So, last week we discussed, we were discussing Chen-Simon's theory, pure Chen-Simon's theory, and we discussed a very useful correspondence between 3D Chen-Simon's theory, two-dimensional chiral algebras, and essentially the point was that once we have this tool, essentially this tool with some more technology that we have not explained, allows us to understand all properties of the Chen-Simon's theory that we are interested in and to perform computations in this theory, in particular to compute all correlators that we might be interested in. Now we mentioned a small piece of this correspondence, in particular we say that if we are interested in what is the spectrum of lines, and there is pin H, we can read it off the chiral algebra because this corresponds to the irreducible representations or integral representations of this algebra, and the dimension, the conformal dimension of the primary, these were H lambda, and H as the dimension of H lambda, mod 1, because the spin is defined mod 1. So, and then this correspondence goes on, and there is more structure here, and one can use to compute everything we want in the Chen-Simon's theory, in particular the Chen-Simon's theory is a solvable theory, one can use these to compute everything we want, and so this allows us to show and prove, we will not prove it but it can be proven, the first duality that I want to present which is 11 rank duality, and so in our definition of Chen-Simon's theory we start, so we have a Lagrangian definition, so we start with some gauge group G and some level K, but what it might happen is that, so we start with two descriptions that look different, so different gauge group, different level, but nevertheless the quantum theory is the same, okay, and 11 rank duality is one example of this phenomenon, in particular it turns out that SUN at level K, let us use this symbol now for a duality, is the same theory, the same quantum theory as UK level minus N, okay, so these of course look different, the group is different, the level is different, but the quantum theory is the same, in particular the spectrum of lines is the same, and all the correlators between the lines if used the dictionary is the same, and this duality as I said this can be proven because both sides are solvable and you can solve them and you can see they are the same, in particular what you can do is to see that both descriptions lead to exactly the same carol algebra, and so if the carol algebra is the same everything that you compute with it is going to be the same, okay, we will not go through the derivation of this, the reservation essentially starts with the two dimensional bosonization, so the fact that free fermions can be described with a WZW model and then one has to do some manipulation and one can prove this, now just to give you some flavor of this duality we can have a look at what is the spectrum of lines, so we analyze this case because one example that we gave of this was the example in which the group G was simple, compact, connected and simply connected, so SON is in that class and we said in that case two dimensional carol algebra is a fine, the algebra at level K and we said what are the integral representations of this, in particular where representations where if you take the weight, the highest weight of the representation and you take the product with the highest root, this has to be smaller or equal to K, now if we translate this in the case of SON what we find is the following, to remember for SON we can represent the representations or if you want these sets of dinky labels in terms of young diagrams, in particular for SON the young diagrams will have two, if I have some young diagram here, so the young diagram should have at most N minus one both, so the height of these columns should be at most N minus one, I'm trying but it looks the same, the young diagrams, so first of all young diagrams that representations of SON should have at most N minus one boxes in the columns and then this condition means that the number of columns should be at most K, so essentially the lines in SON level K are all the young diagrams that you can draw inside the rectangle with size M minus one and K, now we have not discussed this case here but one can, because this group is not for instance simply connected but one can do a similar thing here and it turns out that the lines here up to a small subtlety that I will mention in a second can also be classified integral representations by young diagrams but this time the number of boxes in the columns should be at most K and the number of boxes, the maximum length of these rows should be at most N minus one and so the map of the lines is that you have to take this young diagram and flip it along the diagonal and then it will fit in here, so it's the same rectangle but it is flipped along the diagonal, is this clear? I would like to make two comments about this duality, the first comment is a technical remark, it is the fact that really this duality is not a duality of standard Chen-Simons theories but it's a duality of spin theories or spin Chen-Simons theories, so I don't have time to explain this point, I can give you some more details if you ask in the discussion session but okay, just to mention that one has to do a small operation on this theory if we really want to be precise and really have two theories which are really dual, okay but this is a small remark and then a comment is that there is a special case here, you see if you take N equal to one, okay because if you take N equal to one here, well SU1 is the trivial group with just the identity, so this theory becomes trivial and so what this duality tells us is that the theories, let me write them as UN level one are a bit special, in fact these are examples of what we can call trivial topological field theories, so these are theories for which there is a single gap vacuum on any special manifold, now remember one of the, so topological theories in general describe gap systems, okay, yeah it's not really important because okay I wrote these, so well thank you for the question, I wrote this duality but you can take a party transformation, so what party does is to invert the sign of the transimus level because the transimus actually for writing components, the Lagrangian is a mu d nu a rho plus two thirds a mu a nu a rho and then there is a epsilon mu nu rho, so if you change, if you do a party transformation this changes sign, the transimus level gets a minus, so you can perform, so first of all this theory is, transimus theory is not party invariant, okay if you apply a party transformation it changes the level goes into minus itself and what is a duality, you can apply party on both sides and then you have another duality in which you have SUn level minus k which is due to UK level n, okay, so I will not write the dualities twice, it's always meant that we take positive numbers for n and k and then there are the corresponding ones and so in particular these also are trivial, so topological theories and transimus theories in particular, they discover gapped systems where there are no dynamical degrees of freedom but still as you see they are not just trivially gapped back because depending on the topology of space we can have a degeneracy in the Hilbert space, so multiple degenerate states at zero energy, now if you wish in a trivial topological theory there is one single gapped state for any topology and so really there is nothing non-trivial going on here, up to the fact that still there is a framing anomaly and in fact the fact that the Hilbert space contains a single state on any spatial topology means that the partition function should be just a phase, however this phase should capture the framing anomaly and so all the content if you wish in these theories is the framing anomaly and since there is no dynamical content it turns out that the partition function is fixed classically, okay, there's no dynamics and in fact this partition function is just a local integral of the background fields, so in particular just to be concrete in these theories the partition function turns out to be equal to, so it's a phase and now it's a local integral of something that so let me write in this way minus 2 n gravitational transform term, okay, so this is a classical integral, this is a classical functional of the metric and write it here, so we can write it, so we could write in three-dimensional terms, let me write it in four-dimensional terms, so taking some four manifold whose boundary is the three manifold we are interested in, this is the transformation term constructed with the spin connection, okay, so this object is purely classical, okay, it is just a background field, we are not doing gravity, so G is not a dynamical field that we are integrating over in the particle, it's just classical, but this captures precisely the framing anomaly of the theory, in particular these two tensimons graph is corresponds to C equal to 1, if you work out the numbers, D corresponds to C equal to 1 which is essentially the framing anomaly of a system whose boundary is a real scalar or a complex fermion, okay, other questions? Okay, so now I would like to leave the topological word and start talking about theories with the dynamical gapless degrees of freedom and so the first example that I would like to discuss is particle vortex duality, is not, as I say, so we are discussing just field theory and so this term, this is a function, I don't know if you can see it, it's a function of the metric, it's a purely classical object because for us the metric is just a background field, it's not part integrated over and it's consistent with the fact that this theory is not dynamics, if you wish, there is a phase which captures the framing anomaly but it's completely classical, so the full partition function is a classical integral, a local function of the background fields, yes, it's constructed with the spin connection, yes, sure, in fact, I mean we know that this is a topological invariant up to the framing anomaly because, so we said that if