Да, так что вчера Ян introduce a little bit of Chan-Simon theory and we'll have more Chan-Simon theory today and I want to make kind of some comment, some mathematical wisdom, which I learned from Alexander Kirill of concerning, which is very relevant. It's from, it's a small poem by some famous Russian poet Kazimaportkov middle of 19th century. It's about myosotis. Myosotis is an invasive plant, it's kind of small blue flowers. It's common name is Forget Me Not in Russian's Nizabutka. Nizabutka is the same name. And so it's about some poor guy Pachomich, who is behind the carriage, the place is not sitting, just staying and it's shaking very much.  And then reader in this fable cast off the Forget Me Nots. The two jokes here place it, but conclude this. If you have blisters to get rid of your pain, like our Pachomich, cure them with comfort oil. So what I will explain is three dimensional manifolds, Chan-Simon theory, it's kind of like Forget Me Nots. We shouldn't forget to forget them. Okay, so now I'll start with kind of point of view on Chan-Simon, we don't have any Chan-Simon section, nothing like this, no three manifolds, no groups. So I will start with certain sequence of polynomials. There are some nice polynomials, kind of invented by Euler. You see that E01, EEN01 is n factorial. It counts permutations with certain number of drops, some combinatorial properties. So you have the sequence of polynomials, which satisfies some recursive rule. And EEN plus 1 is equal to x1 minus x dxEN plus 1 plus nxEN. Define them by recursion of these polynomials. In fact, it's kind of a complicated way to see things. You define rational functions through these polynomials and have x is xEN of x divided by minus x to the power n plus 1. And to start, it's much simpler in terms of rational functions. You just take logarithmic derivatives. So I get these rational functions. A, now make new rational functions. R, getting some other sequence of functions. Look how I define them. I say that r0 plus r1 h bar plus r2 h bar square plus blah blah blah. It's equal to exponent. So I use only even indices of polynomials. The rest are just to define recursion. Okay, just a second. So I get these nice rational functions. And the main hero today will be falling guy. So it's not a function formal expression, because this series is never convergent. It's kind of asymptotic expansion. And this satisfies Q difference equation. So actually it's a unique solution of Q difference equations, which has some asymptotic and x goes to 0, goes to maybe 1. The next goes to where? When x goes to a small positive number. You mentioned 0 and 1. Sorry? When x goes to 0, maybe I think it's 1. But yeah, uproar if consider, try to solve this equation. Sorry? There is an h bar. No, I didn't get it. H bar is kind of very small formal parameter. And when you try to solve this equation, it's in this form times certain series you can multiply by freely, by exponent of any series in h bar. And this is normalization. Yeah, yeah, okay, yeah, okay. Let's do like this. Yeah, so get this function. And now the next thing. In all this series, whatever you can call, you study some new functions of several variables, which are given by the following thing. You consider kind of n-fold integral, and dimensional integral. But this function is not defined by one different situation. Sorry? The function is not defined uniquely by one different situation. By symmetric expansion it's uniquely defined. If you write a certain series in h bar. Oh, in this particular form. If you write in this form and put this condition, and with this initial condition it will be uniquely defined here. So it's not a function, it's kind of formal expression. You can see some kind of prefactor times the series, yeah. Now you can see the functions of n variables. T i belongs like in C star, independent on h bar. And then multiply by exponent. And here you do something like this. You take sum of a i j log x i log x j of h bar, plus sum of b i log x i, plus maybe some c h bar. And then also multiply by exponent of t i, divide by h bar, and that product d x i log x i. Okay. And here what you have, you get a, b and c, which you can form to n plus 1 matrix. It will be symmetric matrix with rational coefficients, with n plus 1 coefficients. And what we should do, we should consider various integrals like this. For generic values of parameter t, or maybe for special values of parameter t, the generic values are really nice. For generic values these things have kind of automatically more singularities. For generic it has automatically more singularity, and you get finitely many singular points. And you get finitely many series in h bar. So what's the line below that the h j cannot be? M i, M i. B i, again. It's symmetric matrix, yeah. J is equal to a g i. Okay. So what are critical points? Critical points for the integral is a solution of the system for equations. 1 over x i, t i, product over j, x j, a j. We get the system of equations. And for generic t it will have only finitely many solutions. For special values it could be some variety. And this story about vanishing cycles. But for generic t it has more critical points. All more for generic t. And this expression will have certain form. Of course it will be 2 p h bar 2 power n over 2. Then exponent to something, again some critical value divided by h bar. Critical value depends only on matrix a. Depends on b and this g. And then certain series in h bar, which will be factorially divergent. And what I claim is that all these guys are resurgents. Resurgent. And what people study in terms of some boundary condition, whatever, it's expressions like this. Nothing more goes on. So three dimension manifolds. I forgot what is it. Critical value. But it depends only on aij and variable t. Rational matrix aij, not on b and c. And some variable t. And some of critical values. Sorry, any critical? Some of critical values. But there are only finitely many solutions. So you get finitely many series. It's how many solutions this algebraic equation for generic t. And this is what I think with expansion. This integral in critical point will have more singularity. So there's really no question what to do. And of course when you have kind of bad value of t then you have degenerate manifolds. You get vanishing cycles, story. Right. Since you get rid of channel 7, do you justify that that's exactly what... No. Okay, so... No, no, no, I don't want to hear. I'll do that. I'll do that. Yeah, yeah, okay, yeah, okay, yeah. Yeah. Sorry, you say in synthetic expansion that it's not a function. It's already a series in h bar. Yeah, but since it should be independent. This is critical value independence on h bar. Depends on draw h bar to power minus 1 only in this exponent. And I consider all the rest. The resurgence is already present in each factor phi. In each factor phi is... Yes, yes, yeah, okay. Yes, yes, I will go to it in a second. Don't... Don't rush, okay. Yeah. So get... For this... You get plenty of various series. Maybe depending on parameters. The claims are all resurgence. And if it depends parameter, it will be kind of analytic. Depends of... But the claims that same series in h bar can appear in many different ways. In infinitely many ways. So change metrics, change number of variables and change critical points and get the same series. So plenty of such identities. How parameters depend on... No, no. This is my fable. Forget about... No, no, no. I have no idea. No, no, it's forget it. It's kind of... You have to spoil your brain. Yeah, okay, yeah. Yes, yes, yes, yeah. You know too much, yeah. Okay, yeah. No, no. This was my introduction for this, yeah. Yeah. So there are many identities. So the first things, for example, you can do... Just free transform in logarithmic coordinates, yeah. You can do free transform. I don't have exact formulas or not. But it's essentially the same function of t. It's kind of... Maybe multiply by exponent of log t squared. Let's do like this. Yeah, so if you make formula for free transform, you get the same function. Or you do something... Martin, can you write a little bit that t exponent raised to power of what? Exponent of log x or multiply by exponent of log t squared over h bar. I suppose something like this, yeah. Just look on critical point and get right formula. Yeah, yeah. So there are plenty of identities. Or there's a kind of... Again, you consider one-dimensional integral. Consider integrate. But t will be equal to 0 or to 1. So I don't have... It will be special value. If you want to calculate these things, then the critical values... Critical points will be x equal to... And... Of course, minus 1. Yeah, I choose first one. And the expansion near the first critical point is the following. Is equal to exponent minus 1 over 40 2 pi i squared over h bar. So what's the second critical value? Minus. Minus. It's conjugate number. Yeah. Then we get square root of some crazy algebraic number. Then