So, let us continue with the third part of this course which we started out namely generalized Fourier expansions with respect to various complete orthogonal systems in Hilbert spaces. In this chapter there is one last bit was missing there is a 0's of the Bessel's function we still need to show that if P is real positive JPX has infinitely many 0's in the positive real line. What we have proved is that these 0's are simple, but we still need to show that there are infinitely many of them. The proof will be given in the next chapter after we do the Sturm's comparison theorem and now we turn to this chapter 6 where we discuss the vibrating string and regular Sturm-level problems. Suppose we have a string of length L and linear density rho x stretched along a line segment 0 to L where assuming that the length of the string is L and the string is clamped and the 2 ends and a string is set into vibrations then what are the governing differential equations? The governing differential equations can be written as y double prime plus lambda rho xy equal to 0. You are going to perform the same kind of calculations at the start of the linear wave equation and it is separate the variables as we did for the membrane and here you will get 6.1 instead of the reduced wave equation over there we get equation 6.1 y double prime plus lambda rho xy equal to 0 lambda is a parameter. The string is clamped at the 2 ends. So, we have the boundary conditions BC y of 0 equal to 0 and y of L equal to 0 display 6.2. A lambda for which there is a non-trivial solution of course if I take y of x identically 0 then surely the differential equation is satisfied and the boundary conditions are satisfied but such a solution is called a trivial solution I want a non-trivial solution I want a solution which is not identically 0 such that the differential equation is being satisfied and the boundary conditions are being satisfied the corresponding parameter value lambda will be called an eigen value of the boundary value problem and the corresponding solution is called a eigen function of the boundary value problem. So this particular boundary condition 6.2 is usually referred to as the Dirichlet boundary condition other types of physical problems will lead to other boundary conditions a more popular one is the Neumann boundary condition y prime of 0 equal to 0 y prime of L equal to 0. We shall discuss the Dirichlet boundary conditions and the Neumann boundary conditions these are the only two boundary conditions that we shall be discussing there are yet others such as periodic boundary condition that leads to Fourier series back to chapter 1 and there are Robin boundary conditions that we shall not touch upon. Of course we need to make some assumptions about this density function rho x the density function rho x is going to be assumed to be positive everywhere and it is going to be continuous we are going to make these assumptions about the function rho x. So, let us proceed further. So, a simple example is when rho x is 1. So, our problem simply reads y double prime plus lambda y equal to 0 and for simplicity I am going to assume that the string has length 1. So, the boundary conditions are y of 0 equal to 0 y of 1 equal to 0 they are Dirichlet boundary condition. Suppose if lambda is 0 suppose if lambda is 0 then what happens we get the differential equation y double prime equal to 0 what are the solutions of the differential equation y double prime equal to 0 a plus b x put x equal to 0 and I am supposed to get 0. So, a must be 0. So, solution is simply b x, but when I put x equal to 1 I must get 0. So, b must also be 0. So, a 0 b 0 the function is identically 0 it is not interesting lambda equal to 0 is not an eigenvalue. This condition that the solution should not be identically 0 that is very important remember in linear algebra when you look at a n cross n matrix a when would you say lambda is an eigenvalue if there is a non-zero vector v such that a v equal to lambda v. So, the eigenvector is not supposed to be 0. So, the analog of that is that the solution must not be identically 0. So, now let us take lambda to be non-zero if lambda is non-zero then we know the solutions of the harmonic oscillator y of x equal to a cos root lambda x plus b sin root lambda x put x equal to 0 and the condition y of 0 equal to 0 will immediately give you that a must be 0 because the sin term anyway disappears and cos root lambda x becomes 1 and so that forces a to be 0. So, a is gone from this discussion. Now, you put x equal to 1 we get that 0 equal to b sin root lambda. Now, b cannot be 0 because we are looking for a non-trivial solution. So, b cannot be 0. So, the only other option is sin root lambda must be 0. If sin root lambda is 0 then the possibilities of lambda are root lambda equal to 0 is out because we seen lambda equal to 0 is not an eigenvalue. So, root lambda must be plus minus pi plus minus 2 pi dot dot dot or the values of lambda are pi squared 4 pi squared 9 pi squared dot dot dot. In other words, a non-trivial solution for the boundary value problem exists only for a discrete set of values of the parameter. In short, the eigenvalues form a discrete set. Now, let us discuss the orthogonality of eigenfunctions and once we have orthogonality of eigenfunctions they got a sequence of eigenvalues lambda 1 lambda 2 lambda 3 will have the corresponding eigenfunctions y 1 x y 2 x y 3 x and these eigenfunctions will be mutually orthogonal. And again we will be looking at whether it is complete or not and if it is complete then we can do a generalized Fourier expansions with these. So, that is the idea. First and the most basic is the orthogonality and yes for the boundary value problem on the interval 0 L, y double prime plus lambda rho x y equal to 0 either with Dirichlet boundary conditions or Neumann boundary conditions. The eigenfunctions corresponding to distinct eigenvalues are orthogonal, orthogonal with respect to what? With respect to which space? I will be looking at L 2 of 0 1, but L 2 not with respect to the Lebesgue measure, but with respect to the weighted Lebesgue measure. The measure is rho x dx not the standard Lebesgue measure, the weighted Lebesgue measure. So, integral 0 to L u x v x rho x dx must be 0. This theorem 64 must be compared with the elementary theorem that you