you change this framing, so if you change the way, so if you want, the reason is that there is this huge denominator here, so this one is not properly normalized to be well defined in three dimensions, you remember we have this discussion that we complete with a four manifold and the result is unambiguous, completely unambiguous if when you have evaluated this object on a closed four manifold, you get a multiple of two pi and from this one you don't because this corresponds to C equal to one, in our convention C equal 24 is an object which is, I mean give you phase one, so it doesn't give you anything in three dimensions, but this is one 24th of that, if you take U24 then you don't get any phase at all, other questions? Okay, so I want to discuss particle vortex duality, this was proposed by Peskin, Dasgupta and Halperin, so in order to understand this duality, so let's start discussing the Abelian X model in two plus one dimensions of course, so what is this? So we have a Abelian gauge field, so U10, there is no transformous interaction, it's just young mills, and then we have a complex scalar, we charge one under this U1 and then we take a potential which is a mass term and a quartic interaction which is relevant in three dimensions, but we take M squared negative, so this potential is the Mexican hot potential, okay, we take this mass large, so we can do a classical analysis, and so since this is the Mexican hot potential, there is symmetry breaking because phi condenses, once this symmetry is caged, this is the X mechanism, and so the system is gapped. Now it turns out that in this theory there are vortices, these are some solitons, some solitonic configurations such that, so if we take, so this is our space, it's R2, and the space of vacua is a circle, okay, so you can construct, you can try to construct solutions of the equations of motion which are time independent and such that as you go around a circle very far from the origin, you also wind once in the space of vacua in field space, okay, so you construct a solution where phi and radial coordinates of R and theta is some radial profile e to the i theta, so when you wind once in space, you also wind once in field space, and so you construct a radial rotationally symmetric configuration, and in general you also turn on, you also have to turn on some field strength, and in particular since there will be some field strength to construct these solutions, the ones that wind once in field space, they have one unit of magnetic flux, so essentially these solutions have some bump of flux around the origin, and they differ from the vacuum around the origin, and if you go far away they essentially go to the vacuum, now you can write down, so this is a very simple theory, you can write down the equations of motion, you can try to solve these equations, they cannot be solved analytically, but you can easily solve them numerically, and so you can construct these solutions, and then you can ask, okay, what is the mass of these solutions, you compute the energy of these solutions, and what you find is the following, so if you are just considering the theory with the scalar without the gauge field, you would find that in fact these solitons do not have finite mass or finite energy, because you would find that the energy is logarithmically divergent with the size of your, of your, of your, you construct your solutions, and you see that the solution here for instance for phi, well just for phi because we are considering which there is no gauge field now, approaches the vacuum with a power law, okay, and then you plug into the energy and you find that this energy is, is logarithmically divergent with some infrared cutoff, however if you consider now the theory with the gauge, and so now you have also to do this, and you are once again studying your solutions, you find that now the vacuum is approached exponentially, and so now the energy is finite, abelian x-model, so very different behavior, and so this theory has finite mass solitons, and so the idea is that if we go at very low energies and we turn on a mass which is, which is small compared to the scale set by the, by the gauge coupling, we can describe the theory as a weakly interacting model of, of, of these solitons, and in particular we can write down a theory in which the solitons are described by a fundamental field, and so we describe essentially these solitons as weakly interacting particles, and we introduce some scalar field phi tilde, and we write a weakly interacting theory for some massive scalar field, because these, these solitons are, are massive, and so the theory that we will write is just a theory of a scalar field with some potential with a certain mass, and then we can include the first interaction, which is a quartic interaction, so this phi tilde, this, this field phi tilde represents the vortices. If you want is the creation operator for, for vortices, for these solitons. Now notice, so here m tilde squared is positive, and notice that here up to the fact that we have this positive mass, this is precisely the O2 vector model that Igor was talking about yesterday, okay? This is a complex scalar, you can write it in terms of two real fields, there is O2 symmetry, corresponds to rotating this field, and taking the charge conjugate, this precisely the O2 vector model. Now, what happens if we try to invert, are there questions so far? So what happens if we try to invert the sign of this mass, okay? So let's see what happens if we take now positive mass here, and then negative mass here. Now if we take positive mass here, now this field phi is massive, so okay, if the mass is large, we integrate it out, we are left with u1 level 0, Young-Mills theory, but in fact this is a free theory, okay, this is a free photon, and a free photon in two plus one dimensions can be dualized into a free scalar, but importantly a free compact scalar, we can call sigma, and this dualization is a standard dualization that for instance you do in four dimensions when you want to do electric magnetic duality of an abelian, free abelian gauge field, so essentially you are right, here you have your Young-Mills action written in terms of f, f by star f, you are writing star f as some d sigma, okay, and that is because if you wish the Maxwell equation of motion say that this is closed, and so you write it as the differential of something, okay. Now it is important that this sigma is compact and one way, one simple way to see that this sigma should be compact, by the way compact I mean that sigma should be identified with sigma plus two pi, or if I want it properly normalized, here I should put the correct mass scale, which is probably g, and one way to see that this should be the case is because for instance, so suppose that we are looking at some field configuration on S2 times S1, and then in the pat integral we would be summing over fluxes on this S2, because one of the two pi integral of f should be quantized, and in the pat integral we should sum over all these quantized fluxes, but now if you use this map, you see that in this configuration the sigma is constant, and so if you want to reproduce these field configurations, you need configurations where this sigma is constant on the S1, and so if you integrate it, sigma cannot go back to itself since the derivative is constant, it has to shift by two pi, and okay here I'm not careful with all the coefficients, okay. So this sigma lives in S1. So here I'm doing pure classical analysis, I'm taking the mass large, and the mass is very large, and I do a semi-classical analysis when the mass is large, phi is massive, I can integrate it out. Again, I take large negative mass, and there is condensation. I'm not trying to understand here what I meant for small mass, which is hard, I'm just doing very large mass compared to the mass set by the gauge coupling. Yes, yes. Yeah, I'm starting that, I'm saying what happens in that case? Yes, I'm saying I'm taking some particles with the large mass. This is purely classical analysis. This one here? Yes, we will come to this in a second, but yes. So in this theory we say when the mass is positive, now we integrate out the scalar field, and we arrive with this free photon, which is a free compact scalar, S1. So now what happens in this theory? So now in this theory we take, if you wish, a large negative mass squared, and well, also here there are no mysteries, because if the mass is large, now again we have the same phenomenon, we break the symmetry, but this time we break a global symmetry, and so we have the Goldstone mechanism of the Higgs, and so we have a Goldstone boson, which is S1, because the symmetry that we break is a U1 that rotates this phytid, and so from here we also get some S1 free scalar, okay? And so surprisingly, we started with the Higgs, and attempt to describe these vortices with some dual theory that was working for some value of the mass, but in fact, this duality works also for the other value of the mass, okay? We have a match. Now in this theory, which is the O2 vector model, so in both theories we find for large values of the mass, we find two phases. Oh, yeah, so, I mean, of course, when you do this, if I take sigma to be canonically normalized, now sigma is dimension one-half, so I want to put here something which is dimension one-half, which is G, because G squared is dimension of mass, G is dimension of mass, square root of mass. So if you wish, it is true that this theory is free, and you might ask, okay, so what about the gauge coupling? If it is free, there is no, I mean, this doesn't appear anywhere, but still it looks like it's setting a scale for us, and in fact this scale also appears here, because this is a free scalar, but the radius of the manifold, of the target manifold needs a scale, which is this very same scale. So we found these phases, so let me plot m squared, and so what do we say? So for positive m squared, here there was an s1, a linear sigma model, okay, this would like to be a nonlinear sigma model, but in this case just one free scalar, so