we get h bar to... What is it? Square root of pi. Square root of h bar. Our rational powers of h bar also appear in this game. Sorry. No, no, not rational powers. It's an exponent minus h bar over 40. There's a pre-fact of h bar. Okay, but you have... Yeah, you get up to this square root of 2 pi h bar. You get these things. And this is also a legal expression in this game because you get exponent of rational number times h bar. Yeah, so it's one of identities. I don't know how to prove this, actually. I checked it on the computer. I discovered it on the computer, but... Yeah, so there are many identities. And again, if you want to remember about three manifolds... No, this one expression is equal to another. Yes, yes, I checked maybe 100 coefficients. No, I have an expansion about maybe 100 coefficients. So it's something like this. And kind of analogy is the following. What does mean the same thing appears in many ways? These three manifolds, you can make higar splitting... Make like a surgery of some note, whatever, in infinitely many ways. Infinitely many... Let's say, higar splitting of three manifolds. But it's definitely some kind of game independent of three manifolds and we should understand the source of all these identities between various expansions. Okay, yeah, yeah, so I just said... I didn't really show you any example of resurgence yet. Maybe... Just I want to draw some picture. I just want to keep. We have this equation for function phi, yeah? And let's call this operator y hat. And x hat will be f of x goes to x goes to f of x. Then satisfy quantum torus. You get quantum torus. And you get this equation. Go to classical limit. You get a curve. And this curve is equiblically 1 is equal to x plus y inverse. And when consider a logarithm of norma from c star squared to c, then this curve will be some kind of amoeba.  And it will be certain curve like this. And now what we do? Okay. What will be geometric picture? Now I won't kind of tell you what is geometric picture for this integral. You have, let's say, maybe in one variable. You draw this Lagrangian variety in c star squared. And intersect with some Lagrangian variety, which is straight kind of affine subspace in logarithmic coordinates. Because even consider graph of differential of this quadratic expression, you get affine Lagrangian subspace. So intersect. This thing is kind of various Lagrangian subspace, which are straight cylinders with rational slope. And now we do something similar in many dimensions. We will take many copies of this red guy. And we choose some kind of Lagrangian green guy. And this form said that this Lagrangian is a graph of differential of quadratic form. So it's open cell in Lagrangian-Grasmanian. But one can go to this kind of limiting case. Let's consider something, which is not a graph of one form, kind of a delta function in x variable. So what we're interested in? We're interested in just if you, in this kind of limiting case, when you replace this a, j by like infinite matrix, what you get, and have just one variable, you get the value of f at a given point. So what we are... Sorry? Yeah, no, no, no. The claim that it's this way of writing, it's really complete, because we have to do the second part. Oh, you mean if you have delta function? Delta function, yeah, yeah. So you need two Lagrangian. I need two Lagrangian. One Lagrangian is product of f, graph of differential of product of fx, you see. Yeah, okay, yeah. Yeah, so we should have this expression r. Yeah, just by definition of fx, for given point x you just get its exponential pre-factor constant square root of minus x, and then series with r0 of x. So consider given x in c minus 01, yeah. We get this guys rn, and we get sequence of numbers, yeah. And let's denote something like zeta, it will be 2 pi i log x. I assume that x is not a negative real number. Zeta is different from zeta from the upper number. Ah, it's not Riemann zeta, yeah, sorry, yeah. It's just variable zeta. I'm not complaining that this was another... Okay, now we want to do kind of Borel summation. We want to study series like this. For Borel summation we divide by factorials and make the claim, you get analytic continuation outside of something cuts. But first I just want to write your asymptotics for this rn, for latch n. Claim that rn should multiply by various things. Maybe it's called zeta with index x. Some things, zeta will be variable here and zeta with index x will be specific number. It will be position of singularity. Singularity in Borel plane. And now you do the following. You consider zeta x to power n divided by n factorial. And then the asymptotic expansion will be the following. If n is even and n goes to plus infinity, the asymptotic will be... fn is even will be 2 zeta x r1 divided by n minus 1 plus... Can you raise the blackboard? I'll raise the other one. So r1 at x. At x, yeah. Plus 2 zeta x, maybe cube. n minus 1, n minus 2, n minus 3. r3 of x, etc. And if n is odd, we get 2 divided by n r0 of x. Yeah. And if you've been on my second lecture, they're exactly the same things which happens with stealing, coefficients of stealing formula. And even coefficients have asymptotic control by small odd coefficients and vice versa. Big odd coefficients are controlled by small even coefficients. And what is the natural explanation? Sorry, what is on the left-hand side? There is no r, no rn on the left-hand side. Oh, sorry, sorry, rn. Right, yeah. Okay, yeah. Maron of x, yeah. So I get the things kind of depending on parameter x. The same things called uniformly. What here really goes on? It's a nearest singularity, yeah. And what is going on? Maybe I can use it first with both. Is there a sum on the left-hand side? Sorry? Is there a sum on the left-hand side? I don't know. That's for single term, right? There is no sum on the left-hand side. It's expansion for coefficients for large n, yeah. And these things come because we have, maybe, we have two even and odd, because we have two closed singular points. I will just draw the picture. So what goes on in the Barel plane? I get 0.0, when we start to expand our things. Then I get 2 pi i log x. And start to make a cut here. Then I take 2 pi i of log x plus 2 pi i. Again make cut. And then it will be 2 pi i log x minus 2 pi i. Cut and so on. Yeah, so I just continue cuts here. And I have opposite cuts. So the singularities are all branches of 2 pi i times all branches of logarithm and negative numbers. There are two arithmetic progressions. Sorry? Ah, no, no, it's for large n. It means that this will be the leading term. If we remove this for larger n, it will be this guy. Of course, for finite n, it kind of makes, it doesn't make sense, yeah. So I get this series at this point. Analytically extend to these things. And behavior near all these points. 2 pi i log x plus any integer times 2 pi i. May plus minus. This point is the following. It's called, I don't know, it's kind of like zeta m. Maybe zeta xm, yeah. This n plus minus, yeah. And the behavior will be the following. It will be, it will be holomorphic function of zeta minus, whatever, plus minus zeta xm. Plus, again, plus minus 1. I think it's maybe plus 1 up, half plane, minus 1 in the log half plane, times log of zeta minus this singularity. And multiply by the same series. So the jump will be the same function. It's like for sterling formula, you get just one series, which is appearing everywhere. Here it's the same story, you get the same one, story appears everywhere. Now that's, what? Yeah, sure. No, no, I started this lecture exactly to avoid this question. Now I have no answer to this questions. But I don't think this is a treatment. I have no idea. No, it's a space of a sort of connection. I have no idea. I have no idea what I'm talking about, sorry. Sorry, sorry, I don't speak this language at all, yeah. Connections, I don't know what it's going to be. Yeah, okay, yeah. I just mean this specific example, I don't think comes from a treatment. It's the same example. It's not given that that results in a treatment. Okay, yeah. I don't understand. Let's understand the model first. Yeah, yeah, you have this. Sorry? It's very akin to examples from treatment. And they're covered by your general situation. Yeah, just, now what goes on in H plane? It was barrel plane, now what goes on H plane, we should now make cuts just again exactly the same points, but now we make cuts going from zero. And my kind of resummed function, we should have analytic function in sector, and if we go through this corners, we make some transformations. What are these rays? Rays are exactly the same rays that started from zero. It will be stock's rays, yeah, infinitely many. And for example, one can now have function f up and f down. Choose two kind of opposite domains. So this function on f up, it's defined on a sector, but it's analytically continued to some larger guy. You, if it's always a function defined on a sector, in this formalism it's always