study in linear algebra when you have a real symmetric matrix and you take distinct eigenvalues lambda and mu. The corresponding eigenvectors are mutually perpendicular. A similar result holds for Hermitian matrices except that you will have to take a Hermitian product in C n instead of the usual inner product in R n. So, this is the analog of that. Suppose lambda and mu are distinct eigenvalues and let the eigenfunctions be u and v. So, u is an eigenfunction with eigenvalue lambda. So, u double prime plus lambda rho x u equal to 0. v is an eigenfunction with eigenvalue mu. So, v double prime plus mu rho x v equal to 0 and the Dirichlet boundary conditions are written down. u of 0 equal to 0, u of L equal to 0, v of 0 equal to 0 and v of L equal to 0. So, what do you do? We multiply the first equation by v and the second equation by u integrate from 0 to L and perform an integration by parts. By now this kind of argument has repeated itself several times and so this is a predictable line of proof. So, when you integrate by parts what is going to happen?  Similarly, in the second equation I multiply by u and do an integration by parts I am again going to get minus integral 0 to L u prime v prime I am going to subtract and this term will cancel out. Then what is going to be left over? The boundary terms we get when we perform an integration by parts. Where are the boundary terms being evaluated at 0 and at L? What are the boundary terms for the first one for instance u prime 0 v of 0 with a negative sign but v of 0 is 0. At the other end you are going to get u prime of L v of L but v of L is 0. So, the boundary terms drop out. The same thing is going to happen with the Neumann boundary conditions again the boundary terms will drop out. So, what is left after you go through this rigmarole what is left over is integral from 0 to L u x v x rho x dx lambda minus mu is a constant comes out of the integral. Lambda is not equal to mu remember we are taking distinct eigenvalues. So, what must be 0 integral 0 to L u x v x rho x must be 0 and that completes the proof of the orthogonality assertion theorem 64 has been established. And the case of the Neumann boundary condition is left for you to work out. Now comes the question of simplicity of eigenvalues. To each eigenvalue or the boundary value problem with either Dirichlet boundary conditions or Neumann boundary conditions there is only one eigenfunction up to scalar multiples. Now go back to linear algebra.  You want to discuss diagonalizability of the matrix. Now you know that if you have n cross n matrix and all the eigenvalues are simple and they are distinct and if the eigenvalues are distinct they are simple and that is the easiest situation. The eigenvectors will be linearly independent and they will form an eigen basis. The problem comes when the matrix has a certain eigenvalue and it has got certain multiplicities. In linear algebra you talk about algebraic multiplicity and geometric multiplicity. What is algebraic multiplicity? Algebraic multiplicity means that you take the matrix and look at its characteristic equation and take the eigenvalue lambda and you see what is the multiplicity of this eigenvalue lambda as a root of the characteristic equation. And that number is called the algebraic multiplicity. What are the geometric multiplicity? The geometric multiplicity means how many different eigenvectors are there which are linearly independent. Suppose you got an eigenvalue lambda and I can find three linearly independent eigenvectors and no more then the geometric multiplicity will be 3. So, in other words the geometric multiplicity is the nullity of a minus lambda i that number is a geometric multiplicity. The geometric multiplicity will be less than or equal to the algebraic multiplicity and the inequality can be strict. The inequality is strict then you know that in linear algebra there is a lot of problems then you have to look for a Jordan canonical form. But when you take a real symmetric matrix that does not happen for a real symmetric matrix the geometric multiplicity will exactly match the algebraic multiplicity. So, what we are talking about here are analogs of real symmetric matrix or a complex Hermitian matrix. These boundary value problems are analogs of those problems. But here we got something even better for the Dirichlet boundary conditions or for the Neumann boundary condition for each eigenvalue the geometric multiplicity is one. There is only one eigenfunction up to multiples and as I said there is no concept of algebraic multiplicity there is no concept of characteristic equation it is an infinite dimensional problem. So, let us prove theorem 65 explain to you the significance of theorem 65. Assume that u and v are linearly independent eigenfunctions linearly independent have been written in red and they are both eigenfunctions with the same eigenvalue lambda that means ux and vx both satisfy this differential equation y double prime plus lambda rho x y equal to 0. But they are both solutions of the same boundary value problem right. So, they must satisfy the initial condition. So, u of 0 must be 0 and v of 0 must also be 0 and if u and v vanish at 0 every linear combination of u and v vanish at 0. But u and v are two linearly independent solutions of a second order differential equation. What is the space of solutions of a second order ODE? It is a two dimensional space how do you prove that use Picard's theorem. So, let us do the following let us take initial conditions let us appeal to Picard's theorem let us take y of 0 equal to 1 y prime 0 equal to 0. So, with these initial conditions there must be a solution of the differential equation call it yx. But that solution does not vanish at that origin. But that solution must be a linear combination of u and v because u and v form a basis of solutions. So, that is a contradiction because y of x on the one hand must be a linear combination of u and v. On the other hand a linear combination of u and v vanishes at the origin but y does not vanish at the origin. So, that shows that you cannot have two linearly independent eigen functions with the same eigen value. So, each eigen value is a simple eigen value that is why I call it simplicity of eigen values. So, now we have got eigen functions to each eigen value lambda there is only one