it's actually linear, and here the system is gapped. Now in the case the O2 vector model, we know that in fact, so first of all we know that there must be at least one phase transition in the middle, because these two phases are different, but now we know that in the O2 vector model there is in fact just one phase transition, and this is a second-order phase transition, it's a CFT, and so the claim of the particle vortex duality is that in fact, also the gauge theory, it is dual to that, and so it has precisely one phase transition, and this phase transition is second-order, okay. This is not obvious, but this is the claim of the duality. Now as I say, this is not obvious, but this has been extensively checked, in particular with the lattice Monte Carlo simulation, and as far as we know, everything's consistent, so we do believe that this duality is correct. I think that there are clashing claims, for instance, this is the very case that some people would like to say that there is SO5 and unsymmetry, but it's not clear if this is true. I mean, there are no definite results, right, from the numerics. Yes, I mean, I don't have much to say on the case you won with two scalars, that will be somehow outside of the domain of the claims of these dualities. For one scalar, for one... As far as I can see, yes, I mean, okay, I don't know what you mean by a lot, but I think there is consensus with one complex scalar, the lattice Monte Carlo simulation. That is also some theoretical work that has been done, so one can write explicit non-linear map on the lattice fields, but it's also numerical lattice Monte Carlo simulations. Yeah, yeah, I mean, I can give. So, in any case, I mean, in this, indeed, for this that the following dualities, as I said, we cannot prove them, and so I will state what the conjectures are. We can make checks, various type of checks, but I will never make a claim that some duality is correct. So eventually, we'll have to do numerical simulations and see whether these proposals are correct. But the proposals are sharp, so either they are correct or wrong. So in this case, for this duality, I will use the following notation. So u1 level 0 with phi dual to just phi tilde, which is the O2 vector model. Okay, so in particular, in this notation, I will just write the fields that we have every time there is a complex, sorry, every time there is a scalar, I will implicitly assume that there are a quartic interaction for this guy. We'll not write them, but they're always implicitly there. Okay, so what checks can we do of this duality? So okay, we already checked that the phases match, at least when the mass is large and one can do a semi-classical analysis. We can try to compare the symmetries. So in this, for this theory, the global symmetry is O2, which is a u1 that rotates the field phi tilde times charge conjugation, which is a z2. There is also parity and time reversal. Now what about this theory? So clearly here the symmetry that rotates phi is not there because it's gauge, it's not a global symmetry. However, there is another global symmetry, which is called the magnetic or topological. This is a symmetry whose current is constructed out of the field strength. So this is epsilon mu nu rho, f nu rho, and this is conserved just because of the Bianchi identity. Okay, in terms of form, we'll write this in the following way. In fact, what we can do with this does, well, if you go in the case, so if you consider the case in which this was massive and we're less with the free photon, this current, which is precisely equal to the sigma, what it does is to shift sigma. If you go in this phase, what this current, what this symmetry does is to shift that free scalar, and so in fact, this free scalar is itself a Goldstone boson, and so for this reason we are sure that it cannot receive, there cannot be any potential from some additive corrections because this is actually a Goldstone boson for the broken magnetic symmetry. So this is my next U1, which is mapped to this U1, and then there is also charge conjugation as well as parity and the entire reversal. So the symmetries match. So what about operators? So in general it's very hard if you have a duality to draw a complete dictionary between the operators. In principle, there should be one, but in general it's very hard to write it. However, we can map certain simple operators, especially if we consider the simplest operators with a certain charge. Now here there is an operator which is charged under this U1, it's just the complex scalar phi. So what is the operator here? The corresponding operator which is charged under this magnetic symmetry. So first of all you take the complex conjugate of the scalar field, and then it maps the gauge field to minus itself. This is the general action of charge conjugation, and it turns out that, well you see it from here, since charge conjugation maps a mu to minus a mu, it also changes the charge, so it acts on this current, and that is the reason why I'm using this strange symbol which is not just a product, the semi-direct product, because charge conjugation really acts on this symmetry. So everything matches nicely. Yes, so the operator in this theory that is mapped to the complex scalar is the monopole operator. So let me explain what does this mean. Monopole operators, so monopole operators are local operators, they are called sometimes disorder operators, because they are not defined as the most standard local operators we are used to as some polynomial function of the fundamental fields in the Lagrangian, but rather they are defined as some singular boundary conditions at some location in space. So what does it mean? So suppose that I want to compute a correlation function of these operators, so if I want to define these operators essentially I have to tell you how to compute correlation functions. So suppose that I want to compute a correlation function of some monopole operators at x times something else, and now the way to do that is to set up a path integral, so let me call phi all the fields in the theory. So in general here we insert whatever standard operator we have, however we specify that when we have point x, we cut a small ball around x, and then we impose a boundary condition, some non-trivial boundary condition at x, and this condition, for instance in the Abelian case, so for an Abelian gauge theory, is that there is some non-trivial flux on these two sphere. Let's say that I want to consider the basic monopole operator, so there is one unit of flux on this sphere, and this is some singular boundary condition because since the flux is constant, if I shrink this sphere it means that the connection is, or if one of the field strength is becoming very large, is diverging. So the prescription is that correlation function monopole operators are computed in the standard way, however I have to integrate over field configurations which are not smooth at x, but they have some prescribed singularity at x. So this is what monopole operators are. More generally, if we have some non-trivial, sorry if you have some non-Abelian theory, we should specify that on this S2 there is some non-trivial gauge bundle, and since these gauge bundles are parameterized by pi1 of g, where g is the gauge group, in fact this is the group of magnetic charges that monopole operators can have. These are conserved charges. And in this case here it's in fact a u1, because the magnetic charges are all the integers, so the corresponding group is u1. Now, in the presence of the transimus interaction, what happens is that these, let me call them bare monopole operators are not gauge invariant. They have some, well maybe. So if we have transimus interaction means that the bare monopole has gauge charge. One way to see that is that if we are on a manifold, not three manifold with a boundary, and you do a gauge transformation of the transimus action, you get a boundary term. And so in particular if you try, I'm not doing this computation because I don't have much time, you can try to do it. If you do a gauge transformation, you will get a boundary term on this sphere. When this sphere is very small, essentially you pick up a phase that depends on the gauge transformation and x, and we interpret this as the fact that the operator is not gauge invariant transformed under gauge transformations. And so in order to construct gauge invariant operators, we have to dress this bare monopole with some of the fundamental fields in the theory. So we have to construct some composite object. And because of this fact, monopole operators in transimus theories can also get flavor charges or spin, essentially because you dress them with the fundamental fields, which can be charged under some other global symmetry. Well, I'm jumping between Lorentzian and Euclidean. But no, I mean this, so this definition is both, I mean you can do it in Lorentzian, this is also Lorentzian signature. I mean it's a local operator, so you can do it in Lorentzian, you can still cut a ball around the point and you impose until you have boundary conditions around that point. You can do it directly in Lorentzian. Okay, however, okay, for the particular case that we are looking at, this is not an issue yet because the level is zero. So in fact the bare monopole operator is gauge invariant. And this bare monopole operator in fact is, as we said, is precisely the operator which is charged under this magnetic current. And so it's precisely the operator which is due to these fields, phi tilde. The other piece of the operator map is that if we take phi squared, should be mapped to minus phi tilde squared because this was precisely the operator that we were using to do the relevant deformation to move into the two phases, okay, with the minus sign. Okay, now we can write the duality in a slightly more precise way in the sense that we can include more, a little bit more data. And this will be useful later or tomorrow. So in particular, since we have global symmetries, we can couple this global symmetry to background fields. This is extremely useful