extend to a larger, I think you add 90 degrees on the both side. So f up actually defined somewhere here. And f down is defined somewhere here. So you can compare them in left and right things. It's really very similar to what we have with Steering formula. And in terms of analytic wall crossing structure, I have kind of infinitely many transformations and I compose all of them. And to say that it's analytic, I want to say that it will be kind of analytic transformation, but it will be one by one matrix. Yeah, so what I'll have, I'll have one by one matrix and I have some jump formula for a kind of X in, let's say positive real number line. If you make the analytic continuation, you have certain jump formula f up of h bar is equal to f down h bar. It times some interesting product and similar formula for negative, I will skip it. Similar if you do not invert. You invert, you just invert variables. Yeah, like this, yeah. Where Q1 is exponent minus 2 pi i log X divided by h bar and Q2 is exponent of minus 4 pi square divided by h bar and assumes that h bar is kind of positive. Ah, ah, it's written as positive. Yeah, so things are very, very small. They get convergent series. They get convergent. It's not a formal expression. It's actually analytic function in h bar in this domain. So everything is well defined. Here we see some kind of Jacobi forms and when we make this product it's some kind of Laurent series into variables and you can see what monomials appear here. You get just two arithmetic progressions. But these two arithmetic progressions are exactly what we see that means you have here by applying central chart. When I apply central chart to this picture you get exactly this position. I cannot read what is in this picture. Coordinated somewhat. It's a look on monomials which appear in this expression. Ah, okay. Yeah, so the claim is this guy actually belongs to series in Q1, say, and Q2 divided by Q1. Yeah, it's formal power series, yeah. And the monomials which appear you get just two guys. And if you apply central chart, this is my lattice kind of square. I apply central chart. You get exactly the center points on left-hand side and right-hand side. You get these functions. These are actual analytic functions. And very easy kind of serial claim. These functions essentially the same as up to very small modifications. Fadeev dialogographies is actual analytic functions. And what's central chart? Sir? You mentioned central chart. Yeah, these numbers. It's map from Z-square to... Ah, it's just a value on the elements of the lattice. Yeah, yeah. I shouldn't ask about geometry. No? Ah, this is... I don't know. It's very geometric, yeah? Sorry? Ah, it's some interval, yeah, some periods of commode of pair, yeah. Something like this, yeah. Yeah, I think it's actually commode of pair. You take union of this variety. You have union of two curves. And consider periods of commode. Yeah, a gamma s will be kind of like h2 of c star-square relative to kind of red... This curve 1 is equal to x. That's why my inverse and union x is equal to 1. And you get interval to form commode of pair. And the interval to form will be this central chart. Yeah, so it's a very, very basic example, yeah. But it's kind of an upgrade of resurgence for Stirling formula, which... to the quantum-dolography. And somehow it's kind of new, yeah, because it was paper for logarithm of quantum-dolography, of the Schaeff and Gropholides, but not for dialog from itself. Again, we claim this... It's up to simple corrections. It's just a spadeev dialog function. Do you want to write what is it? Or maybe Yon will write it, yeah. I don't want to go to the sexual thing. Okay, so it's... This is a very simple game. This correction is a number which does not detect anything. It's some kind of... some very little something here, some normalization for this. Yeah, in fact, what I wrote, you said that it's a general pattern.  And there is something about extension, some nilpotent. I think which is really essential. And now I contradict to myself and go to three manifold stories. In three manifold stories, people have observed something very bizarre. You have a contribution for trivial connection and for non-trivial connections. And if you start a contribution for trivial connection, get expansion, then by this extended extension you see other non-trivial connection. But you never see trivial connection. And for trivial connection, you see all of them. So it's kind of... Stock synthesis is really asymmetric. Yeah, so it's... In a kind of simple example, if you get kind of gradient lines going one direction, it will be in another direction. Here it's asymmetric. You get certain... You see when you do... In a barrel plane. Yeah, yeah. So there is something... a bit funny here. Yeah, in all this quantum invariance, there's also... People write some kind of finite num sums. I don't want to go to this in general, but you do the folic. For example, you have n. You consider h bar is equal to exponent of 2 pi i over n. Oh, no, 2 pi i over n, yeah. And q... It will be root of 1. Close to 1. And then you do... Instead of integrals, you get kind of like finite sum. For example, you can see the function... Function on a finite set. 0, 1, n minus 1. Given by... At least your... What are values of this function? So value of this... q factorials. And then... Essentially, you get this a symmetric phi from this story. You should consider the limit when j over n goes to a constant. In integral 0, 1. You consider a very large n, consider a very large j. So this ratio... Say it's a number, then... You can see this story. And if you look on this function, it should satisfy some, again, q d from the equation. You can see the operator x hat. Here will be... You can see this matrix. y hat will be cyclic rotation. So x y hat is equal to q y hat. And it looks it will be solution of the same equation. But it turns out not. So if you apply this equation, this operator, and maybe called function phi n, I know again phi finite. Phi finite, you get vector 0, 0, 0, except the first term. You get some nonzero number, more or less one. So it means that it satisfies... It doesn't something nonzero, and it killed by 1 minus x. So the right equation, which satisfies this guy, is this guy, is this one. So one considers this q... Such q difference module, which will be reducible. It will be not simple module. It will be extension of... reducible q difference module. And... Okay, maybe I just draw the picture. What is the support of this module? If you go to classical limit, you add also vertical line x is equal to 1. So support will be this guy plus another vertical cylinder. If you consider classical limit, you get just union of two curves. Disjoint union of two curves. And now you want to solve this equation and gain wave function in this plane variable. And there will be one solution along one original curve. There will be the original dialog, but you get kind of another solution of this nonhomogeneous equation along vertical curve. But because it's vertical, it's better to use different coordinates not to project to y-coordinate. So now we should intersect with horizontal cylinder. y is equal to constant. And if you look what is going on, you start to solve the equation. If you consider Fourier transform, these things you get 1, 1, 1, function identically equal to 1. So it means that now you have the following equation. Minus 1 minus exponent of h bar y dy times y applied to some function psi is equal to 1. Because function 1 is killed by Fourier transform function 1 in y variable goes to delta function killed by this guy. And for this equation we need solution of the form psi is equal to psi 0 y h bar psi 1 of y that's all. psi i psi 0 psi 1 are polynomials in y. You substitute to get something like this, maybe make the following recursion. polynomial 1 and then for each n greater than 1 it says that psi n is equal minus sum over k equal to 1 to n 1 over k factorial y over dy to power k applied to y times psi n minus k y. If you substitute these things to this equation expansions in series in powers of derivative eventually get this recursion and you get again some things like this c0 equal to 1 then 1 is equal to minus 2 psi 2 is equal to minus y2 plus 2y2 and then maybe show a bit more these are really funny polynomials. You see here this kind of first coefficient is one of factorial and the last coefficient is factorial so things go up and down and again you get this polynomial and claim which is kind of not scientific yet is that for given y if you take sum over psi n y divided by n factorial z to the power n make this barrel transform it will be again analytically continued with singularities at what at very obvious things if you look things about commode of pair and periods dialogue of two plus integer times 2 pi i times dialogue of y plus integer 2 pi i squared so it will be shifted rank to letters by one amount and jumps will be certain integer will