have so many linearly independent polynomials, we can carefully choose the linear combination so that the value of the linear combination is still small. So p of psi is still smaller than h to the power minus one over lambda head of psi. But the, the derivative is rather high, p dashed of psi is at least h. And the, the conclusion from, from this method is that w and star of psi is always at least one over lambda head, lambda n head of psi. So that gives us the low bound for w and star of psi in terms of lambda n head of psi. And I think by, by the time, Darin Potenshmid found this, this relation, it looked, this way, it looked quite promising. And even now, and even now, if we find some good upper bound for lambda n head of psi, that will give us some good low bound for, and maybe some improvement for w and star of psi. But, but at the moment, we, we know quite little about lambda and head of psi. And that's, that's actually another interesting open question about this, the front-end exponents. We actually do not know, do not even know if n is at least three other transcendental numbers, psi, psi, that lambda hat n of psi is strictly bigger than one over n. We do not know. And of course, if we, if the answer to this question is no, then we solve for this in conjunction. Yeah, if there are no, if, if, if lambda n hat of psi is always at most one over n, then w and star of psi is always at least ten, right? But the conjecture is that the answer is yes. The conjecture is that the answer is yes. But as I said, not no one knows. No one knows for sure, right? Up to, up to now, the best general upper bound for lambda n hat of psi is due to Laurent. I'm afraid I don't remember in which year he got it, but he got that lambda n hat of psi is at most the n over two upper integer, upper, upper, upper integer value of n over two to the power minus one. And if we, if we, if we take this, this lower, lower bound and substitute it there, we still get w and star of psi is at least n over two plus something bounded. So it's, it's not an improvement, right? Of, of known results. Right. And now, now I think it's time to introduce our, what time do I have? Our, our result, Schleschitz from 2019. So we actually managed to beat the asymptotics n over two. So we show that if n is at least four and psi is transcendental, then w and star of psi is always bigger than n divided by square root of three, which is, of course, bigger than n over two asymptotically. And moreover, if we, if you consider the, the, the, the ratios w star of psi divided by n, then the limit super this ratios is even bigger. It's, it's at least some delta, which is approximately zero point 64 or eight and so on and so forth. And here you can see the formula for this delta, but you don't have to remember it. I don't, I don't remember it. It's, it comes from the proof and it's very technical. So it's, it's, it's some, it's some delta which, which is bigger than one over two three. Right. Now I'm, I will, I will, I will give some, a little insight into the proof, but very little insight, because firstly I don't have time and it becomes too technical, but they're just, they're just very general ideas behind the proof. Right. So we actually use a combination of the previous bounds and clever, clever links between them. So if, if lambda n hat of psi is, is small, then we use a Davenport and Schmidt estimate, which is let me write it down for, for you to remember, which is w n star of psi is at least one over lambda n hat psi. So if lambda n hat of psi is small, we use this one, but if it is not small, we get, we get an additional information about, yeah, about, about psi. So in that case, we, we get a reasonable lower estimate on one, one of the, of these different exponents, w n hat of psi, w n minus one hat of psi, and so w n minus m hat of psi. And after that, after we get this reasonable lower bound, whatever it is, we use a Bijou-Schleich's estimate, which is, let me remind you, here, which is this w n star of psi is at least three halves w hat of psi minus n plus one half, right. Yeah, so here, here, what we do, we define the sequence of best approximations to psi, psi squared, and so on, psi to the n. Basically, we take the, the, the minimal possible vectors x i, such that this value, which is a maximum of, of x i zero psi to the j minus x i j, which minimizes that maximum, right. And then from, from the definition of lambda n hat, we get this estimate. L of x i is always at most h of x i plus one to the power minus lambda n hat of psi. So that's a standard estimate. It's not hard, but yeah, I'm, I'm, I'm leaving all the details, I'm skipping all the details, right. And after that, we use the following crucial lemma, which is, and the ideas of this lemma come from the work of Laurent. So if, if lambda n hat is, is relatively big, yeah. Then, and you remember, we have, we have vector, minimal vector x i zero x i one up to x i n. Yeah. Then from, if, from, from this vector, we can choose the, the set, the, the, the collection of, of smaller vectors x i zero x i one and so on x i n minus m, then x i one x i two up to x i n minus m plus one, and so on. So each time we kind of shift, right. We take this one, then we take the next one and so on and so forth, right. So all of those are linearly independent, right. And as soon as we know that all of those are linearly independent, we, we know, we can estimate the, yeah, then we, we can translate this, this statement that the, the following system of inequalities has m plus one linearly independent solutions for all large x. And that gives us a, so it has a, I think it's, it gives us a lower, is it lower bound or upper bound? So it gives us the estimate for m plus first successive minimum for, for some value of y and actually for all large values of y of a dual body, right. And since we have, we have so many small values, it gives us upper, upper bound. So upper bound, upper bound on, on, on this, on this m plus first successive minimum. And if we have an upper bound or this successive minimum, we can, from there we can use the Minkowski second theory about successive minimum and get a lower bound. So we get lower bound for the, for the biggest successive minimum from there. And we get some, yeah, so we, we get, that gives us the lower bound for, for this successive minimum. And that gives, that is the exact formula, but it doesn't, you don't have to remember it. And from there, we use a maleduity theorem again to get an upper bound for, for the first successive minimum of, of, of, of, of C of y. So we, you know, we now come to, from the dual body to the initial body. Yeah. And after, after we do all of this, we get lower bound for w hat and minus m of psi, because it's related with the first successive minimum. Right. And, and the rest is just, just, just quite straightforward. So from there, after, after we have lower bound for, for w and minus m hat, we derive lower bound. So after we have lower bound for this, we derive lower bound for w and star of psi, which, which appears to be some complicated expression of lambda and hat of psi. Right. And, and, and then we combine two things together. So we have this, this formula for small values, lambda and hat, this formula for large values of lambda and hat. And that, that's, that becomes the problem from, from analysis. Right. We need to optimize, optimize this, this right hand side. And we optimize it and we optimize it firstly. We optimize it by choosing the right, the right value of lambda and hat. So we want to minimize this expression over all lambda and hat of psi. And after that, we maximize it by, by them. That's, that's something technical, but rather straightforward. Yeah. And, and, and that gives us, finally, in the end, that gives us the, the result that lambda and star of psi is, is bigger than n over root of three. Yeah. I hope, I hope that gave you at least some idea. I'm, I, I, I don't think I was clear enough to explain all the details, but at least I hope that you, you got to grasp some ideas for, from the, from this book. Yeah. And yeah, thank you very much for, for your attention.