in general in quantum field theory. And tomorrow we spend a lot of time talking about this procedure. This is useful because essentially once we couple to background fields, we can construct observables which are essentially the partitions function of the theory on various backgrounds. And of course, I mean it's also useful because if you compute functional derivatives, you compute all the correlators. And so in particular, we can rewrite this duality coupling to the background fields. Okay, let me just introduce a background field for this U1. Okay, in principle, we could do better, but this would be complicated. So we introduce some b mu o. And let me just, as a notation, use capital letters for background fields and small letters for dynamical fields which are part integrated. So I can write the duality in the following way. And this is very schematic. So I'm not careful about coefficients here. The only thing I'm careful about are the coefficients of St. Simon's terms because they should be quantized. Okay? No, so the claim is that this is a duality of, so this is an infrared duality of around the second order phase transition. So if you want they flow, so the second order phase transition is the same CFT. The claim is that if you do small deformations, you get the same. And now if you take larger deformations, I mean, the duality is still correct if you are at small enough energies. In particular, when we said, okay, let's take some mass, for instance, the billion X model. There are these vortices. Of course, if you go at energies which are larger than the mass of the vortices and then you reach the scale, the mass scale set by the photon, of course, you see that the theory, I mean, contains a photon and so on. But if you remain at small enough energies, you just keep... So these are the CFT. Yes, so that is a claim about the CFT. Okay, so here I'm writing the duality. So what I've introduced is the field B, the background field. So here it's obvious, okay, because how I coupled this theory to a background field. It goes in the covariant derivative. Here maybe it's a little bit less obvious. Let me also say that I'm not writing the Emile's term. It's implicit, but it's there. So the coupling is through this term here, and what this term here is nothing else than the minimal coupling between the magnetic current and B. And if you... Okay, this J is star F. If you are writing in terms of forms and you do some partial integration, it becomes this mixed-transiment term. Okay, so this mixed-transiment term is just a standard coupling, linear coupling of B to the current. Then I would like to discuss another example. It's the example of flux attachment, how it's called in the... In the... Or bosonization. So flux attachment is some simple idea, some smart simple idea that I think it goes back to... We'll check. And that is the following. So if we have some particle... So for instance, suppose we have some bosonic particle, and we manage to attach to this particle one quantized unit of magnetic flux, then this particle becomes a fermion. And one way to understand that is that... So suppose they have two of these objects, which is a particle attached to one unit of magnetic flux. Now we like to exchange these two particles. So I can do that by taking one and moving it around the other one by half rotation. Now when I do that, I pick up Aron of Bohm phase. But since this is just half of the rotation, this phase is minus one. Okay? So when I rotate this, I get a minus one. And so this is telling me that these are fermions. Okay? So this is the basic idea. We can realize this idea in the relativistic context of quantum field theory, again with Chen-Simon's theory. And so in particular, we can consider the following theory, which is u1 level one with phi. So very similar to the theory that we had before. But now I have a Chen-Simon's theory and level one. Okay? So why this model realizes this flux attachment? Well, because... So a unit of flux is a particle with a unit of flux is essentially something which is created by the monopole operator. So we look at the monopole operator here. However, for what we said, there is one unit of Chen-Simon's level. And so because of that bare monopole has gauge charge one. It's not gauge invariant. How do we make it gauge invariant? Well, we have to dress it with one mode from phi star. If you want the compressed conjugate, which has a gauge charge minus one. Okay? So we have to dress it. What does it mean that we dress it? So for instance, we can define this operator in radial quantization. And if we do that, we would go to S2 times R. We would put one unit of magnetic flux because this is the basic monopole operator. And then we would put one zero mode of this scalar field phi star. But now, if we look at this lambda problem, so we ask, okay, what is the spectrum of a scalar in this magnetic flux? If one of these problems is solved, so the spectrum of the Laplacian for this field here. And this problem is solved by the magnetic spherical harmonics. And the result is that, in fact, there are two zero modes. And these two zero modes form a doublet under a rotation. So this is a spin one-half. And so when you dress this monopole with one of these zero modes, the gauge invariant operator becomes a spin one-half operator. So it becomes a fermionic operator. So if you want, this was the bare one. And the gauge invariant one has a spin one-half. The claim, which again we cannot prove, of bosonization is that, in fact, at low energy, if we, maybe this is a point that I have not emphasized before. So if we tune value of the mass, even in the previous case, there was a mass term. And if we want to hit the CFT, we have to do a tuning of it. So here as well. So if you tune the mass appropriately, the low energy tier, in fact, is a free fermion. So this spin one-half operator, in fact, this kind of a free fermion. So you want one high. It's just a free fermion. And so in particular, as you said, the monopole operator, the gauge invariant monopole operator is mapped to the fermionic operator side here. And for instance, the mass term, and this we are going to check in a second, is mapped to a mass term here. So in fact, if we propose this, we should check if this makes sense. And so, okay, first of all, we should check the symmetries. That works exactly the same way as before, because this side is, yes. Yes. So I will, I only want to discuss gauge invariant operators. Yes. Otherwise, I will write bear if it's not. I'm almost done. Yeah. So the analysis of the symmetries is the same as before. It doesn't change. So there is u1 times charge conjugation here. There is magnetic symmetry and charge conjugation here. What about the phases? So what if we deform? Clearly, the phases of this theory is quite different than before, because this is a free fermion. If we give a mass to the fermion, we have a gap system on both sides. We don't have a Goldstone boson. If we do the analysis here, well, when the mass is negative, it's the same as before, because this field condenses and there is x mechanism and this is gap. It's the same as before. The difference is when the mass is positive, because now we are left with u1 level 1. It's not u1 level 0. And this is one of the theories that we discussed before. This is a trivial topological quantum field theory. So it has a single gap vacuum on any spatial topology and so perfectly matches with a fermion. Okay, let's stop here.


Okay. And then if you don't mind just reading it out loud. My name is Jamie Lynn. I recently stayed in your facility from June 9th, 2018 through June 14th, 2018. I wanted to take the time to reach out and share with you some of my experiences with the staff. Dr. Yu took care of me in the ED. He was always attentive and I, although I know he had other patients, I never felt as though he forgot about me. I always felt as though I was his priority. My first nurse I encountered was Toby. Toby was very nice. She was always smiling. No matter how many issues she had going on, she never let her stress show. She helped put me at ease and I was grateful for her. I also want to take time to recognize Ivana. Ivana is the superhero on three east. I cannot explain how great she was as I do not have the words to explain it. I would also like to recognize Mariela. She was my overnight nurse. Mariela was very sweet and took the time to explain everything to me, even the smallest thing. She spoke softly as to not wake my roommate. She was nice enough to take care of anything I needed, whether it be getting my water or figuring out how I could get a few hours of rest. I also had Okasha. Who is a delight? Okasha always made sure I had everything I needed. Each time it was medication time, she would make sure I had plenty of water. If there wasn't much left, she brought me fresh water. She was such a pleasure to interact with. I also had the greatest pleasure of meeting patient advocate Mark. Mark was the shining star of my hospital stay. He made everyone feel better. After he walked in, he brightened their day. I hope only good things for the future, sincerely. Jamie Lynn Case-Lac. She's so cute. When I get these letters, I feel really thankful, but I really just feel like this is what we do. Truly, it's like it's really a team effort. I really don't think I do it by myself. This is kind of a sure medical center that I always strive for. I like to be the light of this community. I'm glad she felt safe here. It makes me feel good. Hey! Hahaha! I remember! How are you doing? I'm doing well. Oh my God! How are you doing? Are you doing okay? I'm doing well. Are your headaches okay? They're okay. Jamie! Hey! Oh my God! Oh, Jamie! Oh, thank you for that beautiful letter! How are you feeling? I'm feeling much better. I'm glad that you remember me.  If I can make a difference every day with a patient, that's all I ask for. You make a difference with a lot of patience. Thank you. I really appreciate it. And just remember that. And keep up the good work. Thank you. Thank you.  Hahaha! Thank you. Thank you so much.