be certain integer stocks factors and you get your original guy yeah so it will be kind of like one extension of another and jump from this we know yeah and this is the whole picture but jumps so we are trying to calculate with Veronica on computer yeah it's quite funny but it's ah it's integer stocks factors and multiply by this guy okay yeah so you see that it's I think it's kind of really the simplest possible example when you have this extension behavior but we still don't understand it in whole totality yeah I think it's simpler than any whatever 3 manifold story you have it's really the most basic example and now I just want to finish kind of this very general remark about resurgence yeah you see rational functions, rational coefficients or polynomials with rational coefficients if you substitute rational number you get series with rational coefficients or and what is amazing that after dividing by 10 factorial you get to something whose singularity will be some interesting numbers and what I see we have examples in kind of 4 different kinds what's the original story when consider integral exponent of integral of let's say polynomial divided by h bar times some volume element and consider such guys then singularities will be difference between two critical values yeah critical value one minus critical value zero something like this it's difference between two critical values and if you start with kind of things of rational numbers you get algebraic numbers you get algebraic numbers or you get algebraic functions if you get things depending on parameters this case of dimension 1 I have now integral of have one form instead of function and here I get new things for example things I get singularities will be more general in periods of one dimensional integrals for some point to another point then here in this situation we see things like 2 pi squared dialogues 2 pi times logs yeah it's two dimensional integral and then 2 pi times logs by by by Cajay Iwaki and Marcus Marini we see that if you do something some grom of written invariance and some of some Galabios reforges compact or not compact then we get I think in local case we get 2 pi times two dimensional integrals and maybe three dimensional integrals for three forms of cycles in Galabios reforges in Marcus talk which is that even here we miss something should be maybe some periods of case resurfaces depending on parameters should be some kind of natural sequences of rational numbers of polynomials depending on some functions of rational functions of some parameters and said that singularities will be like periods of case resurfaces or maybe general two dimensional integral and definitely we have kind of next level complexity what comes next versus periods periods of high dimensional varieties appears singularities some barrel transforms, some natural gadgets defined to rational numbers ok thank you questions if a question about this last way there is an integrable system for this you vary your whatever what is integrable system here it's a bit shaky and here it's transcendental integrable system yeah about this kind of difference equation I had a comment 20 years ago we studied something which was very similar in fact your psi I guess is the exponential of the solution to a different equation and we were studying the inverse of the difference operator itself when you can write the inverse of the difference operator using decomposition but in reality in the background you just had decomposition of one of the hyperbolic tangent as a sum of simple poles so the consequence is that when you take the Borel transform of a simple pole you get an exponential and so we automatically get for the solution for the logarithm of your psi we basically get a series which proves that you can study the singularities and we get exactly that pattern and more or less it's meromorphic in the Borel plane but then when you take the exponential you can apply the rules of alien calculus and you understand this is one possible explanation for the resurgence phenomenon that you have pointed out here so I can show you the details but it's really strange to take lower pole to see it well maybe not exactly that because you have the dominant term with the i logarithm to remove first here just stop it exactly that can be we combine by generating series I mean there is a super trick at the moment I can show you more questions? no 0, 1, 2 its pair of complex programs somewhere 3 partially if your calabria is local but you still multiply by 2 pi i respect to integrals you add c star we have conic bundle and period of conic bundle okay more questions? thanks again for your questions


And he's moving towards the back post, but Jensen tries to catch out Netto. And there were some claims that that ball had crossed the line. A check of the watch by Bobby Madley, who's still looking down towards the equipment. And he's going to give the goal. Mateus Jensen catching out Netto. And again, Brentford come up with something special from a set piece. Solanke striding forwards, one-on-one with Ben May here. It's still Solanke looking to turn inside. And he draws Bournemouth level. What is 100th career Premier League appearance? Dominic Solanke makes it Brentford won, Bournemouth won. And perhaps you could say as well that it is a goal which has been coming. Well, he has been very threatening, doesn't he, Dominic Solanke? Christie. Another charge by Tavernier, but he won't get there first. A lovely pace of Rico. Henry's so good. The back pass though, woefully short. A chance to take the lead here for Bournemouth. And it is a chance that is taken by David Brooks. It is a gift owing to the mistake from Rico Henry, who shakes his head. And Bournemouth on course for a first Premier League victory under Andoni Iroola. Bournemouth, the goal to beat here.


Lagedo Gipai Matus, located within modern-day Brazil, is an incredible ancient site that just like Gornia Shoria within Russia, is of such a tremendous age and the stones incorporated into its structure are of such a huge size that mainstream academics passionately attest to the site being merely geological. However, the megalithic wall located at the site, which is uncannily similar to many others, each claimed as geological, yet the symmetry in the construction, the fact that the blocks are placed in what we now call stretcher courses, is a technique which can be seen within brick-built buildings all over the world. This unnatural, repetitive technique makes the walls the strongest possible using single-layer blocks to build with. It is highly unlikely that this repeating pattern would appear naturally, however, there are many other features at the site that not only prove it was indeed an ancient settlement, now all but eroded back to nature, dolmens of a similar age, which litter the site, are arguably proof of an artificial origin exposing what we have long claimed to have been a reality that a now hidden civilization's ruins are being actively dismissed as nothing more than geological features. The site is approximately 1.5 square kilometers, and is home to about 100 large rounded stones, each weighing up to 45 tons. Some of these stones have been placed upon tiny base stones, and others have seemingly been hollowed out from the base, making what is unquestionably some of the most intriguing ancient dolmens to be found anywhere on Earth. According to geologists who have explored the site, yet have seemingly ignored the evidence to suggest that many of these stones have artificial origins. The rock formation is the result of soil wear over millions of years due to natural cracks and large temperature variations. As aforementioned, the most curious and seemingly most famous block is the hollowed out dolmen, which is commonly known as the Helmet Stone. Additionally, along with the Neolithic dolmens which litter the site, on some of the stones there are cave paintings, which are attributed to the Carriere Indians who lived in the region about 12,000 years ago. Legend has it that later the site became the home of someone known as the Hermit Healer, an individual claimed to have lived in the region in around the 18th century. Many people from this area sought his consult, yet any concrete evidence as to who this individual was, or what they were capable of, has eluded modern understandings. We feel that due to the stretcher courses found within the megalithic wall, currently claimed as a natural formation, along with the evidence at the site of Neolithic dolmens, with surviving art which also dates from this era, are all compelling proofs of an artificial, advanced yet ancient and now hidden origin. Who built Legerogipaimatus? What was the site's original purpose? Just how old is Legerogipaimatus? Thankfully, the more people who explore the site and collect and compile photographic studies, the closer we will get to finally answering these burning questions regarding our past. It is a site which we find highly compelling.