So the video I did last week about triple syrup is actually doing a lot better than I expected. I mean I'm not pulling in numbers like this guy and I'm miles away from getting monetized, but still. For a guy who's relatively new to this, it's exciting. I picked up a bunch of subs, which is great, and one of my new subs asked for a video on how to make it. And I initially didn't want to because making syrups is pretty straightforward. But then I remembered that this is a bit more complicated. I mean you are making three syrups, okay four if you want to be a legalist, and I did get pretty efficient at making this stuff. Plus doing this buys me time while I work on other videos. So right now I'm going to show you how to make a small batch of triple syrup. It's the perfect size for a few cocktails and great if you want to play around with it but not have a bunch left over. Here we go. First pour yourself some water and set it on the stove to warm but not boil. The rest of this is pretty straightforward, you just need two measuring cups, something to measure ounces, and something to stir with. Add two and a half ounces to one of your measuring cups. You don't have to use this jigger, but it does measure two and a half ounces up to the top, so if you got it, use it. Next add two and a half ounces of room temperature water, and give it a good long stir. I prefer making simple syrup with room temperature water. A lot of people will tell you need to use hotter boiling water. This isn't true. Room temperature water works just fine, plus it tastes better. If you think it makes no difference, make two batches. One with room temperature water, one with hot water. You will be able to tell the difference, I guarantee it. That'll leave you with almost exactly four ounces of simple syrup. I want a little light on the water this time, but that's okay. Next add one ounce of agave syrup, another ounce of water, and give it another stir. To your second measuring cup, squeeze yourself three ounces of honey. Add one ounce of hot water from the stove, and yes, this time it does have to be hot water. And take a moment to admire the shot of your unmixed honey syrup with steam coming out of it. And stir to incorporate. I mentioned in the other video that I prefer two to one honey syrup in cocktails, but three to one is what works in triple syrup, so that's what we're making. Delicately add one ounce of your honey syrup, give it one last stir, and that my friends will yield you about seven ounces of triple syrup. Perfect for a night of drinking your face off in the name of experimentation. And the nice thing is that leaves you with some honey syrup to play around with, so you can see how these syrups perform in different drinks. If you liked it, hit like. Consider subscribing if you have it already, and if there's something you think I should try, let me know in the comments. Take care, and I'll see you soon. And to my new subscribers, thank you for being here. It means the world to me.


Why do Chinese ESL students have so many troubles when they learn English? With English being one of the most widely used languages in the world, many individuals are learning English in China. The learners include children, businessmen, etc. Although the learners have their own reasons for studying English, there are three main problems that the Chinese learners face while trying to learn English. Drilling vs Understanding The first issue is that learners pay too much attention to memorizing a new vocabulary while ignoring the phonetic symbols. In China, memorizing English words is the standard approach to learning English. However, this learning approach is not a comprehensive technique for learning English. In the memorization-oriented learning approach, the learners write down each word without knowing its phonetic symbols. This exercise is carried out for several days until the learners can speedily recall the words. Although the exercise may allow learners to know more words, it is imperative that learners should more concentrate on phonetic symbols. In fact, a learner may be proficient at writing the word rather than saying it. The learners rely heavily on memorization without practicing phonetic symbols. Therefore, to effectively learn new vocabulary, learning phonetic symbols are also equally important as memorization. Exams vs Communication Actually, language is a facilitator of communications. Language learning is essential for human communications. However, in China, most learners focus on written exams rather than speaking in real life. For example, Chinese students spend at least 10 hours at school studying. Moreover, the teachers are more focused on rote learning techniques to enable students to improve their written grades, rather than stimulating the students' initiative to speak. In China, English is such an important subject because students and parents hope to get high marks in exams. This assists students in their quest to secure admission at renowned high schools or universities. Therefore, learning English specifically for exams is a social problem. Selfishness vs Open-mindedness The last issue is that the majority of the learners are introverts. This makes them hesitant in communicating with people in English. They may not be open to expressing their own thoughts and ideas to others, especially while using other languages, which learners are not familiar with them. For many instances, the Chinese are not used to disclosing their feelings to others. Rather, they express their feelings in a subtler manner. It is a common behavior in China to openly point out learners' mistakes. Such social behavior hampers the self-confidence of the learners and they often become too self-conscious to speak in public. Therefore, people generally tend to avoid occasions or situations wherein they are required to speak in English. As the most crucial function of language is to facilitate communication, if the learners are hesitant to communicate, it will be difficult for them to improve their verbal English skills. ESL students all over the world need professional teachers. In conclusion, learning English is a huge challenge for Chinese people. It is important to view English as a tool to communicate, rather than as a subject of examination. If learners want to acquire comprehensive English skills, they should focus on phonetic symbols rather than just memorizing words. Furthermore, learners must practice verbal English and verbally communicate in English more often. Speak with an ITTT advisor today to put together your personal plan for teaching English abroad. Send us an email or call us toll-free at 1-800-490-0531 to speak with an ITTT advisor today.