Hi, here we are again with exercise number five entitled electoral excesses taken from the VLC transcription series where I explain to you the techniques of phonetic transcription. And here is our task. Again we have to transcribe a text. This time the text electoral excesses using the LPD notation represented in the Longman pronunciation dictionary and of course the reference phonological dialect we have to use is received pronunciation. As usual our text contains line numbers and stress marks to make the transcription and referencing a bit easier. It is subdivided into three parts as usual. So here's the first part. Let's go through this part line by line and again for those viewers of these transcription videos that are not too familiar with the vocaleic system of the LPD notation, I recommend to have a list of the monophones and diphthongs ready to look at. And as you notice it doesn't only contain the 20 vocaleic phonemes of RP but also the two weak vowels that are used in the LPD notation. If you want you can have consonants available for you but I don't think that's necessary, they're much easier to remember. Okay, ready? So let's start. Here is the headline electoral excesses and quite important the plural where the is is of course used to denote the ES plural. Line two, I shall be glad when the next three weeks are over immediately you might want to have a linking R in a rover. I will say something about it in a second. Line three, what do you say? Well here I use the contraction what you say, I shouldn't say and then line four that I find them so bad at all. That I find them so bad at all. That I find them so bad at all. Some of you might want to stress so okay in which case it would become a strong form. Let's look at connected speech effects, weak forms, quite a number. I already mentioned the weak form. Do you, where in as an alternative you could have used, let me write it down like here where you could have written do you as well with a weak value. I use a more weakened contracted form due, both are correct. Well and then here we have so as an occasional weak form down here. So and as I said this is occasionally weakened if you have a stress marked here it would be easier that I find them so bad at all so you can stress this line and then you would have to use the strong form. We don't have any strong forms apart from that option but we have liaison in a linking R as I already said we could insert the optional linking R in weeks a rover linking R not an intrusive R linking R so a liaison effect and we have some elision possibilities here again they're optional next three shouldn't say and find them so next three shouldn't say find them in all three cases we have the three consonant rule where the internal consonant can be elided as an option. Let's look at part two here we have another weak vowel in certainly where the LPD often uses this notation sir oh sorry sir ten so they're using a superscript schwa well I don't recommend this to my students so I recommend to use the non schwa version straightforwardly because superscripts violate to some extent the principles of the international phonetic association which says avoid diacritics where possible okay if you present this as a solution we certainly would have to accept it well in line six we have an alternative for schwa where you could of course use schwa which is an alternative transcription whoops second colon where's a colon going there it is and in line seven we have contraction again already commented on the possibility of contracting do you to do if both are weak well and I'm in line eight we have a nice optional assimilation but I will perhaps you found it already well let's look at it in a second here are the weak forms quite a number we have one strong form does an election go on there well it is not stressed but it occurs at the end of a sentence and we have liaison in but we're certainly better off than they are in there in the states both are optional we could easily say certainly better off than they are in the states as I said liaison is always optional and so is the linking are in this context well and we have as I said assimilation here in this last line it can be well in both cases we have regressive assimilation where in the first case the villa plosive influences the alveola plosive regressively and in the second case the bilabial plosive influences the alveola nasal regressively so that the optional result could be it can be it can be for months and months let's continue with part three well really then we can congratulate ourselves well in fact as you may have already assumed there is an alternative representation in the lpd for congratulate you could for example write it or transcribe it like this congratulate here you have a weak here you have a weak in this context so this is an alternative another alternative would be a combination of both where you could have instead of the short or in con you could have the schwa so you see there are various alternatives for congratulate line 10 is a nice line to represent the varieties of back vowels in our P we have the short or in on we have the long R in R and we have the wedge in lucky so this is a nice representation of low central and low back vowels this line weak vowel in we twice well and in line 11 we don't have to go through all that well there's nothing especially interesting we will say something about having a second and in the last one line we must thank our lucky stars we have another occurrence of a short a which we should now understand why it is used in the lpd notation let's look at connected speech effects weakening well quite a number of weak forms we have two strong forms one of them is half we don't have to go through all that as I said quite often half is never a weak form if it is the equivalent of must have to it's always strong even if it's undressed well and that as a demonstrative at the end is stressed so it is strong anyway assimilation well there's one case of regressive assimilation where the bilabial or the labial vela approximate influences the alveolar nasal and as a result then we can optionally become them we okay the print version of the solution is as usual available in the vlce lecture library and if you're a member if you're a participant of any of our classes you have free access to all these exercises well as usual so thanks once more and see you again


Those of you who have the lights please put them on. I know at a birthday celebration you blow out candles I think the more appropriate thing to do is to light the candles bring more light into the world I've been privileged to know Mayor Eric Adams For at least 35 years. I officiated his bar mitzvah some years ago But I always recall a story this mayor told To some of us who were there when he was installed as a state senator of the state of New York he talked about his campaign and Going around collecting funds for the campaign a woman Who didn't have much? gave him a jar of pennies and He looked at it and she said I'll tell you why I'm giving you this job firstly. I don't have More money to give you But secondly, I want you to look at this jar and always remember The people who are not so fortunate in this world And he would keep that jar on his desk and Daily recall what she had said and keep that promise Don't forget the little people so-called the people who made it possible for him to become The mayor of this city, so I introduce to you the hundred and tenth mayor of the city of New York and the next Speaker here tonight at this program He's right. I'll just a long time friend and Advisor and a person That truly love this city and the people in this city and we have been side-by-side on many occasions When we saw the ugly face of hate Exposed itself. It didn't matter if it was fighting on behalf of our brothers and sisters from the Muslim community when Women were attacked for wearing a hijab If it's someone that draws a swastika on the building or desecrate a church statue or Harm someone because they're from the AAPI community. There's just a consistent Understanding that we must lift each other up and he represents what's best about us I say all the time members of the greatest race alive the human race and you are truly a representation of that We know and no matter what people say on other parts of the globes or in other cities We know that New York is the Tel Aviv of America We have the largest Jewish Population outside of Israel right here and all my two visits are there and getting ready to return again We know what the Israeli people stand for and what they represent across the entire globe Built into your culture. It's what you call Mitzvah You believe in giving back you believe and ensuring that you help your fellow man and women That is who you are and so when we stand here and celebrate Your anniversary your independence of your Creation that is also a celebration for those who have touched in many ways and we also Must reflect on a reminder that the dark and ugly parts of what has impacted your culture and your people when I was in Cracow and went to the camps walking through there seeing The tragedies and horrors that is unspeakable The number of young people who don't know their great grandparents and great aunts and great uncles Because they lost them during the Holocaust It must be a reminder that we never can stand by again and watch hate Start out as words and turn into action. That is my commitment as the mayor of this city To say first thank you for being part of this great city and saying that I am looking forward to raising this flag To show the solidarity that New York City has with the people of Israel Let's continue to uplift each other Let's continue to stand for what is right and let's continue to raise the flag in solidarity with Israel Thank you very much. Thank you Rabbi Are we asked concert general Israel needs on mayor Adams to please raise the flag here this evening? Would you all please rise? We're gonna sing the national anthem United States and national anthem of Israel United States