eigen function up to multiples. And so, we can take this set of eigen functions it is an orthogonal set. Is it complete in this L 2 space with measure rho x dx? Is it a complete orthogonal system? The answer is yes. The theorem is often stated under a stronger hypothesis. For example, you can look at Courant and Hilbert's methods of mathematical physics volume 1 page 293. However, if you look at E.C. Titchmarsh's book eigen functions expansion associated with second order ODE's volume 1 it proves this theorem of completeness with substantially weaker hypothesis I am giving you a page number. One can also discuss mean convergence but we shall not do so here. So, that concerns the completeness of eigen functions. Let me state this theorem 66 the possibility of expanding a reasonably nice function f of x as an infinite linear combination of these eigen functions. This is a complete statement for the term level problems in this question that is you are looking at y double prime plus lambda rho x y equal to 0, rho x is positive, rho x is continuous and we are looking at either the Dirichlet boundary conditions or Neumann boundary conditions. Then several things happen you have an infinite sequence of eigen values lambda 1 less than lambda 2 less than lambda 3 and these eigen values will tend to infinity and the set of eigen functions will be complete in the following sense. Each Lipschitz function on 0 L can be expanded as a four-year series f of x equal to summation j from 1 to infinity c j phi j x and the convergence is point wise on the open interval 0 L and the coefficients are given by the usual formula. Multiply both sides by phi j and take the inner product with respect to rho x dx. When you take the integral integral with respect to the measure rho x dx so when you right hand side you get c j integral phi j squared rho x left hand side you are going to get integral fx phi j x rho x dx so the c j will be given by integral 0 to L fx phi j x rho x dx divided by integral 0 to L phi j x squared rho x dx so the four-year expansion with respect to a eigen functions corresponding to a Sturm level problem that is a boundary value problem for a second order od y double prime plus lambda rho x y equal to 0 with Dirichlet or Neumann boundary conditions. Here are some exercises for you show that the eigen values of y double prime plus lambda rho y equal to 0 with y of 0 equal to 0 and y of 1 equal to 0 are positive real numbers that is this eigen values must be positive how do you check that the eigen values are positive let us do that let us multiply the differential equation by y and perform an integration by parts perform an integration with parts what do you get y double prime y integral from 0 to 1 the derivative will shift from y double prime to the other factor you are going to be left with minus integral y prime squared boundary terms will drop out because I am looking at Dirichlet boundary condition what was the second term lambda integral 0 to 1 rho x y x squared and that the first term had a negative sign so we get lambda times integral rho x y x squared equals integral 0 to 1 y prime of x squared so lambda must be positive that completes the problem. Determine the eigen values and eigen functions of the stem level problem y double prime minus 2 y prime plus 1 plus lambda y equal to 0 with boundary conditions y of 0 equal to 0 y of 1 equal to 0. The third problem is an interesting problem determine all the eigen values and eigen functions of the stem level problem x squared y double prime plus x y prime plus lambda y equal to 0 how do you do these exercises second one you will try the solution to be of the form c1 e to the power mx plus c2 e to the power m2x and you will try to fit the boundary conditions and so on and m of course has to satisfy the characteristic equation m squared minus 2m plus 1 plus lambda equal to 0 so you get the characteristic equation and you will try to fit the boundary conditions the second one here you see a Cauchy Euler equation x squared y double prime plus x y prime plus lambda y equal to 0 and the indicial equation is m into m minus 1 plus m plus lambda and you write the general solution and try to fit the boundary condition this boundary condition is different from the Dirichlet or the Neumann boundary conditions these are called periodic boundary conditions so there are some variants in the exercises show that the eigen value is the boundary value problem y double prime plus lambda y equal to 0 y of 0 equal to 0 and the boundary conditions are slightly different y of 1 plus y prime of 1 equal to 0 they are given by the equation lambda equal to k squared the eigen values are given by lambda equal to k squared where k satisfies the transcendental equation tan k plus k equal to 0 so again the general solution of this will be a cause root lambda x plus b sin root lambda x equal to 0 put x equal to 0 straight away a becomes 0 and then put the other condition and you will get this equation tan k plus k equal to 0 now this tan k plus k equal to 0 has infinitely many roots remember how does the tan function look like look at the graph of the tan function tan function is periodic with period pi it is an odd function so first draw the graph of tan x from minus pi to pi it starts from below and it passes through the origin and goes off to infinity it has two vertical asymptotes x equal to pi and x equal to minus pi two vertical asymptote and this picture repeats itself periodically with period pi so you draw this graph of tan k and then you take this k the diagonal y equal to x in the graph in the in the graph paper just draw the line sloping at an angle of 45 degrees with the x axis passing through the origin this line and the graph of tan x will intersect at infinitely many points there will be exactly one point of intersection in each vertical strip of width pi so that is how you will prove that there are infinitely many roots now this kind of boundary value problem appears in certain physical problems and this is discussed in Byerley's text on page 117 in section 67 the problem as such will appear in many textbooks a very popular exercise that you will see in almost all books in undergraduate text on boundary value problems but only Byerley gives you what is the origin of this boundary value problem the next two exercises are