Welcome to the presentation of the STM32H7 Master Directory Memory Access Controller, or MDMA. It covers the main features of this module, which is widely used to handle data transfers. The Master Direct Memory Access, or MDMA, is optimized for data transfers between memories, since it supports linked list transfers that allow performing a chained list of transfers without the need for CPU intervention. This keeps the CPU resources free for other operations. The MDMA controller provides a Master AXI interface for main memory and peripheral registers access, system access port, and a Master AHB interface only for Cortex-M7 TCM memory access, or TCM access port. Each of the DMMA controller channels provides a unidirectional transfer link between a source and a destination. Each channel can perform single block transfer. One block is transferred. At the end of the block, the DMMA channel is disabled and an end-of-channel transfer interrupt is generated. Repeated block transfer. A number of blocks is transferred before disabling the channel. And linked list transfer. When the transfer of the current data block or last block in a repeat is completed, a new block control structure is loaded from memory and a new block transfer is started. The MDMA also features incrementing, decrementing, or non-incrementing or fixed addressing for source and destination. The size and address increment for both source and destination can be independently selected. MDMA is useful to collect data from other DMMAs, DMA1, DMA2, and BDMA, and make data available to the CPU in the D1 domain in DTCM or AXI SRAM. DMA linked lists are used to perform a set of DMA transfers without the need for a CPU intervention. Can be used to prepare data for other DMMAs and then set the DMA configuration to start transfers. It is used to support scatter and gathering. This means that the source and destination areas do not need to occupy contiguous areas in memory. The source and destination data areas are defined by a series of linked list descriptors that control the transfer of data blocks. It can be used to pass data to a JPEG decoder and DMA2D to accelerate image drawing. The MDMA supports incremental burst transfers. The size of the burst is software configurable up to 128 bytes. For larger data sizes, the burst length is limited, as to respect the maximum data burst size of 128 bytes. For example, 16 by 64 bit or 32 by 32 bit. For the TCM memory accesses, the burst access is only allowed when the increment and data size are identical and lower than or equal to 32 bits. The size is selected using the TRGM 1 to 0 trigger mode selection field. The size of the data array to be transferred for a single request will be the buffer transfer size when the TRGM or trigger mode equals 00. The size of the data array to be transferred for a single request will be the block size when the TRGM trigger mode equals 01. The size of the data array to be transferred for a single request will be a repeated block when TRGM equals 10. The size of the data array to be transferred for a single request will be a complete channel data until the linked list pointer for the channel is null when TRGM equals 11. Each channel has programmable priority. If two channels have the same programmable priority, the lower channel number has higher priority. An arbiter manages the MDMA channel requests based on their priority. When MDMA is idle and after the end of each buffer transfer, all MDMA requests, hardware or software are checked for all enabled channels. A buffer transfer is the minimum data size to be transferred by the MDMA without starting a new arbitration between MDMA channel requests. In case of a block transfer, after transferring an individual buffer, the MDMA will enter into a new arbitration phase between new external requests and internally memorized ones. If no other channel request with a higher priority is active, a new buffer transfer will be started for the same channel. Higher level MDMA requests will not be blocked for more than a buffer transfer period as the channel arbitration is performed after each buffer transfer. Two data array size parameters have an impact on MDMA and application responsiveness. One buffer transfer size. Data transfer lengths which are uninterruptible at the MDMA level from other channels requests. It is the length of the data to be transferred on a channel before checking for MDMA requests on other channels. Two burst size. It defines the maximum data transfer length which may be uninterruptible at the bus arbitration level. It is the length of the data transfer which may be transferred in burst mode. It may block other masters from gaining access to the bus. It is important to select the correct burst and buffer transfer size considering the real-time requirements for other MDMA channels and masters. A buffer transfer is the minimum logical amount of data up to 128 bytes which is transferred on an MDMA request event on one channel. An MDMA buffer transfer consists of a sequence of a given number of data transfers done as single or burst data transfers. The number of data items to be transferred and their width, 8-bit, 16-bit, 32-bit or 64-bit are software programmable. The length of the burst used for data transfers is also programmable independently. After an event requiring a data array to be transferred, the DMA peripheral sends a request signal to the MDMA controller. The MDMA controller serves the request depending on the channel priorities. The request is acknowledged by writing the mask data value to the address given in the mask address when these registers are set. A block is a contiguous array of data up to 64 bytes which is transferred by successive buffer transfers. Each block of data is defined by the start address and the block length. When a block transfer is completed, one of the following three actions can be executed. If the block is part of a repeated block transfer, the block length is reloaded and a new block start address is computed based on the information in the CXBRUR register. If it is a single block or the last block in repeated block transfer, the next block information is loaded from the memory using the linked list address information from the MDMA CXLAR. If it is the last block which needs to be transferred for the current MDMA channel, MDMA CXLAR equals zero, the channel is disabled and no further MDMA requests will be accepted for this channel. The block repeat mode allows repetition of a block transfer with different start addresses for source and destination. When the repeat block mode is active, repeat counter is not equal to zero, at the end of the current block transfer, the block parameters will be updated. The BNDT value reloaded and SARDAR values updated according to BRSUM-BRDUM configuration, and the repeat counter is decremented by one. When the repeat block counter reaches zero, this last block will be treated as a single block transfer. The linked list mode allows loading of a new MDMA configuration. CXTCR, CXBNDTR, CXSAR, CXDAR, CXBRUR, CXLAR, CXTBR, CXMAR and CXMDR registers, from the address given in the CXLAR register. This address must address a memory mapped on the AXI system bus. Following this operation, the channel is ready to accept new requests, as defined in the block repeated block modes above, or continue the transfer if TRGM 1 to 0 equals 11. The trigger source can be automatically changed when loading the CXTBR value. The TRGM and SWRM values must not be changed when TRGM 1 to 0 equals 11. The channel configuration or channel link address LAR must be in the AXI address space. LAR value must be aligned at a double word address, such as LAR 2 to 0 equals 0X0. This table describes the MDMA requests and their mapping to devices. An MDMA channel can be triggered by the end of transfer of the DMA1 stream. In response to this trigger, the MDMA can perform data transfer from SRAM D2 to D1 RAM, or reprogram the DMA1 0 flow for a new transfer. To enable the MDMA to efficiently offload the CPU, MDMA channels can be triggered by device interrupts to automate data exchanges and processing. Examples of peripheral triggers are described in this table. For each MDMA channel, an interrupt can be produced on the following events. Channel transfer completed. Block transfer completed. Block transfer repeat completed. Buffer transfer completed. Or transfer error. The MDMA is active in run and sleep modes. DMA interrupts will wake the STM32H7 from sleep mode. In stop mode, the DMA is stopped and the contents of the DMA registers are retained. The DMA is powered down in standby mode, and the DMA registers must be re-initialized after exiting standby mode.