Welcome to the Rich TV Live podcast. That's very bizarre, here we go. Some technical difficulties to get us started. Welcome to the Rich TV Live podcast. I'm your host Richard DeSousa. Today we're gonna talk about the hottest stocks of the day. So first and foremost, BRSH leading the way up 101%. This is the yearly chart and you can see these charts, I've been marking them up and they all look very, very similar this year. There's the Magnificent Seven that continue to do very well and that continues on today. And there's these small caps, penny stocks that have really, really struggled this year have been going down and I started bounce off bottoms as we're going into what looks like a Christmas rally. So very, very nice. And obviously we're going into Thanksgiving so it's a short week in America. So definitely you need to be aware of that as well. Here's another pick doing well today, NOGN. You can see the chart looks very, very similar, been much higher, bouncing off a bottom and doing this dead cap bounce. And up 81% of the day, NOGN. So put NOGN on your radar and on your watch list, they're up 81% of the day. Here's CDIO, this one has also been much higher and came down like they've all pretty much done this year with the exception of the Magnificent Seven and a few others and now is bouncing off a bottom and is huge bounce from 18 cents all the way to $1.91. So this one's a little different. It's gaining a lot of momentum, a lot of steam. Definitely one I think you need to keep your eye on and they're also focused on AI based heart disease. So anything with AI right now is hot. So I think you definitely need to put the CDIO on your radar and on your watch list. In fact, I'm gonna write this one down cause I didn't even know this was an AI stock. So I'm gonna write this down, CDIO, CDIO, which is now up 94% and AI, AI based heart disease. All right, let's take a look at what else is popping. So AFIB, so I really like this and I like the way this chart looks and I think we have a gap to fill and this could go to six bucks, just the way it's looking based on momentum. Here's AFIB and they're another penny stock and they're up 33% on the day AFIB and one of these charts that looks once again pretty similar where it's been higher, been lower and starting to bounce off a bottom. So AFIB up 33%, put them on your radar and put them on your watch list, PROK. PROK, another one of these that's been higher, came down and now doing a dead cap ounce and they are currently up 44% on the day PROK. Here's YPF, YPF is up 40% on the day. YPF, you can see they've been higher and they were also lower and now they're getting very close to a 52 week high. So keep your eyes on YPF trading at a 52 week high or around a 52 week high. CYTO, a lot of the same, I've been actually marking this one up and showing you guys they're up another 36% today. So definitely another one to watch. Coinbase, I've been talking about Coinbase lately, very, very bullish on Coinbase, told you I thought it was gonna break 100, today it did. So congratulations if you're in on Coinbase up 6% on the day and running as the price of crypto, Bitcoin and Ethereum and all top cryptos are starting to climb and we're getting closer to Bitcoin having. Here's NVIDIA, NVDA, absolutely on fire. They are trading at a 52 week high and NVIDIA now officially over $500. Price oil up today, oil doing well. In fact, let's just take a look at MarketWatch. All right, so this is MarketWatch and we can see here that the Dow Jones is having a nice day today, back over 35,000. So very bullish for the Dow Jones, up 244 basis points or 0.7%, the S&P 500, a big day for them too, up 37 basis points or 0.83% and the NASDAQ, big day for the NASDAQ, up 1.18% or 166 basis points. So big days for them, oil up 2% at $77.50 gold down today at 1980 and the VIX, the volatility index that typically goes up when the market goes down and down when the market goes up is down as the market is up. So that is the MarketWatch. All right, so let's just head back to the markets and take a look at where we're at. So this is Microsoft, Microsoft is trading at a 52 week high Microsoft is getting heavily involved in AI. They wanna become one of the world leaders in artificial intelligence and I wouldn't put it past them. They're now trading at $378 and absolutely on fire having a monster year, they've been killing it. I mean, this was a stock that not too long ago was at 200 bucks. They're not now at almost $400. So it's been an epic move from Microsoft. I mean, one was the last time they're at $200. They're at $220 almost a year ago to the day, November 3rd, 2022. They're $220 today, they're at 378. So almost the double in a year for Microsoft and they're one of the magnificent seven that has really carried the markets all year. Here's Netflix, almost everyone has Netflix at home and they're trading close to a 52 week high. So keep your eye on Netflix, they continue to go higher. Here's Ethereum. All right, Ethereum is being talked about a lot because major institutions are now looking to file a Ethereum ETF. So it looks like we're not only gonna have a Bitcoin ETF, but it looks like we're gonna have an Ethereum ETF which is gonna give you the ability to buy Bitcoin and Ethereum in the stock market without having to have any of the risks associated to owning an account, having coins on an exchange that could go bankrupt, getting your coins hacked, forgetting your password to your crypto exchange. So there are advantages to these Bitcoin and Ethereum ETFs and Ethereum is really taking advantage of that momentum and you can see they're trading over $2038 US. So big move for Ethereum. COMT, one of my top dividend holdings having a nice day today up 1.54%. They pay around a 30% annual dividend but they pay you one time a year and that payment is coming within a month. Here's Meta, formerly Facebook. Meta is having a big day today and they are trading at a 52-week high. So a new 52-week high and I believe it might be an all-time high. Yeah, we're trading right around a 52-week high and an all-time high in Meta. So Epic move for Meta and I remember it wasn't too long ago, they were under 100 and now they're at $339. So it's been an Epic move for Meta. Here's Uber. Uber is doing extremely well and they're approaching a 52-week high. They're actually at a 52-week high. They're approaching an all-time high. Is Uber and I'm very bullish on Uber. Disney. I've been telling you guys that I think Disney is gonna turn this around. I think that they will go back over $100 soon. So keep your eyes on Disney. Keep your eyes on Disney and I feel like this will be a $100 stock very, very soon. Here's DraftKings. DraftKings having a huge year at a 52-week high. As you can see, really ripping and approaching an all-time high is DraftKings. Well, all-time high is still a ways away, about $70. But it looks to me like they are on their way to all-time high. So I still think there's a gap to fill here. I think there's some upside and I'm a big fan of DraftKings as sports gambling is getting really huge. Apple. Apple trading around a 52-week high. It's getting very, very close to that $200 mark and they are one of the biggest companies in the world. One of the magnificent seven. One of the seven that has done really well and one that I have sold this year and taken profits waiting for a drop so I can reposition myself. Here's Bitcoin. I'm a holder of Bitcoin. They're at 37,600. They're approaching a 52-week high. It did hit 38,000, as you can see here. It did hit 38,000. So definitely going to watch it closely and Bitcoin all-time highs are around 69,000. So we still have a ways to go to all-time highs but it looks to me like Bitcoin is on its way and I believe we will see all-time highs with Bitcoin in the next, I would say, six to 24 months. Anywhere from the next six months to 24 months we will see all-time highs in Bitcoin. In full disclosure, I'm a holder and owner of Bitcoin, not telling you to buy it. And remember, Rich TV Live is strictly for information and education purposes. Please do your due diligence, do your research before you invest in anything we talk about or discuss and past performance is not always an indication of future results. I am a holder of Bitcoin, have been and I've been talking about it for years. When I first started talking about Bitcoin, it was at 1,000. Today it's at 37,000. So that's a 36 extra money since 2017. Here's skin, they had a decent week last week. They're up slightly today. Keep your eye on skin. AMD, number two chip maker behind NVIDIA. They've been doing well this year. Keep your eye on AMD. They've pretty much doubled in price. Google, one that I've sold this year, took profits. They've maintained a strong upward trajectory waiting for a pullback to enter into Google. Some people believe these prices will continue to go higher. I'm not really interested in buying them at these levels, so I'll look for other opportunities. But if these quality companies, the Magnificent 7 dip, I'll definitely be a buyer. Amazon falls in that category as well. At $146, love the company, but not interested in buying at these prices. Tesla, at 235, another one that I absolutely love, but not really interested in buying at these prices either. Love to get them on a dip. Not sure if and when it's coming, but if it does, that's where I would be a buyer. All right, marked up this really, really weird. Maybe I'll just clean this one up completely. 18 drawings, okay, let me just remove them all. And you can see here how Tesla has been an just absolute rocket. And these dips have been buying opportunities. So definitely looking for another dip to get into Tesla. If we can get back to that $100 remark, I would definitely be a buyer. Or a long ways away from that $100 remark, currently at 235, but quality company that I've won every single trade on, I've ever taken on Tesla. And that's because I just buy the dips and sell the rips. Roblox, very bullish on Roblox. I think that there's some unbelievable potential here. And upside here, I think there's a gap to fill on Roblox. And I would definitely like to take advantage of that. And it's one that I'm looking at very, very closely at positioning myself into. Okay, as you can see gold in the red today, struggling at that $2,000 marks can't seem to breach it. Target, I think Target had a really good quarter. I think the upside is tremendous for Target. You can see I've got the arrow up. I feel like it's gonna go higher. So it's definitely one that I'm watching closely. And I think there's a huge gap up opportunity here. All right, Ripple is one of the coins that I'm closely monitoring and watching. They're kind of struggling around 61 cents. Keep your eye on Ripple and SGML. This is a lithium stock that I really like, has had a nice move, kind of doing a little bit of a pullback. Keep your eye on SGML, a lithium play that I think has tons of potential. All right, those are my plays of the day. Those are the hot stocks that I'm watching and cryptos. Hope you're having a great day. I'm your host of the most, your boy Rich from RichTV. This is BRSH. As you can see, having a huge day today, that was the gap up pre-market and then the consolidation and sell-off. So obviously these markets are very volatile. Sometimes they gap up and then they just sell-off. So it's very difficult to chase these once they've made that move. I'm not going to, it's not really my style. But at the very least here on the RichTV Live podcast, I can show it to you, kind of tell you what my idea is, give you my game plan and hopefully as a community we can make some good quality decisions where we can make some money. Hope you're having a great day. Wanna wish everyone in America a happy Thanksgiving. And we're like a month away from Christmas. So we're having the Santa Claus rally. Absolutely love it. I hope you do too. I'm your host with the most, your boy Rich from RichTV and I'm out. I'll see you tomorrow. Peace.