interesting a rigid body is rotated with uniform and fixed angular speed about an axis that is not specified how would you choose this axis of rotation so as to maximize the rotational kinetic energy formulate the problem mathematically and the other thing is the variational characterization of eigenvalues and eigenmeters these two exercises are basically items from linear algebra why is it that we are bringing in ideas from basic linear algebra because I want to first discuss the problem in the linear algebra setup which is more familiar and then take over to the differential equation setup where some highly non-trivial complications proper so I think this is a very good place to stop this capsule and we shall continue this next time with a discussion of these two problems we will begin by discussing the rigid body problem and this problem on variational principles of eigenvalues and eigenvectors maybe you want to think about this problem number 18 you probably want to consult some elementary physics books on rigid body mechanics and find the formula for the rotational kinetic energy of a rigid body maybe you want to take a cube and ask yourself whether the axis of rotation should be a diagonal for instance or should be an axis passing through one of the sides of the cube how should you choose this axis of rotation so we will stop this I have given you some interesting questions to think about thank you very much


In this video, we are going to examine shear in a beam subjected to transverse loading. Now in previous units, when we introduced a new type of loading and looked at the stress distribution, resultant from that new type of loading, we did it in a particular way. We first looked at the deformation that would occur to that type of loading, then looked at the compatible strain distribution that matched that deformation, and then used Hooke's law to convert that strain distribution into a stress distribution. This isn't quite possible to do with shear stresses in a beam subjected to transverse loading, and we're going to show you why by looking at a simple beam. In the past unit, we looked at beams subjected to pure bending or moment loading, so that when we took a section, saw an internal load equal to that moment, and isolated an element, we had an element subjected to pure moment loading. We could do this and look at the deformation of this element, and use that to derive the normal stress distribution. Now if we look at a beam subjected to transverse loading such as the beam shown here with a point load V applied to the end, and we take a section, we see that we will have an internal shear force and bending moment. And then if we isolate a small element, we see that there will also be an internal shear force and bending moment. So we can actually isolate shear in a beam subjected to transverse loading. You will always have shear and bending. But if we actually take a closer look at this element that we've drawn here, there's a small mistake. If we look, there is a distance here in our element. Even though it's an infinitesimal distance, it does have some distance. And so the two shear forces V will create a moment. So the internal bending moment actually has to vary from one side to the other to maintain equilibrium. Now what this actually means is that there is a variation in the internal moment distribution as a result of a shear force. Hopefully this relationship between internal bending moment and shear force is not too big of a surprise. Earlier in your studies when you learned how to construct shear force and bending moment diagrams, you already established this relationship. You found that the derivative of the bending moment diagram, or the rate of change of the bending moment with position along the beam, was precisely equal to the internal shear force. We can exploit this relationship in order to derive the internal shear stress distribution in terms of bending moments. So we see that there is a relationship between bending moment and shear force. So there should also be a relationship between the bending stresses and the shear stresses. So what do we know about the bending stresses first of all? Well we know that due to that bending moment loading we will have a linear varying normal stress distribution as shown here on the left with a similar distribution on the right which will be slightly different. It will vary by a small amount d sigma due to the variation in our bending moment. Now if we look at our shear stress distribution, we know that there has to be some sort of vertical shear stress distribution acting on those two faces. But we don't actually really know anything about the nature of that distribution. However, since the internal moment and shear forces are related, there must be a relationship between these shear stresses and normal stresses. So let's take a closer look at our normal stress state and see if we can define this relationship. I will redraw our element in a sort of a three-dimensional view so that we can better see what's going on. If we look at our stress distributions it actually does look like this element is not in equilibrium because the magnitudes of the stresses on the left are smaller than the magnitudes of the stresses on the right. However, you need to recall that the normal stress distribution due to bending is such that the resultant force due to the stresses on one face is actually zero. So the compressive stresses on one face create a resultant force that is in equilibrium with the resultant due to the tensile stresses. This is true for the entire section of the beam. However, if we take a section of our section, so we'll cut a line at a distance y' from the neutral axis, we can now create a smaller portion that we remove and now it will no longer be in equilibrium because we've removed the compressive stresses at the top of our beam. We've cut them away and now the resultant tensile force on the left face will be smaller than the resultant tensile force on the right face. As a result, a shear stress has to be formed along our new section plane to maintain equilibrium. So an applied shear force results in variation in bending normal stresses along the length of the beam and this variation necessitates an internal horizontal shear stress within the beam that varies with position y' in the beam. But