Baw, what's up everybody? Once again, it's Brandon Van Sean and we got to talk about the underdog theory and how people like Lil Wayne, Gary Vee and even Tyra Woods have used it to their advantage. So first, what inspired this video? Well, let's look at the fact that Lil Wayne is one of the biggest artists of all time. This guy was killing the game in the early 2000s, no competition, but oddly enough to be as big as he is when the Carter five dropped. This guy was looked at as an underdog. Most people get that big and they're overrated and people get tired of them. They've been winning. They've been winning. People could care less if you win again. That's just a day's work for you. But then Lil Wayne had them issues with baby and he couldn't get his business together. There was all this suing going back and forth and the project got delayed about three years. At least Lil Wayne kind of got positioned in the public as the person being bullied in this aspect. He couldn't release his own music. That reposition, this man who had been the overdog for so long has an underdog all over again and people were rooting for him when Carter five drops. Even people that weren't die hard fans at least just wanted to see him stick to land it. It didn't have to be great. It just needed to not be trash. And then another example is Gary Vee. Many of you probably already know him. But if you don't know, he's a marketing influencer. You can check him out on social media at Gary Vee. And he's also the CEO of VaynerMedia, a company worth over $150 million. He has all kinds of investments. Do got money. Still, you find it where a lot of people are rooting for him to be successful and to keep going, keep going. First of all, he does humanize himself and he's constantly grinding. He's showing you that he's put into work and he's helpful for people. But he also uses this positioning as an underdog by projecting this huge vision. What you talking about, Sean? For anybody that watches Gary Vee relatively often, you know the fact that he loves the Jets and not only does he love the Jets, he wants to buy the Jets one day. And although he's rich as hell, he's not anywhere near in a position to buy the Jets yet. At least that's what he says. I ain't the IRS. And the fact that he's still chasing a goal that so far away allows people to join him in his journey and to see him as an underdog who could one day become successful overcoming that goal.  Of course, another example is Tiger Woods. The man was a beast just dominating the game for so many years. But then he had one of the most interesting nights of his life to say the least. And ever since then, the divorce, the public backlash, his injuries has just made his way back to even being able to play golf difficult and him winning again is just a sight for people to see. The last match he won had people so excited just to see him back. And it was a sight to see. So what's the point of this? I know a lot of people who are on the rise are obviously an underdog. When you see the public the first time, you're going to be the underdog like Harubi was an underdog coming from the strip club into the successful Cinderella story. But as you see her up top for more and more time, you will see her position as an overdog. She will need a new mountain to climb and to be able to communicate that vision to the public. For them to then look at her as an underdog, breaking new barriers. Russ does this with his audience by making himself a rage against the industry, the industry's this big giant, this nebulous giant that isn't necessarily even real, but he creates this enemy of sorts that allows people to rally around him as an underdog against it. And Madem did the same thing back in the day actually. As a matter of fact, he was a bully for the most part. He was bullying these individuals, but still painting them as a part of this grand industry, which was the giant. So once again, how do you position yourself as an underdog? First of all, if you're new to the game, you are an underdog already, but you can make it even stronger if you have a story and communicate that rise just like Cardi B's story from being from a strip club. And they talk and a lot of people being able to talk about those stories because they knew her in that time and watching her rise to who she is today. And then if you already have a little bit of cloud and you've had that for a while, you need to create a new mountain, a bigger mountain, from where you are now. In the same way, Kanye did hip hop and then he did the fashion industry. He's constantly talking about these bigger grand goals that help those people who are super Kanye stands feel like there's some other place to go and there's a new battle to fight. And of course, I want to know what you guys think. So put the things in your brain in the comments below. And of course, you guys know every Sunday I answer questions on G. So follow me at brand man Sean. And other than that, if you liked this video, go ahead and hit that like button. If you like it, mind as well, share it and if you're not subscribed, you know what to do. Hit that subscribe.


Rooster now up against Zanka, one-on-one. He's got Fraser in Ocean to space. Fraser running onto it, and Bournemouth double their advantage in the first corner of the game here. It came from a Huddersfield mistake on the half-way line, but Bournemouth made them pay. Two-nil. Cherry's over the top, looking for Defoe, trying to sneak in to paint the phone. In behind, what a shot of goal! What a goal! Oh, goodness. Jemba, who, from an impossible angle, right-footed, has lofted it over Spironi and has silenced the whole of South London. College two, Bournemouth two. Fraser. And Codd! Incredible stuff. That's why we love this league, that's why we watch it. That's why everyone's come out here today, just praying for this.


Welcome back to my channel and welcome if you're new here. It is Monday, so it is meal prep day I have three absolutely fantastic recipes for you We are going to be making a delicious breakfast lunch and a really good cake Yes cake inspired snack that is whole real clean food and WW friendly So if you want to see what I have in store for you for this week's meal prep stay tuned For breakfast this morning, I'm going to be making strawberry Shortcake oatmeal. I'm so excited about this really good whole food real ingredients. I cannot wait I'm gonna pair this with some eggs that are zero points on the blue plan So let me first show you where I found the recipe and secondly what is in this week's breakfast? So this is the cookbook that I picked up not too long ago I showed this into what I eat in a day. This is the instant loss eat real lose weight cookbook from Brittany Williams Now she's lost about 125 pounds And so she put out this cookbook that has a lot of instant pot air fryer recipes Now, of course, you can always take an instant pot recipe and cook it on your stove or an air fryer recipe and cook It in your oven, but she does a lot of instant pot air fryer recipes So today's is actually going to be made in the instant pot But again, you can simply make it on the stove if you don't have an instant pot regardless I highly recommend her cookbook. There are seriously some Fantastic recipes in here. I cannot wait to make today's breakfast. So this is the cookbook that this recipe came out of I will link this down below for you guys So let's get into what is in our strawberry shortcake oatmeal first You're going to need some milk or milk alternative of your choice I'm going to be using my favorite forage or cashew milk. You'll also need some world oats mine came from thrive I've talked about this a lot, but if you're new you guys check out the thrive marketplace It's an online market Everything that they sell is good food organic delicious at Fantastic prices right now. They have a promotion where if you sign up for a membership and you guys the membership is so cheap It's about five dollars a month for the year membership You will get twenty dollars of free products of your choice Every order will include free products, which is amazing. They throw things in there so you can try different things Which is really nice and it's always for free and you get free shipping. You can't beat it There's a link down below to join the thrive market Highly recommend especially if you want to recreate a lot of my recipes because I'm going to be buying a lot And I already have through the thrive market because I'm literally obsessed with it So these are the organic rolled oats from thrive. You always want to if possible buy your oats organic They are heavily sprayed with glycosate, which is the active ingredient in roundup So oats are one thing that organic is best and thrive has a great deal. So this is a big bag of organic rolled oats You'll want some flaked coconut unsweetened and this is optional to top your oatmeal with I am going to do this because I love Coconut and I think it's going to add a nice texture and flavor to the oatmeal pure maple syrup coconut oil salt of course some strawberries and Lastly some vanilla extract. So let's pull out the instant pot and let's make some oatmeal All right. So the first thing we need to do is do our strawberries. So I have my organic strawberries here We're going to go ahead and chop these up I'm going to place them here in a Ziploc bag because we need to mush these up before they get added to our oatmeal So I'm just going to put the strawberry pieces in here and then kind of smash them up in the Ziploc bag So let's cut up some strawberries So So let's get everything into the instant pot again if you don't have an instant pot You can simply cook this the same way on your conventional stove So in my instant pot, I'm going to be adding two cups of my cashew milk And I added one half of a cup of water as well just to kind of thin it out and save a little bit on the smart points I'm also going to add one cup of my organic rolled oats from Thrive I also have my squished up Strawberries and we want about a cup of strawberries now I figure if this is a little more than a cup I'm not mad about it because I love strawberries and strawberries are zero points So if you add a little more no fret there We're also going to add a little bit of vanilla extract. So about a teaspoon worth or so of the vanilla extract