Boom What's up money geeks? Mr. V here welcome to another video guys. So in today's video We are going to talk about my top five AI stocks I recently did a video where I told you guys about the industries that you should be investing in so we talked about AI as well as Semi-conductors these two industries are kind of tied together So they're both for on that technology, but again They distinguish themselves from the different parts of technology one, which is the actual software that's running And then the other one is the semi-conductors what helps those software actually run better So we talked about it and I promise you guys that I was gonna do a video of my top five AI stocks So that's what we're gonna cover into this video But before we get to the guys if you're new to the channel We took about how to earn money how to save money how to invest and build wealth So that's something that interests you go ahead and hit that subscribe button and the bell notification so they don't miss out on new Content so when it comes to AI I have talked about it here on the channel And I kind of give you guys an update that moving forward I'm not just gonna talk about stocks, but I'm going to show you guys Different tools that you can use to help you earn more to help you save more and part of that would be talking about Technology and AI would be one of those things So again focus today is my top five AI stocks and for that I've actually recruited my buddy Daniel to tell us about his top five AI stocks take it over Daniel. Thanks, mr. V It's an exhilarating ride with AI stocks becoming the new gold rush in the investment landscape From healthcare to retail AI is transforming industries making these stocks a promising bet for the future And we're not talking about some distant future. It's happening right here right now Now with the future looking brighter than a supernova for AI. It's time to unveil our top five AI stocks Kicking things off at number five. We have international business machines corporation IBM These guys are a leading player in the AI powered healthcare space with their cutting-edge Technologies, they're conquering diseases improving patient care and driving efficiency in medical research This stock could be the prescription for your investment success Marching forward at number four. We have Amazon.com Inc AMZN their pioneers in AI driven e-commerce solutions and personalized customer experiences They're reshaping our online shopping by leveraging customer data and machine learning algorithms Trust me. You'll also want to share of this company once you see their impressive numbers Turning up the heat. We have Microsoft MSFT at number three Microsoft is a leading provider of cloud computing services and it is also investing heavily in AI The company uses AI to improve its Azure cloud computing platform Office productivity suite and other products and services Microsoft is also developing new AI powered products and services for businesses and consumers Just missing the top spot. We have alphabet Inc Google at number two Alphabet the parent company of Google is one of the biggest investors in AI research and development Google uses AI to improve its search engine Advertising platform and other products and services The company is also developing new AI powered products and services for businesses and consumers Their advancements in natural language processing and computer vision are absolutely mind-blowing Trust me. You'll be amazed by what they're bringing to the table Taking the crown at number one. We have the tech titan NVIDIA corporation NVDA NVIDIA is a leading manufacturer of graphics processing units GPUs which are essential for AI computing The company is also developing its own AI software and hardware platforms Which are being used by a wide range of customers including cloud providers data centers and enterprises The company's relentless pursuit of AI superiority makes it a compelling choice and that wraps up our top five AI stocks for 2024 back to you, mr. V Thank You Daniel. That was wonderful. You did an excellent job again guys just for quick recap And this is in no particular order the top five AI stocks that I'm looking at for 2024 would be NVIDIA Google Microsoft IBM and Amazon so if you are already invested in these companies, I'll take continued to build your position But if you haven't already you should at least start looking at these companies to at least pick one and invest in you Don't have to invest in all of them pick one of these companies and start putting your money in NVIDIA would be in a great one I'm gonna do a kind of a recap video here because back in 2022. We did a video of an NVIDIA I'm gonna do a recap here so we can see what transpired from when we did that video till date what transpired with NVIDIA But definitely something that we can go back and look at itself and see the work that we do here on the channel But again AI is a space that you need to pay attention to whether you like it or not. I know people are getting sick of it But where we're heading as far as technology AI is the future So I don't want you to be left behind if you recall again I'm repeating myself here because I've said this on the channel a lot more times Back in early 2000 late 90s to 2000 when the internet just exploded Companies that people invested in back then like the Microsoft the Amazon the Google Look at where they are today if you were to invest it say again 5,000 in those companies back then you you would have been a millionaire fast forward to Late 2000s when we started having a ton of Facebook YouTube and social media just put it that way people that invested in those early Social media companies end up making making a ton of money and then now we're moving into the face where AI is taking over so just a timeline here We went from we just use Google to search and get index information that we can Curious through it and see which one we want. We went through that and then now we're moving to a face where you search on Google It doesn't just bring you back index web pages. It brings you back a word Curated document that you can actually present Do you want to do that exactly without changing it? That's for you to decide But it brings back a well-organized when you say give me the top 10 Saka players in the world. It doesn't just go back and say oh, here's the list of the top 10 soccer players No, it gives you a presentation You presented in such a way that you can take it and go to a meeting and present it That's I mean, it's just unbelievable. So again, my point here is AI is the future You don't want to be left behind and so get on board as soon as possible I'm gonna do another video here on the channel where I'm gonna cover my top five ETFs and index funds because for those of you guys that are not comfortable investing in individual companies I want to give you the opportunity to invest in ETFs and index funds And so I'm gonna cover that here on the channel as well as my top five semi-conductors Companies that you can actually invest in so again, let me know in the comment section Do you guys who want to see? Some did some of these tools the AI tools and how they work and how they can help you Become a better investor help you save money or even help you generate money help you make some income I can do some of those videos here because I said I don't just want us to be Pigeon hole I want us to expand so that you can learn how to make money using some of these tools So again, let me know in the comment section the responses I get would determine if I should make those videos Or not like share subscribe, you know, see you guys in the next one


I have Victor Hotel, 78, 84, and 61, 41. All right. And then I'll read. Yep. All right. I just wanted to double check because he's just seen me. I'll be one. He's probably the farthest away. I'm just waiting for him to finish all the radio check. He's grinding for the artillery. I think I might need my truck. I'll be over. All right. I'm going to double check. All right. All right.