how does this help? We are interested in the shear stresses acting vertically, not horizontally. Well, this is where the principle of complementary shear stress comes into play. If you recall back from our videos on stress and strain, we derive that every shear stress has an accompanying or complementary shear stress acting perpendicular to the original shear stress. If we apply this principle to the horizontal shear stress we examined, we can see that the vertical shear stress is precisely equal to the horizontal shear stress at every point in the beam. In the next video, we will look at deriving an expression to describe the distribution of shear stress through the thickness of the beam. However, before viewing the next video, please take a moment to think about what you can say about the distribution based upon what you have learned in this video. Where would you expect the maximum shear stress to occur? What about the minimum shear stress? And can we actually say anything about the nature of the distribution? Once you have thought about these answers, you will be ready to go on to the next video where we will derive the expression for shear stress in a beam.


The following is a presentation of TFNN. Trade what you see with Larry Pezzavento. Call now toll free at 1-877-927-6648 or internationally at<PHONE_NUMBER>. Now Larry Pezzavento. Good Lewis, we are going to have Stan Harley as our guest at the break today. No, what do you call it, hail today folks, no rain, no hail. So we should be okay. I posted the chart from Dennis Cartman showing the fear greed index, which is a rough way of saying overbought, oversold. And as you can see, we are overbought. We're in the greed area at 89, which is a pretty high level. However, we need to talk about something we've been watching here for quite some time. And that is the natural gas. Mr. Z happens to be chatting about it. Those of you that follow this, you'll notice that the natural gas came down last night and filled that gap at 273 and we're now trading up around 281. But that was a big ABCD pattern, folks. We backed off just a little bit. Now, if we go above that 290 level, we are looking at some real serious prices to the upside. So right now this ABCD is complete. It's backed off. It's made its first retracement. So this is going to be a very, very interesting situation here as we look at natural gas going forward. Any move below 273 now would not be very good. But right now it's acting exactly as it should.  It was at 1220, which was 220 in the morning. We had announcement coming out of supposedly China or Timbuktu, wherever it was. But I just wanted to show you folks. You wonder, you know, you folks asked me about the AI program and stuff. But let me show you what it can do sometimes because this was done long before. But look what happened right at 2 o'clock in the morning when there was supposed to be a big move in the S&P. Look at that. It was exact. And it actually went through the whole day. There was no sell-off at 5 o'clock. It just went sideways after that, which is not unusual because it's best the first three quarters of the day. But the fact is what I can do is I want to show you also this. I happen to be in this one because I've been really embarrassed this one. And this was the gold market. I actually was not watching the gold. I was actually watching the stocks because the gold had just made a 38% retracement up there at $14.96. Remember, it bounced exactly $15 off of the bottom. And we made a new low today, folks. So we went down to $14.82 today almost exactly. In fact, we'll get that up here so you folks can see it almost exactly at the time. Hold on just one second here. Bye, Golly. Got to get these little technical things worked out. Don't we? All right, here we go. We'll get this up here. And the low actually came in at $14.82. I was posting it this time getting ready for the show. But $14.82 means we took out that low the other day and haven't got any. We've had a little bit of a bounce, $4, but really not very much. I'm getting more friendly to gold now if we can stay above $14.80 today. This will be a real key thing here. That's it. Well, Bill, everybody has that feeling because if you think that China doesn't play games with us, folks, you haven't been around long enough. I've been doing this business for a long time. I've been watching them do shenanigans in the grain trade. And it used to be back when we had the Russian grain robbery. It was the Russians that were doing it. But they do the same thing. They give misinformation. You think Mr. Buffett doesn't give misinformation? Give me a break. No, but that's just all part of the game. And that's why I'm a technician. You know, I don't know what these guys are saying. And I don't understand three-fourths of it. That's on the low end, probably closer to 89% or 78.6%. I don't know. Anyway, that's neither ear to there. Now, we need to show a couple of charts here from our good friend, Mr. Z, because this was one we talked about yesterday. And we're doing the same thing that we did yesterday. We had a $15 rally. And what did we do? We came down $17 and nearly made that low. We did not quite take out the low at 79 as of yet. Now we could, but so far it is held. So we've been 15 up, 15 down. And that's pretty much what's been going on. So not too much going on. If we get below $14.79, we believe we're heading towards that level of $14. What is that level? I think it's at $14.55. Oh, Ruby's saying that the piggies may open limit up. Ruby, I would not bet on that. And the reason why I'm saying that is I'm looking at the grains and they're not acting like there's a big deal going on in China. We got corn up $0.03, wheat up $0.03, and beans up $0.04, at least the last I checked. And that means let's just double check it here and see if I can get some, yeah. Well, yeah, beans are up $0.33 and weeds up $0.02. I mean, that's not the exact kind of move that you want to see when you're looking at a market that is, you know, we'll see what happens. Anyway, you're right. Buy them when they're crying and sell them when they're yelling. Anyway, Ruby, let me know when they'll be opening soon. So let me know if they open limit up. I'll be quite surprised if they do. The last price I saw on the hogs was around $0.66. Is that correct? I haven't checked them because I've been doing other things tonight, watching the pound and the Euro and the pound had a really nice move. We'll cover that here in a minute. And we'll just get on a fact distance. We'll have a break here where we're coming up soon. Here's that British pound. We pointed out this huge ABCD that was up there at the 78% level. That came in at $1.30. We're now trading below $1.28. The $3.82 retracement on this, folks, comes in at $1.2710. Watch that. That's an ABCD. Very, very important one, I believe. So sort of keep your eyes on that. That would be very interesting. $64.68 is where they closed. If they open limit up, my hat's off to you because they're at major support here. Any little bit of weakness here.  