We also want to add just a pinch of salt just because that helps bring out a lot of the sweet flavors And then the last two ingredients are going to be Organic maple syrup we want two tablespoons on my tablespoon here And I'm going to put in my two tablespoons of maple syrup That along with the strawberries is what is actually going to make our oatmeal nice and sweet And this is such a great option for a sweetener And then the very last thing that we want to put into our oatmeal is one half of a tablespoon of our coconut oil So we're gonna go ahead and add one half of a tablespoon of Coconut oil and that's also going to add that little bit of fat here to our oatmeal and make it nice and creamy and delicious Once everything is added you just want to take a spoon and just give that a nice stir by adding that coconut oil It's going to make it so the oatmeal doesn't stick to the instant pot So that's nice. You don't have to worry about it all sticking to the bottom of the instant pot So you're just gonna give that a quick stir, and then we're gonna go ahead and put our lid on our instant pot We're gonna set this on high for eight minutes, and then we'll go ahead and release it when those eight minutes is up Pop the lid off of our oatmeal. Oh my gosh. Yum Look at how good this looks it smells So good in my kitchen. It's strawberry dream in here So I'm going to let this sit for just a couple of minutes And then we're going to put this into our meal prep containers And I'll be back to show you what I'm having for breakfast and give you the smart points So I've let my oatmeal cool for just a few minutes you guys look at this Yum, and I'm not kidding when I tell you it smells so good So I it makes for serving so I have four of my meal prep bowls here So what I'm gonna do is start with a half of a cup of the oatmeal per bowl Because I want to get as close to an even amount each day that way I don't have more one day and less another so I went ahead and started with the half of a cup I'm gonna go ahead and fill all four bowls, and then I'll go back with that same half of a cup and We'll keep going until we're out of the oatmeal mixture. So I still have quite a bit left So I'm gonna go I think I'll go about half so about another quarter of a cup I'm not sure that I'm gonna have enough here for a full half of a cup but I'm just gonna keep going until my oatmeal mixture is gone and then everything will be nice and even and Then I'll show you exactly what I'm gonna do for breakfast and kind of talk about What I'm gonna choose to top my oatmeal with and we'll go over all of the points. So here is breakfast for the week you guys I'm really excited. I wish you could smell how good this oatmeal smells And you're getting some good fats with that coconut oil. I can't wait for this It's going to be a filling delicious breakfast So I went ahead and divided it out evenly into four bowls It ended up being just shy of a cup of oatmeal purple And then what I'm going to do is top it with about a teaspoon of these organic unsweetened coconut It's zero points for a teaspoon if you go up to a tablespoon you it's only one point So you could do a whole tablespoon and just add a point But I'm just going to do a teaspoon of this for zero and just top my oatmeal with that And then I'm going to pair that most likely just with one or two eggs So just kind of depends on how fast I need to get out the door as far as eggs go and then eggs on blue plan are zero points So as far as points go the oatmeal itself is five points on both blue and green and only three smart points on the purple plan Now for the coconut it's zero and if you're on the green plan, of course You need to add points for eggs But for me this is going to be a five smart point breakfast for lunches this week I'm going to be doing an Emily bites recipe But I am just making a few modifications to make it a little bit cleaner a little bit more whole fat full fat food So let me show you what is in our Emily bites Pimento chicken cheese salad You're going to need some mayo I am going to be giving you the points with light Substitutions for those of you that aren't following a whole fat clean food diet I'm going to give you the points as well so that you can work this into your plan But I'm going to be using the chosen foods mayo I am going to be using non-fat Greek yogurt just because I want to make sure that I use this up And I figure the amount that's in this whole recipe no big deal that it's fat-free save myself a little bit of points I'm also going to be using this organic light whipped cream cheese from Trader Joe's Pimento's the cheese that I'm using is this shredded mozzarella from Trader Joe's Spices you're going to need some paprika onion powder garlic powder Salt and pepper and then of course some chicken This is just the simple truth organic chicken breast that I hauled in this week's grocery haul And I'm actually going to put my chicken salad on one of these azequiel pita breads I got these at my local health food store. These are only two smart points apiece So I figured this was a better point buck than two slices of bread that would cost me four points So I'm actually going to put my chicken salad in one of my pita's so let's get started on this week's lunch So the first thing we need to do is cook our chicken So I just went ahead and sprayed my pan with some non-stick cooking spray I'm going to cook this chicken down Until it's fully cooked through and then we'll shred it up with a fork And this is going to be what gives us that chicken salad texture and while this is cooking We'll put together the rest of the ingredients for the chicken salad all right while our chicken's cooking You can actually hear it in the background. We're going to go ahead and make the sauce for our pimento salad sandwich So what I'm going to be adding is all of the rest of my ingredients So I'm going to start with two ounces of cheese. I went ahead and weighed this out on my food scale And again, I'm just using mozzarella You could use light cheese fat for you whatever you prefer and then the recipe calls for about two tablespoons of Pimentos I went ahead and just did the jar that I bought it was a pretty small jar and it ended up being about Two and a half tablespoons so close enough and then also on my food scale I weighed out two ounces of my whipped cream cheese and you want your cream cheese to be at room temperature That's going to help it mix a little bit better with all of the rest of the ingredients And then in my bowl here I have all of my seasonings so salt pepper paprika onion and garlic powder Doesn't that look pretty and we're going to go ahead and add in all of those seasonings and then lastly We have one quarter cup of the non-fat Greek yogurt And that's just going to add some extra moisture without adding any extra points And that's kind of why I decided to be okay with the Greek yogurt being non-fat Also, because it is only a quarter of a cup And I'm gonna get a lot of fat in this quarter cup of the chosen foods avocado oil mayo So I'm gonna go ahead and add that as well And then we're literally just going to mix this all together And then we're gonna put this in the fridge set it aside until our chicken is done And we've got it nice and shredded and then we're just going to add our chicken directly to This sauce for this chicken salad. So I think this is gonna be really good This is pretty wet as far as the sauce that we're gonna add the chicken to so I think it's going to give it a nice moist creamy texture and then we're just going to have this filling directly to our bread or our Pita pocket so pretty simple as far as the main portion of our lunch So I'm gonna go ahead and throw this in the refrigerator until our chicken is done. All right, the chicken is coming along I just keep kind of flipping it as it's frying up in a pan It is just about done and then I'm just gonna go ahead and shred it up really quick with a couple of forks You can also use your hand mixer. Whatever is easier. This is just three chicken breasts So it's gonna be super easy with some pork and then we'll be ready to add it into the sauce that we made I was young and I won't still care for the void We don't need to pass in our lives for tomorrow So I went ahead and shredded up all of the chicken. It looks delicious. I'm not a fan of boiled chicken I think it makes it spongy So I like to just kind of cook it in a pan get it nice and crispy and then shred it up And then here I have the sauce so very very simple We're just going to add our shredded up chicken directly here into the sauce And by the way, the sauce smells really good with the pimentos and everything yum So we're just gonna go ahead and add that in stir it up And voila, we have an emily bites pimento cheese chicken salad sandwich So very very simple. You can serve this warm or cold. I'm choosing to serve it cold So I'm just going to divide this out evenly Into my containers and then I'll just add it directly into my pita bread at lunch time But look at this doesn't that look really really delicious? So let's put together exactly what we're having for lunch All right, so let's put together meal prep. So first I have the Chicken salad.  