Hey guys, what is up? Welcome to my channel. For today's video, we are going to be talking about one of the newest releases for Mark Jacobs. This is the iconic multi-finish eye palette in terrific in the very merry cherry edition. With that being said, let's get into it. Hey guys, if you're new here, my name is Morgan. Basically, I am a product knowledge enthusiast. It brings me joy to know about what's new on the makeup market and I like sharing that with you guys. So this weekend, Sephora had some sneak peek items for VIP Rouge members where we got 24 hours to pick out a few selected early releases for the holidays. One of which was from the brand new very merry cherry collection from Mark Jacobs, their holiday collection and literally the night before this launch happened. I had actually posted on my Instagram how excited I was for this collection. I thought the packaging was just adorable. So this is just one piece in the whole collection. The collection is actually set to come out October 28th online at Mark Jacobs Beauty and then October 16th online at Sephora. So we did get very lucky that we had one piece come out early in the collection along with the eyeshadow palette. It looks like there is also a highlighter, a mascara in limited edition packaging. You have some lip creams, lip oils, skincare. There's a lot of things and then there's lots of like little packages of sample sizes in the cherry packaging. I don't know. I thought this collection was really cute based on your guys' initial reaction. Some of you said it reminded you of the Norvina palette, which once you mentioned it, I was like, yes. Some of you said it looked very cheap and childish and I will say this. Mark Jacobs is quite a luxe brand and for the most part, I think they've only come out with really luxe sophisticated packaging. And this is kind of not very sophisticated. Even my mom kind of looked at it. She said it kind of looks cheap, but then, you know, she was like, but it is really, really cute. Personally, I like luxe and sophisticated, but I also like cute and adorable. So the packaging did get me for this. I am thinking about picking up some other things from the collection, but I am very happy to see that the palette came out because I'm the eyeshadow palette porter. Okay, so let's take a closer look at this. So this was 4950. Like I said, though it's not available now, it will definitely come back out again. It is a limited edition palette that features seven ultra-pigmented, cherry-inspired shades. This has a 12 month shelf life and this one is made in the USA. So I'm not a big expert on the Mark Jacobs iconic eyeshadow palettes. I do have a couple in my collection, but I definitely don't collect them, but I do like picking up the ones that do have limited edition packaging. So everything is very cherry-fied in this collection. So this is what the box looks like that it came in. It has these cute little cherries on it. And by the way, I specifically chose these earrings for this palette review. You guys actually made these earrings. Actually, I think I made all of the jewelry that I'm wearing. If you follow me on Instagram, one of my hobbies over quarantine was making jewelry. And I told some of you guys I was going to come out with an Etsy shop with some of the stuff that I made. I still am planning on that so you can guys can pick up a few of the pieces. I'm just waiting to get a little bit more into the swing of thing for teaching online because it's a lot and it's taking me a lot to get into that. So once I feel more comfortable with teaching and I have a little bit more time, then I will totally get on the Etsy shop. But for now, tell me what your favorite pieces are and what you want to see. Anyways, self promo. So the packaging is the same component that it's always in. Obviously just decorated differently. So you have this beautiful light minty green color, which I personally like with gold accents. Then you have one simple cute little cherry on the top. I love cherries. I think cherries are super cute. You have all of the colored names. Side note, I love how the names actually have the colors. So you know what to call the shades. And when you open it up, you have your seven shades. Now looking at this, I will say it's not a very original palette. You probably definitely can do all of these colors in your collection. For me, it's more so about the novelty of it. I love holiday makeup items. I love the packaging. I always set money aside every year to kind of go a little bit ham on the releases as opposed to during the normal year. So I knew I was definitely going to get this. So texture wise in here, I would say you're getting three true mattes. It's going to be this shade, this shade and this shade. Then you're getting one true metallic shade, which is right here. You're getting one satin shade, which is the shade right here. And then you have kind of like a glittery shade right here. And this shade is a little bit different. It's more of like a subtle lid topper. And this is the only shade that I'm disappointed in in this palette. Yeah, this shade I felt like was very lackluster. It just wasn't what I was expecting. The pigment on it is very weak. You'll see in my tutorial that I put a color underneath to put this one on top. I'm okay with a shadow not being extremely pigmented, but then the finish of it better be gorgeous. And I found the finish of this to be very subtle and just like meh. So for me, this is kind of not a very good shade, but the rest of them, amazing. Like you will see in my tutorial, I was so obsessed with it. I think the biggest surprise in this palette that I loved was this shade right here, Juicy. It is a satin shade. It just looks like a normal cream shade. And when you're swatching it, you're like, eh. But on the eye, it has the perfect sheen for an underbrow highlight. I definitely think this is a very versatile shade. And then this shade right here is the glitter shade that I have on my inner half of my eye. And I am so obsessed with it. All of the mattes blended very nice. You do get a lot of fallout with the deeper shade. So just be aware of that. I would suggest doing your face makeup after your eyes. Particularly, I didn't notice a lot of fallout. I don't usually struggle with fallout because I tapped the heck out of my brush. And even still, I had a little bit of a mess under here. I wouldn't say I really love this color story. I love the whole story of the palette, I suppose. But as far as colors, I would wear a lot. I mean, probably not this one. I didn't need it. But if you really like the color story, I think it's really nice. And I think it's very easy to create a look with the way that this palette is laid out. I think it's very user-friendly. So if you like these colors, I like all of the dimension that you get in here. And I just feel like it's very easy to create a look with this. That being said, speaking of creating looks, I'm going to get into my tutorial for you guys so that you can see how I created this look. So the first shade we're going into is Juicy. I'm using an Esum S33. And this shade is the Perfect Underbrow Highlighter. It has such a gorgeous, soft sheen to it. And it actually can be built up to be quite white and pigmented. But that's why I'm using a blending brush to apply it. I love this color. With an Esum 34, I'm taking the shade Delicious. So this is going to be my inner corner crease color. So just in the beginning half, and