Oh, well, are you long? Have you got an opening indication? I haven't even seen it. I don't even know what the opening indication would be. So I shouldn't even say that. Have cattle opened yet? Yeah, let's just double check this. I think they have. No cattle haven't opened yet either and nor have the hogs. So I don't know what's going to happen here. $64. All I know is if they get below $63 in those hogs, you know, that's neither here nor there. Ruby, this reminds me of a situation back in 1983 when I was, excuse me, I was 83. I was back on the floor. I was short two pork bellies and there was a cattle, a cattle, not cattle on feed, but a cattle inventory report. And it was so bullish. They said that everything was going to be up the limit three days in a row. Cattle had been going crazy to the upside anyway. Bellies had been in a little bit of a retracement pattern and I'd shorted two bellies on Friday. This was Monday. I saw that news and I said, oh my God, I'm going to get killed. I walked over to the pork belly pit and I tried to get my order set on the desk. You know, get on top of the deck, which was illegal. And I got chewed out for that. But he showed me the deck and it was to sell 2,000 pork bellies at the market. Cattle didn't even open just a tiny bit higher and went limit down for three days with a very, very bullish report. So just because China and the U.S. are saying something, folks, just be careful. That's all I know. One other pattern that is very interesting and I'm going to cover that after the break is if you like Fibonacci and you like symmetry and you like sacred geometry, you're going to like this next pattern. Maybe<PHONE_NUMBER>. E.T.F.'s Commodity Futures and Forex. Are you in the market for buying or selling real estate in the Bay Area, including the surrounding St. Petersburg, Tampa and Clearwater markets? Tiger Real Estate, LLC, is a firm that has extensive experience in the Tampa Bay Area. Whether you're looking to sell your current property for maximum value or you're looking to sell your current property for maximum value or you're looking to sell your property for maximum value, you're looking to sell your property for maximum value, you're looking to sell your current property for maximum value or you're in the market for a second home or investment property, Tiger Realty has the experience across all areas of real estate in the Tampa Bay Area to help buyers and sellers make the most informed decisions across all price levels. From the price you should be paying per square foot in certain up and coming areas to the type of cash flow investment properties are capable of creating, Tiger Real Estate can help you make the best decision when it comes to all areas of the market. For more information on Tiger Real Estate, or any of your financial future, call Tiger Real Estate, LLC today at<PHONE_NUMBER> or email us at Tiger at TFNN.com that's<PHONE_NUMBER> Call us today. Many of our new listeners have heard about the Tiger's Den. The Tiger's Den is a lively community where professional traders and investors can meet, exchange ideas and information in a comfortable moderated atmosphere. Hear all of the TFNN shows see all of the charts as they happen live and have access to archives of all of those charts. You can test drive the Tiger's Den absolutely free for 30 days and greatly enrich your knowledge of these markets and how to make your money work for you. 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Toll free at 1-877-927-6648 Internationally at<PHONE_NUMBER> Okay we're back folks and I'd like to put the chart up of the NASDAQ this is as of last night of course we did hit 826-0 that completes double ABCD patterns on the daily as you can see up there there's a 1.27 and a 1.618 it is a butterfly and it is a three drive pattern going back to last April whether it works or not I don't know but all I can tell you is this is a completed pattern we hit 3091 I believe last night we're trading at 3087 in the S&P so we'll see what happens but the NASDAQ has already sold off 30 handles from that level I don't know if it means anything or not it's come back halfway but we'll see what's going on but it is complete so we'll do one thing at a time now we got to get to where the pedal meets the metal and the real players play we're going to take a look here folks at the old Bondolis let's get up here and get the old pattern in here because we've done something very very important you notice this really dark red line that's here right now I put this in last night at about 2 o'clock and we were getting ready to take out those lows from September the 13th if you remember that was a big new moon I was doing this subject in London and we were looking to buy the bonds there and of course we had a pretty good rally but now we've taken out that low by just a little bit we've been down as low as 115 13 I believe we're trading around 157 15 right now so watch it because this is a really important number here in the Bonds taking out those lows and going now the notes have broken that shattered it I mean they have really hit it really hard so the thought of negative interest rates right now is a little less positive than it was just a few months ago so we should be watching it anyway no matter what what we're looking at I hope that helps but those are just a few of the things now Mr. Z also brought one up on the copper that is really interesting because it is he's been very bullish copper recently and as you can see here on this chart that he sent to me and he sent it to you guys here I noticed that it is on the verge of a breakout