My name is Dr. Manlik Arjun. I'm a consultant immatohoncologist and bone marrow transplantation physician at Manipal Hospital, Bangalore. During this extraordinary times of COVID-19 pandemic, we all know that the individuals and communities have suffered a great deal because of this infection. What we also must be mindful that there are individuals who are suffering from other serious medical disorders, cancers, cardiac illnesses, who also need equally timely care. Here at Manipal Hospital, comprehensive cancer care, we continue to run our OPDs, both physical and virtual consultations every day. I also want to reaffirm that no emergency services are stopped. I want to reach out to the patient and the families that the fear of COVID-19 infection should not stop them from seeking timely care. We continue to care for individuals with blood cancers, individuals with lymphomas, and individuals with other medical oncologic emergencies if and when needed.  I also want to reinforce that any physical consultation is being done every day in our hospital. We have also opened facilities for online consultation. There are home care departments who will reach your home to collect the blood samples, the reports are sent back to you and through video consultation, the prescriptions can be safely sent to you. I'm sure we all will work harder to make sure that the patient's safety, continuity of medical care is done in these extraordinary times of disruption caused by COVID-19 infection. Please make sure that your medications are continued. Please make sure that the fears of COVID do not stop you from making sure that you meet the doctors on schedule. My message to our patient and families is that if you need any kind of help, please log into our hospital website or reach us in any possible way. We'll make sure that help reaches you.


Assistant Professor, D. R. G. Solapur, Department of Electronics Engineering. Today in this video, we are going to see discussion over L-section filter. In this video, we are going to understand the working of LC filter, then we will analyze the performance of LC filter, then the concept of bleeder resistance. Now, we will start here, we already know about this the filter that uses capacitance and we know here the ripple factor of that filter is given by 1 upon 4 root 3 fc into RL, which confirm that the value of ripple is inversely proportional to the value of load. And that is why we say that this filter is recommended for those circuit in which the value of RL is very high that is it is nothing but called as a light load. Secondly, we also can use inductor to provide the better ripple that is we are going to define the ripple factor for inductor filter that is the ratio of RL upon 3 root 2 omega L. That is in this case ripple is directly proportional to the value of load. So, we know here the value of ripple is very low when the value of RL is very small. So, we say that this inductor filter is suitable for a heavy load. Now, here we are going to combine the features of L filter and the C filter hoping that the ripple value will be independent of the load variable. Now, in this circuit the inductor is connected in the series with the load as we know inductor offers a very high impedance to the flow of AC current that is why it is connected in the series of the load. And whereas the capacitance is connected across the load that is in the parallel with the load because we know the capacitance is providing me a very low reactance path to the flow of AC current. And that is why when we combine the features of inductor and the capacitor we are going to get a better ripple reduction. Now, this is a circuit that uses a full rectifier circuit along with this L and C component. Friends just see closely the inductor is in the series with the load whereas C is across the load. So, the output voltage of the rectifier circuit without any load is defined by the Fourier series. So, in that we are having number of components there you see that the 2 Vm by pi component it has got no frequency component. So, it is normally called the DC component whereas the terms in the bracket carries frequency terms that is in terms of omega. So, these are basic terms. Now, we know here normally in the output the harmonics above second harmonics are not going to contribute much in the output and they are also seen that they are going to decay very rapidly. So, usually the output of this rectifier circuit is defined by the equation we limited only up to second harmonic. Now, we can modify this DC term here that is suppose if I put a load in the circuit because I say that VDC is 2 Vm by pi under no load condition. So, when I put a load in the circuit the DC output voltage available across load will be equal to the 2 Vm minus IDC into r where r is nothing but the sum of rf then the r choke and the rs. But usually the values of these all components that is they define this value of r they are quite small and practically we normally negate them. Whereas, we also can define the AC component from the equation 1 that defines the AC voltage across the load here also can be called as a ripple. So, V ripple is defined by this value 4 Vm by pi 3 pi is magnitude and cos 2 omega d is the frequency component. Now, we want to define the ripple current in the circuit. So, I will define that is 4 Vm by 3 pi divided by the value of impedance. The impedance is not defined by this Xl and Xc and Rl or we can define this z equal to Xl plus Xc in parallel with this Rl. Normally the value of Xl is very high as complete with the parallel combination of this Xc and Rl and therefore, the ripple current available in the load is given as 4 Vm upon 3 pi into Xl. Here, Xl is the reactance offered by the inductance is given by this. Now, after that we are going to define the ripple factor. Now, we will express this ripple value of a current in the form of Rms here and we know here the ripple value its Rms form is given by I ripple upon root 2. Hence, we can redefine the above equation as root 2 by 3 into Xl into Vdc. Now, we know here this ripple current is now flowing through the parallel combination of Xc and Rl. Now, we know here for the given frequency the value of Xc is very small as compared with the value of Rl and therefore, the AC current will prefer the path to this Xc. Therefore, this ripple current is going to provide AC voltage only across the capacitor. That is we rearrange all the equations that we written above. But, we know here the value of ripple is defined as the ratio of Vr Rms and Vdc. So, we can rearrange all these terms here. So, we can define this ripple as Vr Rms upon Vdc which is same as root 2 into Xc upon 3 into Xl. Now, we can provide the values of Xc that is 1 upon 2 j 2 omega c and the value of this Xl is nothing but 2 omega l. When we replace the value of these two factors in the equation, the value of ripple factor is coming equal to 1 over 6 root 2 omega square l into c. Now, when we look this formula of this ripple factor closely, you will see that there is no any load value is available. That is the equation is independent of the value of load and that is why we can say that this type of filter is very good in the case of a load which is not the constant that is a variable. So, it is a solution for that power supply in which we are going to get variable loads there. Now, friends we got one more difficult is experienced here in the circuit. That is we know here whenever a current is flowing in the inductance it is suppose interrupted here we found that we generate some emf across the inductance here. Now, we know here the emf we generate across inductor is given as Ldi by dt which confirm that in the case of direct current means a constant current here there is no change in the current which means there is no di by dt that becomes 0 here. So, the value of emf across the inductor is always 0. But we have to confirm that this value always remains 0 otherwise suppose current is get interrupted so that we can create some voltage across inductor and that is get applied as a black emf across the diode and the capacitor. Now, the value of this emf may be so large that it can exceed the value of PIV of a diode that can burn the diode here. Even this voltage will be above the voltage rating of the capacitor that can damage the capacitor. So, we have to carefully design the value of resistance or some value of the component here that confirm that they will be always a flow of current in the inductor and there is no interruption in the current here. So, we recommend one resistance that is called bleeder resistor here which is connected across the load and normally we choose the value of RB very high as compared with the value of load. Friends, this RB is connected across the load here that is shown in the given diagram. The value of RB is very high as compared with the load. Now, how we can design the value of RB? Let us concentrate on this waveform here. Now, dotted line shows me the DC current flowing in the choke and whereas this sine wave shows me the AC component coming across the choke here. Now, actually in the current example here, the value of R is such that the negative peak of this AC current which is flowing in the choke here is exactly touching to the 0 here. So, still I can say that the current is flowing here continuously in the given load. But suppose if I decide if I change the value of this IDC below this given value here, then we can see that the variation in the current will be stopped here because that goes below 0 and that provides me some back MF here and that can damage the choke or the capacitor. Let us try to analyze this happening here. Now, to ensure that this IDC is always at the given level at least here and we can confirm that the current will not be interrupted at all here. So, this IDC should be always more than IP to peak upon 2. So, when I replace the values of this IDC and this IP peak by 2 and by solving this equation, we will see that the value of this RB is always coming more than 943 times L or practically we can use the value of RB is equal to 900 times L. Now, these are my references friend. I hope that you understand the working of this LC filter. You understand the working of this reader. I hope that this video will help you to understand the L section filter. Thank you friends. Thank you.