then whatever's left over on my brush, I'm going to blend all the way out. But this is going to be our base color. Gosh, these shadows just apply so beautifully. Can't tell I'm liking everything so far. With the BK Beauty 202, I'm taking the shade Extra. Now be very, very careful with this shade. It does give you a lot of fallout. So make sure you pat your brush out. It's very, very pigmented, but it can be a bit messy. Even though I tapped my brush off well, I still am getting a little bit of fallout. So this has a lot of fallout. So you need to use it accordingly. Maybe apply it before you do your face makeup, but I like to live on the edge that way. So it's fine. And then I'm kind of creating a little bit of a winged out shape. And I'm applying a little bit at a time and then building just to keep the look pretty mess free. With the Morphe N507, I'm also running that shade down the lower lash line. Next, we're going into the shade on top. This looks a little bit more brown base, but I would say it actually is the perfect depth color in this palette because it has a plum element to it also. So I'm just applying it on the outer part of my lower lash line and then whatever's left over, we're going to work inwards. And then also apply some up here just like that. I'm taking some of the extra shade again and I'm actually just going to use a flat shader brush. This is the ref for number two brush, which is in their core collection, which by the way, in October, the whole core collection from Reffer will be going on sale for like 50% off. So something to keep in mind, I'll have to post a link for that for you guys because there is a sign up link. But I'm just putting on the other half of my eyelid with my finger. I'm taking cherries. So the reason why I applied a base color first before applying cherries on top is because I found this color to not have as much of an impact as I wanted it to have. It almost has more of like a topper level of pigmentation. It does need a base layer and I was hoping it would be a little bit more of a thicker consistency that would pack a bigger punch on the eyelid with a little bit more dimension. It's very soft and pretty. Don't get me wrong, but I just expected something else. This shade is just not quite as over the top as I was hoping for it to be.  This is the shade decadent and she is decadent, you guys. I think that this shade is stunning. This is what I wanted cherries to be and more and I'm just applying that all over the inner third of my eyelid. So you can do a soft layer like this or I really built it up. I really loved the dimension that this shade gave and you can put this on top of shadows, whatever base color you want, but oh my gosh, everything about this eyeshadow. You guys see that? It looks wet. It looks like diamonds on your eyelid. This shadow is a 10 out of 10, you guys. So that's all I have for the shadow. I'll finish line your lashes and all the good stuff. So overall, as you can see, I had a very positive experience with this palette. I'm so very impressed with this glitter shade, with the satin shade, how all of the mattes blended and overall, I think you are getting a luxury palette with the exception of this shade. I also feel like this, as far as the depth of this palette, I actually think that this palette is going to work for a large range of skin tones and it's a really fun fall palette. So while the color story maybe isn't the most original, if you do really like the packaging of the palette and the color story and you feel like this is a color story that you would actually wear, I do recommend this palette. I think Marc Jacobs' palettes and his quality is very, very nice. If you're not maybe taken by this color story or you don't find yourself reaching for colors like this, I do think this is a palette that you can pass on and it's not anything really revolutionary color story-wise, but it's very nice. I'm very happy that I have it and I'm definitely going to be looking into more products from this collection. So that is all I have for today's review. I hope you guys enjoyed it. If you aren't subscribed to my channel already, I would love it if you would consider taking the time to do so and I'll see you guys in the next one. Bye.


Right now Kaleas Campbell is the Ravens leader in sex and second behind him is their best cornerback Marlon Humphrey. So does that mean there's a problem with the Ravens pass rush or is this by design? Is this Baltimore Ravens team overrated? Who's the perfect wide receiver for the Ravens that nobody's really talking about? Please and many many more questions on this episode of NFL Questions from Subscribers. The two team keep it clean. What's going on? The same Graven here with another video, another episode of NFL Questions from Subscribers. What Questions from Subscribers is a series where you can ask me any NFL question you want to based off of any NFL team and we answer in the video just like this. Now if you want to be part of NFL Questions from Subscribers just send me an email to teamkeepitcleanatgmail.com. Do not send it to any other emails because if you send it to any other emails your question will not be in Questions from Subscribers. So send it to the right email please. Anyway if you do send it to the correct email then we will answer your question in the video just like this or live stream episode of NFL Questions from Subscribers like we have done in the past. Team keep it clean. I appreciate y'all. I love y'all. Let's get into these questions. First question came from a boy, John B. He said Campbell is leading the team in Sachs at four and he's only getting older. Our second leading person in Sachs is Marlon Humphrey. Do you think that's just by the design of our defense? No. Or do you think there's something else seriously wrong with our pass rush? Alright he said keep up the great work. If that is accurate, I haven't looked it up for myself but if that is accurate, that's a no-winno. That's no good. I mean not that it's a bad thing but it's not necessarily a good thing because your pass rush, your top corner, if your top corner is your second on the team in Sachs that tells a lot. And you know how we say that stats don't tell the whole story, that pretty much does tell the whole story of the Ravens pass rush this year. But hopefully it's one of those things where after the buy things can get better. We'll see if they make any changes, any trades, any adjustments, any pickups, any signs, any this, any that. We'll see. But on defense, I don't really feel like they'll make a trade on defense. I don't even feel like they'll do anything with the defense really. Like I said, I think in order of the moves that I can see them making, I will be for a right guard, either a right guard, receiver, pass rusher in that order, all three being super close to each other. But I just, I really don't see them making any moves for anybody on defense. I know that like I said, we know they tried to before but it obviously failed but I just, I don't see them making a move over there. You never know though. You never know. But yeah, that does say a lot. It says a lot about where our pass rush is coming from and actually who's getting home and finishing. Of course the cornerback coming off the edge or whatever, he or coming out of the slot blitzing from the slot, he may go unblocked so that helps but still it just, it says a lot about the current state of our pass rush and that's, that they could definitely use some improvement. Next question came from my boy, Rodeo. He said, Lamar, are you serious? Okay, I see what you did there, little word play. He said, my guy, what's going on? Hope you and the family are doing well and feeling better. I come to you today with this, no disrespect. With all due respect to my QB, but is Lamar the problem? Now, when I say this, I absolutely mean no disrespect at all. I love my QB but let me break it down. I'm glad you put that because I know a lot of people, when you ask a question, they automatically assume that you may be hating on somebody.  