this is high-grade copper we're trading up around 730 and remember he was really interested in it around the 256 level so that's been a heck of a move my hat's off to you so it looks like it's going and the ABCD structure on this folks if you want to do the math you had your low down at 248 you're high up at 270 so that's 22 points 22 you had 22 to 252 it's going to take you to at least 276 so it's got another 6 cents to go just to complete the ABCD so we'll just keep an eye on it that's going to be very interesting I don't know if there's any running inflation yet but there might be down the road we have to do one thing at a time do that but that's neither here nor there now we need to talk just a tad bit coin we've had several questions about that and we want to get this up here so you folks can take a quick look at it this comes from our good friend Karey Cismansky lives about 3 miles away been my buddy here for 28 years and that's when I first met him and we got together and he certainly learned this stuff good oh he's calling that a Gartley by pattern as you can see we posted that a few weeks ago now look at this sideways action folks after that big gap up you don't see many gaps on Bitcoin you can see one back in May you see where it left a big gap in May and the reason why this thing trades 24 hours a day on these these different exchanges that they have so it has that gap and we haven't even made a 382 retracement yet so this is really positive expectation here for Bitcoin it really does I mean this sideways action it is very very powerful so we need to watch that because well you can watch it I'm not trading it but you know people are talking about it and when the president of China the premier of China is talking about it should pay pay attention for it yes I'm aware of the fact that we're going to have in fact I'm very happy being at my age bracket as I run into the eighth furlong we're going to have free Medicare for all I'm hoping for free food free travel I'm not so much concerned about the education anymore folks as I'm done going to school I've done enough learning in these markets so I don't need to go back to school well I probably should but anyway we'll see what happens I don't know oh what one other thing this was a chart that hold on a second yeah that's right I can see I can see them being able to take out all of the healthcare companies folks let the government run our let the government run our health system that would really be a good thing yep Marshall now that's not nice I don't know anything but I know one thing you don't want the government in there doing anything that's one thing for sure here let's get up here and take a quick look here at this I know you're teasing me here's the chart from Enzo we last night with all that bullish news the thing popped up quite a bit it's a matter of fact folks you know as you as you look at this today the stock market I would I would have thought last night if the stocks would have come up and had a run where the China thing was done deal and everything I would have thought that it would have been up 300 points in the Dow and it might be before the end of the day that's for sure that there's a possibility of that of course but that's neither here nor there okay let's move on here and we want to do some other things here we got the bonds making a new low down in here folks and I on these puppies because if they collapse from here boy they're going to go down a long way as I say hold on a second here might have a costume here could we have a rally soon I don't know let me the I don't know what you mean 140 to go and what I don't know in the Euro well the Euro is we've been talking about the Euro we said it yesterday remember when it broke below that really key level where was it here it is right here remember we talked about this all the Euro the Dow yeah I can't go easy do that you can easily see here that we've got this ABCD that form we rallied a little bit and then we've rolled over we're now trading below these levels and that's a bad sign we weren't even able to rally to a 382 retracement yeah the 30-year bond does look sick it certainly does and remember well I think I've got the note chart up here folks and the open interest in the bonds has dropped three days in a row now whether that means anything I don't know or not but here's what you're looking at in the bonds I'll put a print it up here and show it to you again because this is really important you'll notice here that I didn't draw it in but there's an ABCD pattern there at the high we made yesterday at $159 in change that's almost an exact I missed it by one pip of being a 382 if you measure that 382 retracement that one takes you down to $155 so it's got another two large to go so I'm not sure so we'll just do one thing at a time I hope that helps that's all I can tell you one thing at a time alright let's move on here any question oh we got a break coming up and then we got Mr. Stan Harley coming on to talk to us Stan was fortunate enough to move here to Arizona and by golly he missed the fires because he lived right over there where all those fires are in California so we're glad to hear that so we'll be right back with Stan Harley of the Harley Stock Market Ladder Larry Pezzavento has just started his brand new service Fibonacci 247 and he's already delivering content to his subscribers on a daily basis when the markets opened and even on weekends each Monday you'll receive Larry's written report that provides detailed commentary and a summary on the charts and videos that Larry sends out and throughout the week when warranted Larry will send out via charts or videos or both the key markets that he is watching during the day this will be up to the date active trading information that will help you in 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when warranted don't miss out on this great chance to get a 30 day free trial to David's daily newsletter the path of least resistance with no obligation to pay anything David has been delivering solid recommendations for his subscribers recently and if you'd like to see the type of newsletter he delivers every morning then visit the front page of TFNN and you'll find the path of least resistance under trading newsletters for all the details and to start your 30 day free trial