Impending planetary disaster should unite us, yet we remain more divided than ever. Charles Bukowski has a quote, we are all going to die, all of us. What a circus. That alone should make us love each other, but it doesn't. We are terrorized and flattened by trivialities. We are eaten up by nothing. Terrorized and flattened by trivialities eaten up by nothing. I think about this quote a lot, not just as pertains to the inevitability of our individual deaths, but to the looming death of the entire world. The website antiwar.com has been doing a good job keeping track of all the many US Cold War escalations against Russia and China, which seem to be coming out on a near daily basis right now. Just right off their front page today, there's a story about the US considering putting more military aid in Ukraine on the allegation that Russia is plotting an invasion. Another about Moscow claiming US bombers just practiced a simulated nuclear strike on Russia and that they have greatly increased their activity along its border. Another about Beijing's anger over increased US warship activity in the Taiwan Strait. Another about Australian Defense Minister Peter Dutton's assurance that Australia will join the US in a war against China to defend Taiwan. And yet another about Beijing and China signing an agreement to deepen their military cooperation to counter hostilities from Washington. This, along with the myriad symptoms that our biosphere is showing us of impending collapse. And we still somehow manage to remain terrorized and flattened by trivialities, eaten up by nothing. Divisions and hostilities are hotter than ever, even in those political sectors where people are fully aware of just how bad our ecological situation is and the horrifying realities of Cold War nuclear brinkmanship. We should rationally all be coming together at this point in history. Our collective plight alone should make us love each other. Instead, we're at each other's throats more than ever before. And it's not just this ideological faction versus that ideological faction. Even among socialists and anti-imperialists there are sub factions, sub sub factions and sub sub sub factions, all of whom despise each other. And all of those divisions are far worse and far more inflamed in online forums. People will spend months on end engaging in online sniping at others over some perceived difference that would be undetectable by someone with a more mainstream perspective. Like that episode of Star Trek where a group of aliens who are black on the right side and white on the left are warring with a group whose colors are the opposite and only they notice the difference. Our precious new found ability as a species to network and share ideas with each other like never before gets bogged down and petty squabbling instead of organization toward a movement into health. Part of it is information because the only large-scale distributors of information in our society are controlled and manipulated by the powerful. Most people see very little evidence of just how much trouble the systems sustained by the powerful have gotten us into. Part of it is perspective because most human behavior is driven by ego. A lot more of our interest and attention goes toward the petty differences between ourselves and other humans than large scale problems which threaten us all. So you will see even relatively lucid minds spending their time talking about obscure sectarian disagreements or about the dangers of political wokeness or about the entirely empty theatrics of mainstream electoral politics even as the destruction of our entire world dangles above our heads suspended by a rapidly eroding thread. That alone should make us love each other. That alone should make us focus on what matters. That alone should bring us together to move as one against the globe dominating forces that are going to end us all if they are not stopped.


I'm going to try this patch remodeling here with another Tick Mill Charter to draw your attention this morning to a developing opportunity in the Kiwi Swiss from the Daily Time Train. So we've got a nice sending wedge pattern here developing and we just trade it up into the top side with the sending train line resistance, getting some supply here as denoted by the tails and these candles and we've got a bearish reversal candle yesterday through the five-period VWAP. I'm looking for a break now of the weekly pivot at 64.40 to set up a test of the 63.60 and if we can get through there I'm not really looking for a retest of the 63 level and I'll be using a protective stock just above the predicted monthly range resistance at 65. As always trade this, plan the trade, trade the plan, and most importantly manage your risk. So next time, thanks very much.


As I progressed through medical training, I could see the ground was definitely shifting. The conversation moved from treating and reversing individual cases of heart disease to an overdue requiem for palliative cardiology altogether, the year I graduated from medical school. In other words, resolving the whole coronary artery disease epidemic altogether through plant-based nutrition. So it's the latest. Ornish's first major study, more than 20 years ago, only included 28 patients on his plant-based diet, 28 patients that would go on to change medicine as we know it forever, but 28 patients nonetheless. Since then, he's published studies involving the reversal of heart disease in thousands of patients, proving that it can not only work in hippie California, but in Nebraska as well. Now, Ornish's just diet. It's a combo of low-fat whole foods, plant-based diet, rich in fruits, vegetables, whole grains, beans, peas, lentils, and soy, along with moderate exercise, a walking few hours a week, and in addition to stress management. Now, other studies have focused exclusively on diet. For example, Neil Barnard's team recently published the first workplace intervention study, Geico Corporate Headquarters. A couple months of just educating employees about the wonders of plant-based diet, along with a few healthier options of the cafeteria, without changes in exercise, compared to a control worksite where employees were kept in the dark. And within a few months, with their newly acquired knowledge is power, the pounds and inches came off.


At this point in my life, I am very happy with where I am. I live in Brooklyn, I've got a great paying job, I've always been a problem solver. Even if it's crossword puzzles or Sudoku or games, I've always been interested in those logical problems. So my first FileMaker database was when I was working with my parents at their manufacturing firm. I had ten months to learn a software package, build a solution, and work out all the kinks because within ten months I was going to be moving to New York City for college. I looked into a couple of different tools and I found FileMaker. Within about six months, I became proficient enough to call myself a FileMaker developer. FileMaker has definitely launched me into this world of business technology applications. It's just a very fascinating world to be in. I've been working at ASoft for eight years now. I started working there when I was an intern in my freshman year of college. I moved up through the ranks and am now the Director of Product Development. I get to learn about how different businesses operate. I get to go on site to the clients, I get to interview the end user, figure out what the root cause of their inefficiencies are. I get to meet the person behind the phone call and at the end of the day it's extremely fulfilling when somebody says to you, you know what, you truly understood what my problem was and you have truly implemented a solution to that problem.


Okay, the main focus of my current research activities is the definition of the tumor ecosystem and in particular the relationships between different immune cell types into the again to the tumor ecosystem. This would be really relevant because our ability to manage the function of the immune system is critical to try to define new therapeutic avenues. We started a couple of years ago this project together with the Fondazione Vodafone and the Fondazione ART. This is a project in which actually we are asking to the citizens to collaborate with us in the analysis of the single-cell or any sequencing data that is a huge amount of data that we are obtaining in the characterization of the tumor ecosystem using this technique. And actually using the one app that is possible to download on the different mobile device, the different citizens can actually help us in the analysis because they are actually performing a work of data analysis on their devices. There are a lot of opportunities in Italy. We have a fantastic educational system that is creating a very nice background of young people with a lot of passion and culture for science and the challenges are more I think related to having enough funds and probably also to our ability to create the right networks and cluster of collaboration.