Anyway, he said, Justin Jefferson, 9 receptions, 166 yards and 2 touchdowns. And Kl'chase Claypool, 4 receptions, 74 yards, 2 rushes and a touchdown. T Higgins, 6 receptions, 125 yards. When I look around the league and see this, I wonder, is it simply Lamar? When I say this, I'm asking if Hollywood Brown, Miles Boykin, Pro-Shea and DuVernay were in another offense with another QB. Would their numbers look like these or is it still that we don't know how to transition while receiving from college to the NFL? It seems other teams are getting their whiteouts the ball any way possible, whether it's passes or runs. It's frustrating because last year was Hollywood's rookie season and he was hurt. Six games into this year? What's the excuse? I know it's a ton of football left but you can't expect me to expect him or them to cut it on in the playoffs. I want to see it now and I want to see consistency. We have to build on each performance in order to build up confidence. Is this Greg Roman and his game planning? Is this Lamar's development as a QB holding the wide receivers back or is it simply the whiteouts aren't who we thought they were and we need to clean house? To me, Hollywood is a 1B. He is not a Tyree Keele. He is not a number one receiver. To me, Hollywood can be and should be similar to Edmund. Put him in a slot and he will literally be unguardable. At this point, Miles Boykin should be a healthy scratch. Chris Morbeck? Wow. Every week, Lamar throws at least one pass to Miles and it's either Miles under the route or overrunning the route. Will he see this good for one catch every game? Why is Pro Shade not getting reps? Just wanted to know if these guys were elsewhere. Would they be blossoming? Now I think yes to that question. If any of the Ravens receivers went anywhere, they would be killing it. Well, maybe not even killing it but they would be doing better than what they've been doing with the Ravens. The reason that I say that is because this is the Ravens history. This is the norm for the Ravens. Ravens have had this thing when it comes to young wide receivers to where it just hasn't really consistently clicked. Of course, Tori Smith has been the best one so far. He's been the one for where it was that immediate impact and that consistent impact from jump. From jump. He did play in the first game but he didn't start. But then Lee Evans got hurt and then Tori Smith, he started starting from that second game against the Rams and his first three catches were all touchdowns and he established himself as that deep threat. Him and Flacco, of course, they grew together. They had the connection and it was just a beautiful thing. Besides Tori Smith, young wide receiver, rookie receiver, second year receiver, it hasn't been pretty for the Ravens at all. They has, like you said, been at lack of consistency. It's been at lack of consistency. So we're just wondering and waiting for somebody to step up. Who's it going to be? And then you ask the question, is Lamar a problem? I think it's just been a mix of everybody. The part that Lamar would need to take responsibility for is just looking to spread the ball around more to other people other than Hollywood and Mark Andrews. Now in the game yesterday, I think he was really trying. In the game yesterday against the Eagles. I think he was really trying because he would hold on to the ball and he would hold on to it and hold on to it and hold on to it and hold on to it. Sometimes he ended up taking a sack, sometimes he ended up just having to throw it away. But I think he was really trying. But maybe just nobody came open. He's one of my guy, Carlo, I, and Adam, he made a good point about how sometimes the receivers, you got to break off your routes, man, and you got to come back to the ball.  Say for instance, the pressure, I mean, the offensive line breaks down and the pressure is coming in. Hey, come back and help your quarterback. Come back for the ball. You got to turn around, see what's going on back there and see where you can run and try to help him out so he can hit you. With Hollywood, again, there's been the consistency with him where you know he's going to get like four to five catches a game. You know, Lamar going to find him and Hollywood going to find that ball. And then with Mark Andrews, same thing. But with everybody else, yes, Need, usually one catch a game, Boykin is usually one pass on his way of game and like you said, it's just always that disconnect. So it's going to take a lot, man. They just really got to get on the same page and I don't know, man. It's just a mix of so many, not so many, but it's just a mix of different things. So Lamar got to get the other guys involved. Other guys, they got to get themselves involved. They got to get open, come back for that ball, really attack the ball, man. Attack the ball. As receivers, attack the ball. Be aggressive with them catches and with the play calling to find, find different ways to get guys involved, find, use them. If y'all are going to make a move for some, but even if you are going to make a move for somebody before you make that move, I know we got a bye week, of course, so we got to wait, but use them. Use your guys. Hey, next game that the Ravens play is Steelers and you know, Steelers got a good defense. They got a good pass rush. So you know Steelers, Steelers are not dumb. They're not an inexperienced team. They're not a poorly coached team. They are going to key in on Mark, I think on Mark Andrews especially, but on Hollywood and Mark Ant, you know they're going to be all over both of them. You know they are. So Ravens ain't going to have no choice, but for other people to step it up. So it's time to come up with a game plan in order for everybody to get on the same page, because if you, if you're not going to be on the same page, if it discontinues, then like, like my guy Rodel said, come play off time, that ain't going to fly. That is not going to fly. So they need to get on the same page quick. Next question came from my boy Brandon L. He said, are the Ravens overrated? And I think to answer that question, it depends on how you look at it. The way I look at it is that they're not overrated because for instance, we, we know, trust me, we know, we address it every week that the Ravens have plenty of stuff that they need to fix. They have plenty of stuff that they need to work on as a team. They got a lot that they need to work on. But at the same time, despite having a lot that they need to work on, despite having a lot that they need to improve, they found a way to win five out of their six games. And that's obviously the most important thing. They found regardless of who they play because I know some people, oh, well, they didn't play anybody. They can only play who's on their schedule, just like everything. I mean, the same question that got asked about the Pittsburgh still, hey, all that still is overrated.  