These are the leftover strawberries from breakfast I went ahead and just wash them and cut them up and then again I am serving this on the Ezekiel pita pocket So basically what I want to put into my meal prep container is my salad And I have to get five servings out of my chicken salad So I'm going to be as careful as I can to make this Five servings because I want the points to make a lot of sense So I'm going to go ahead and add about one fifth of the chicken salad And then I'm just going to pop in some strawberries and I'll divide these strawberries out as well over the five meal prep containers and then each day I will put together a Sandwich with the Ezekiel pita pocket have some strawberries and then I may have something for dessert I'll show you that when I show you my snacks, but let's put these meal preps together And then I'll give you the smart points What do we do to love the lunch meal prep is done doesn't this look so good you guys I'm so excited So let's go over the points the chicken salad made five servings So on the blue or purple plan it is five smart points and this is without the bread So this is just the chicken salad if you use the chosen food mayo If you choose to go with a light mayonnaise, you're going to save yourself a point And it's going to be four smart points And then you would add the points for whatever bread you choose now on the green plan the same principle applies But it is seven smart points just for the chicken salad Without the bread if you choose the chosen foods mayonnaise or you can have it for six points If you choose a light mayonnaise so essentially by going light mayo you're going to save yourself a point So that's totally up to you But for me, this is five smart points for the chicken salad Each one of these pita breads is two points So that's going to be seven smart points for my lunch and that includes of course the strawberries which are Zero so seven smart points for this week's lunch for a snack this week. I'm so excited about these I'm going to be making a no bake cake ball. Yes, my friends. We're making cake on w w It this comes from another really fantastic cookbook So I'm going to show that to you guys too. This is the other cookbook I bought This is the true roots by Kristen Cavalleri. Oh my gosh, you guys I am obsessed with this cookbook You can see all my papers. I mean that's how many recipes that I want to make she follows Just a well here a mindful kitchen with more than 100 recipes free of gluten dairy and refined sugar So basically she follows a really whole food approach to her recipes So I can't wait to make this this I will link down below for you guys as well Highly highly recommend. I love both the cookbooks, but this one I mean look at this. I am so excited about this one. So I'll link that down below for you guys This is where the recipe came from So what is in our cake balls is first you're going to need some almond flour So you saw me haul this this last week from trader joes You'll also need some coconut flour again. I got this off a thrive Best price you guys definitely check out thrive. That is linked down below as well for you Also some coconut sugar. This also came from the thrive market. Love coconut sugar It is the best sugar as far as regular sugar that you can use It's made from the palm of the coconut so it has a low glycemic impact on your blood sugar Fabulous love love love it. You're going to need some almond milk. I'm using my favorite forager cashew milk vanilla extract salt Coconut oil and maple syrup. So let's get started on these no bake cake balls We're ready to start these cake balls. You guys I'm so excited for this So first I'm going to go ahead and add my one and a half cups of almond flour I'm also going to add in one third cup of coconut flour And then I'm going to give this just a quick kind of preliminary stir I just want to make sure those two flowers get nice and combined Coconut flour tends to suck up any moisture So I want to make sure that I just don't have a big ball of coconut flour That's going to suck up all these wet ingredients So I want to make sure it's mixed in really well here with the almond flour And then from there, we're going to go ahead and add one quarter cup of your milk of choice your almond milk We're going to do one teaspoon of our vanilla extract We want just a pinch of salt again. That also helps bring out the sweetness I went ahead and melted down three tablespoons of coconut oil So we're going to go ahead and add that get all that out of there And then lastly I have my maple syrup here I went ahead and measured out three tablespoons of maple syrup Now the best way to do that is on your food scale.  You should have a dough like consistency So it shouldn't be too wet, but it also shouldn't be too dry Because we need to roll this into little balls, which then makes these cake balls So I'm so excited. The recipe says this literally tastes like cake. So I'm here for it So let's get this nice and mixed together. We'll start rolling these out We're actually going to roll these in the coconut sugar before they go onto our sheet pan But look at that. It already actually looks like cake batter. So we're ready to roll these out We want to get about 18 cake balls. So I'm not sure the size I'm going to have to try to Wing it a little bit and get as many balls as I can if I get more than 18 great It'll just lower the smart points, but my goal is 18 So I'm going to go ahead and roll out the little cake ball And then we're rolling it in the coconut sugar.   I actually ended up getting 23 So these would be pretty good size if you only got 16 And I also wanted to show you this is how much sugar I have left So this was a quarter of a cup and I probably use half of that I probably used about an eighth of a cup of sugar So with using less sugar and actually getting 23 cake balls instead of 16 It actually cut the point in half, which is awesome So each one of these little cake balls is two smart points Originally my recipe they were four But because of cutting down on the sugar And getting more cake balls rolled out it really cut those points in half So each one of these is two smart points full of really good whole ingredients You've got some fat in there from the coconut oil. Oh my gosh. I'm excited about these I'm going to throw these in the freezer for about an hour You want to get them nice and hard and then we'll throw these into a container with a lid And we'll just store them in our refrigerator So here are my snacks for the week. We're keeping it simple. I generally have a smoothie So that's why I have really limited snacks here. Again. I don't eat all of these every day I like to change it up, but I've been loving my smoothies and I've been loving this cottage cheese combo So what I've been using is this good culture whole milk cottage cheese. You guys this cottage cheese I don't know what it is about it. It's a very small curd. It's nice and thick here I'll show you guys you have to see this. So see it's nice and thick. There isn't much liquid in here Oh my gosh. I seriously love this cottage cheese. So I have one serving of this cottage cheese And it is three smart points. So One half of a cup three points. There's your nutritional information Really really good ingredients seriously the flavor There's no comparison between lighter fat free cottage cheese and this cottage cheese I take this any day of the week. There's 14 grams of protein So I'll have that for three points and then I'll pair that generally with one or two points worth of my crackers I'm obsessed with the simple mills brand. These are the rosemary and sea salt I picked these up off of thrive Again, another great reason to join the thrive market. These are so good and also from thrive These are really really good as well. These are the mary's gone crackers Super seed everything crackers. These have good ingredients. These have amazing ingredients like nothing Questionable at all really really good ingredients and you guys they're so good and hearty Oh my gosh, they're just full of seeds really really good So I like to dip those in my cottage cheese so good So that'll be one snack and then of course I always like to have a belt bar So I went ahead and pulled two out for you this one the black cherry chocolate These are three points So the majority of the bill bars are three points with the exception of any of the bars with nuts But then there's an exception to that So all of the bars are three points including the coconut almond Any other of the nut base bars like the peanut butter here The toffee almond those are all four points because of the nuts now for me I'm okay taking the extra point for the peanut butter because one it's delicious and two It has 20 grams of protein seven fiber and seven grams of fat So it has more fat in it fiber and protein which keeps you full and It's made with organic peanut butter with little chunks of peanuts. So I like the nut base bars I'm more than willing to spend the extra point But in the event that I want to save a point or just want a different flavor These ones are also a great option for three points. They have 15 grams of fiber Or fiber protein that would be a lot of fiber 15 grams of protein six fiber and four fat So still a really really good option. I love the bill bars. They are not a clean food They do have a couple of questionable ingredients But like I've always said for these smart points, you're not going to find a better bar for your smart point bang buck Buck bang whatever you're not going to find a better protein bar for the smart point value than the bill bar So I highly recommend them if you're interested I do have a code for them that will get you 10 off and free shipping It's here on the screen and there's also a link down below if you click the link It'll automatically apply the discounts and the free shipping. So check out bill bar. It's just nice to have these on hand They taste really really good like a candy bar and again for the smart points Slash the ingredients. These are a great option. So those are going to be this week's snacks Thank you for joining me on another weekly my w w meal prep if you're new to my channel welcome Just to let you know, I do follow the blue plan on w w But I do take a clean approach to my eating which means that I try to eat as clean as possible Little to no processed foods. No sugar free fat free light anything I try to just eat food in its most natural state whenever possible So that is kind of the plan that I follow here on my channel So these recipes fall right in line with that speaking of recipes They are all linked down in the description box below for you As well as all of the links and discounts to some of my very favorite things And the link to come on over and join my facebook group. We'd love to have you be part of our community We are almost 15 000 strong and it is a very loving supportive Wonderful place to be lots of great ideas tips and tricks are shared there So come on over and join us if you're new welcome welcome Make sure you're subscribed and your notification bell is turned on so you don't miss a single video If you love meal preps give this video a big thumbs up It really helps out my channel and of course leave those comments down below I want to know which of these recipes or all of them are you super excited to try Thank you so much for spending some of your monday with me and i'll see you in my next video. Bye guys