They destroyed the Browns because they're probably tired of hearing all that noise. Now they play the Titans next. So that'll be another tough test for them. But with the Ravens, they, I can't say they overrated because they've been taking care of their business. They've been taking care of their business for the most part and they've been winning for the most part. They just, they have a few adjustments here and there, a few things they need to improve on if they're going to go the distance, if they're going to go through the long haul of the season and make it through there successfully and then so on and so forth in the playoffs as well. But overrated, not overrated, but definitely they're not at the top of their game yet. This question came from my boy Chris H. He said, what's up, big bro? Hope you're chilling up there in your state of yours, grilling some chicken, living great and slaying out the way as usual. I can't appreciate you. Just like in Ravens theme song, Team Keeper Clean, don't get mad. It's just what it is. Shout out to you, man. He said, and that is Miles Boykin and Lamar Jackson not being on the same page and still trying to force the issue. Miles Boykin is bona fide practice squad and we continue to see time and time again. Just like last year, he's only used to create space for the other receivers. 6-4-2-20 running a 4-4 for what? Just to be out there running and being in the Ravens system isn't helping him. Look at the history of developing their own receivers. Hollywood is definitely on pace to be the best one we've developed so far. Devon Duvenay is third best receiving option on the team. There's no way Boykin should have more snaps. Ozzy was always so aggressive for these defensive players, but the last time I checked, defense doesn't score points. And by the looks of it, EDC isn't any different. Besides Mark Ingram and DJ Flucca, he's done virtually nothing on the offensive side of the ball in the two years he's been with the Ravens. The two years he's been the GM of the Ravens, because he's been with the Ravens like forever. Lamar is the new Flacco. Flacco was so scrutinized by the media and even Ravens fans, but why not Ozzy? The only time they got him help so coincidentally, they won the Superbowl. Do you think the Ravens need the guy at receiver to reach the ultimate goal? Because eventually the Ravens are going to be put in the position to throw the ball and we're not the Patriots. As soon as we get in the playoffs, there's just going to be some huge turnaround. No, I wouldn't mind that though, but highly unlikely. My bad with the repetitive receiver question. Pretty sure you got a lot of these. Take care my friend. No, that's all good. With Miles Boykin and Lamar, like we talked about, they definitely not on the same page. And I don't, forcing the issue, I just, I don't think it's a matter, I don't think it's that they're forcing the issue, because Lamar doesn't give me many looks. I think they need to address the issue, hopefully on this bye week. Well, I guess on the bye bye, bye week is really time for them to relax or whatever. But I know they can't go nowhere. I don't, they're not allowed to travel on the bye week anymore. So maybe throughout, throughout now in the Steelers game, like we said, they this is the time, man. This is the time you got some extra time, some downtime. They got to get it together. They have got to get it together because again, Miles Boykin is out there a lot. You see that number 80 out there a lot. So defenses, they're not even going to pay him any mind if he's not even getting any, any looks, they are not going to pay him any mind. Even if they send him on a slant, send him on a slant.   What the cornerback going to be five, 10, six foot, depending on the cornerback, who it is, depending on who we going against. But Miles Boykin will already have that inside leverage.  Then you're going to be able to high point that ball. He going to be able to high point the ball. But even if it's not high, however you throw it, Miles Boykin is going to have that advantage, that inside advantage because, and he could box him out. He like it's, it's just like, I feel like there's so many simple ways to, to try to fix this thing. I feel like it's, it's, it's just, it's not hard. And they just start with the simple stuff. Start with the simple stuff. You ain't got to do no route with any timing route with Miles Boykin yet. Just start with the simple stuff so y'all can start to get on the same page and y'all can really get a feel for each other that way. Start off small and then gradually increase whatever y'all are doing. But it's, it's ways to try to fix this thing. And they, but then they got to try to fix this thing because it just, it hasn't been pretty so far, man. Um, and yeah, Ozzie deserved a lot of the blame for the whole thing with Flacco and, and EDC as well. Um, but EDC, I think with EDC, the difference between him and Ozzie is that he's at least trying. He's trying with the young guys. And that's something that with Ozzie didn't really do too often because he usually brought in some older veteran talent at Y Receiver. But EDC said, uh, we're gonna, we're gonna go young. Let's go young, see how it works out. And I could understand why he did that. Cause I, I even suggested that they do that. Y'all remember those older videos? I suggested, hey, go, go with the young boys, man. Go with the young dudes, man. Cause this could be, this could finally be our chance for these guys to develop. Just like with Flacco, the one of the receivers that he did the best with and had the best connection with was the receiver that he had from that receivers rookie year, that being Tory Smith. They had the best connection. They just knew each other. It was, it was just chemistry like crazy. And Flacco had him, his entire rookie contract from jump. And now with Lamar, he's had Hollywood, they obviously got a connection on and off the field, but with Boykin, they still, they're still working to get there. So they need to keep working to get there. So things can eventually just take off. Next question came from a boy, Ramel B, he said, uh, this may be the receiver that we go get engraving. And I know you're going to love it because this acquisition will give me that Angkwan Bowden feel. This to me is a low key vet wide receiver that is great at finding the open gaps when plays break down. And I think Lamar will love him right now.  This guy's a dog. He literally faces double coverages every week because he is the only jet player worth stopping on offense and he still produces. In addition, I just believe this guy is what we think is born to be a raven. He will be the yin to Hollywood's yin. Okay. All right. See, I don't know much about Jameson Crowder. That's not the one who used to play for Washington, is it? I'm not even a hundred percent sure, but I don't know much about him. So I would have to do a little digging on what he's good at, what he's great at, what he's bad at, um, and just see, just really watch him. Cause I just, I'm pretty naive to Jameson Crowder's game. And if he would be a good fit or not, uh, with the Ravens. So we'll see by the time we play Steelers, you should have your answer if they did it or not. He like the Ravens, like the Ravens and you know, just what I made you to take. Keep it clean. You see my boy. He like I'd have made it, I'd have made it. Well, that's my homie. Ain't that right?


Hi, my name is Julie Turner and I am a principal architect with Sympraxis Consulting and prior to that I worked for Blue Metal Architects as an architect. So I came to SharePoint in 2007 when I was in internal IT for a small medical device company and then I decided that I'd like to get into consulting so I shifted to consulting and sort of stayed in the SharePoint world and sort of been moving in that direction as the versions come out all the way through to Office 365 in Azure. I went to the first dev kitchen that they had and so I had exposure to the web parts there and then just playing around with it back at the home office and sort of seeing what it could do and that kind of stuff but none really in production. You know I think it was impressive like how fast they got something out. They said a lot of things in the May 4th event last year, they had a lot of stuff to get out and it was impressive that they got it all out and tooled it out and got to GA. So my impression is that they're working really hard at it and to be open source so non-Microsoft I think that's really great. I think they have a long way to go though. I mean the roadmap as I've seen it has some really good backlog items and they're just all necessary. I mean I feel like you could do some stuff and if you're going to do a web part and it's you know pretty basic and you don't need to talk to anything else and all of that stuff. The idea that you can be on Classic and Modern that's awesome but we really need things around like being able to deploy to the site collection versus the tenant and just allowing a little bit more flexibility and flow around those kinds of things I think is critical.  And so the ability to have that workbench and just be able to like spin it up and see how it's going and you know and really debug and get your bits together before you really have to deploy to the production or even to a dev tenant or dev box it just really makes a big difference. We just need a way to provide a deployment mechanism that gets things out to the site collection and not have to go to the tenant. The actual other thing is you know we need a good story around the ALM model and where we're going to put those bits those bundles you know for access to the web parts and how we're going to update them and that story really needs to coalesce. It really feels like we need some support with the UI fabric for more than just react so you know the angulars the even just core basic JavaScript really needs to be there a little bit more fully supported so that we can really exploit all the different platforms that people might want to use. I think it's going to be adoption you know I you know we talk about this all the time you know the traditional SharePoint developer is going to come from you know a C sharp background you know strongly typed you know and you have TypeScript but moving from that visual studio to you know all these weird technologies gulps in your NPNs and your node and how to use that tool set is going to be a huge challenge and I think adoption is going to be slow. Definitely think they're full in on this you know and to that end there it's first party and third party right there they're using it to build the components that we're starting to see in modern pages and stuff so they're definitely going to be full in and full bore on it. I'm hoping that the adoption will pick up as people understand how to use this new new thing and that they get more functionality out there right because we're missing a lot of stuff in modern around you know well what JS link was you know script injection that kind of stuff and once that is there and so this is a full story about what you can do in a modern page with the SharePoint framework then I think you know things will really pick up.


Okay, in this video, we're going to go ahead and create the JMS service. So in the Docker compose file, you can see that I've got the definition up there. You can see that we're pulling from the image view remerial, active MQ Artemis, and then we are exposing two different ports, and that's for the JMS communication. So we don't have to worry about any environment property. So we're good to go there. And this is going to be fairly simple. So let's toggle over to the command line and create this. So here, first we want to create the deployment file. Create deployment, and we are going to call the service JMS. And this is going to be from the image equals be remerial, active MQ Artemis dry-dash run equals client minus O for YAML output, like so. And we say cube CTO, ply minus F. So that creates the deployment, the actual pod that is being created. That's going to be the container. And then we can also do, clear the screen, get towards the top again, cube control create service this time. This is going to be exposed outside the cluster. So we'll give it cluster IP JMS. And now let's expose the ports. We want 8161, and then also we need to 61616. Again, that's going to be dry run, output of YAML, type O there, TCP equals, ply minus F, JMS service this time. And this is going out creating service. I clear all this. And getting all, we can see that we now have a JMS pod. A MySQL pod. We have the two services that we've created, JMS and MySQL. So that's exactly what we want to see here. If I do clear, if I do a Docker PS, we can see that we have two containers running in a Docker context on our local host. So let's toggle over to IntelliJ real quick and we'll review what we created. So the first thing that we created was this JMS deployment. We used the cube control command. We haven't had to touch anything in this file. So this was created through cube control. We didn't have to override anything. So no edits were made to this file from that command. And then also we created the same with the service. You can see that we did use the TCP parameter twice. And that was created, created those two port mappings for us. So exactly what we want here as far as exposing the ports.