today so please log on to TFNN.com now TFNN is excited about our new software charting program the art of timing the trade charts in collaboration with Tom O'Brien and using his best selling book the art of timing the trade your ultimate trading mastery system David White has programmed an outstanding piece of software that will complement any trader's methodology using this first of its kind program the art of timing the trade charts allows you to scan thousands of stocks for Fibonacci system setups including Gartley's ABC's Butterflies and much more the art of timing the trade charts is designed to help you when scouring the markets for stocks just beginning to form the trading patterns that many investors spend days weeks or even months searching to find and right now we're offering licenses available at only $79 a month we are so confident that you're going to love this new charting software that will even give you a 30 day unconditional money back guarantee don't miss out on this new software get your copy of the art of timing the trade charts today by visiting tfnn.com this segment is brought to you by thinkorswim for more information just click the thinkorswim banner on the front page of tfnn.com okay folks we've got Stan Harley of the Harley stock market letter on the line Stan I understand that you made the trade of the century when you move from the fire infested California to Arizona is that true absolutely Larry I love California just like you you know we used to live there I lived in California 34 years beautiful place but now I'm proud to call Arizona home how close were the fires to where you live Stan were they in any danger at all oh I was in I lived in Ventura County yes very very close yes and yeah yeah wow that I know I lived in Westlake LA side so wow it's really at least you got through it at least it's better anyway California so screwed up now I don't understand how they're going to survive you know I almost moved out of California in 1970 because the taxes on the houses were going to go to 13% then they had that Jarvis Gann initiative and so I stayed I stayed in the I stayed there but boy I'll tell you I'm really surprised at what's going on what I see in the news and what's going on hey we got trouble here in Arizona you know where those people were killed that's 90 miles to where I live Stan I know I know that's really close yeah that's really close and let's talk about the markets let's talk about the markets you've got it brother you've got it I sent you a couple of charts a little while ago I'm not sure whether you've had a chance to I posted the one with the Gann rule of four I'm a I'm a table-pounding bull here Larry I think we have an interesting pattern developing Gann's rule of four he many many years a hundred years ago noticed this pattern what he found was as a market a stock an index commodity anything moves up to some resistance threshold and that threshold of resistance can be horizontal it can be upward sloping it can be even occasionally downward sloping but the point is the initial three attempts to break through that line of resistance a result in a failure and the fourth push is essentially maker break time the fourth push if it bounces off that and and and goes the other way then you get a pretty sharp drop on the other hand if the market or index breaks through to the upside on that fourth attempt it tends to sprint very rapidly and never looks back and I think that's what is happening right now here's a chart of the down industrials I see you've got it up on the screen this is a couple of days ago we actually now are right just above that line that I have that's a Gann angle it's about it's a one by four Gann angle I've drawn on there and this is the fourth push and if Mr. Gann's theories from a hundred years ago still hold true today and I believe that they do we should continue to push higher and see new highs across the board led by the down industrials and never look back and I think that's what's taking place now we're up at about 170 odd points on the Dow and the second chart I sent you is the S&P 500 and we have a similar structure there we have a one by two angle being projected off that high in January of 2018 and it portends a very similar pattern we got the fourth push up against this overhead resistance and we are already in new high territory and if Mr. Gann's theories hold true as I said we should continue to push higher and never look back and Larry that's what I think is happening well it's certainly happening today my friend I happen to be up at two o'clock in the morning when that thing happened and yeah well you know I have no well mother nature has played some weird tricks on me as I pass the seventh furlong and so I was up you know just taking care of business I well anyway yeah well you know what happens you know you get up so many times anyway I happen to just check and it was just exactly at the time in fact it was almost at 2.22 in the morning because you know 2.22 is a garlic batter and I think it was a 10 after or something like that and as soon as it took off I walked over to the TV and I turned on Bloomberg just to see what was going on and I saw the Chinese deal and stuff in fact I was surprised that the stock the Dow had not jumped 300 points or more you know but that's neither here nor there but it might be 300 for the days over but that's what you got the chart of the S&P up on and this is from a couple of days ago we are now at the fourth touch point on that rising one by two angle and we are breaking through and we are pushing to the upside and we're making gee we're right now as you and I speak we're making new all-time highs in the S&P 500 doesn't take much it doesn't take much it's going to be a steady grind I believe higher and I think you're going to see the other components that make up what I call the big five and for me Larry the big five are the Dow industrials Dow transports the New York Composite the S&P 500 and the NASDAQ I look at all five of those all the time and I want to see either confirmation or non-confirmation right now we've got three of the five in record high ground that is we got the Dow industrials we've got the S&P we've got the NAS we've got the big five or the the Dow transports and the New York Comp and those are really packing my head of steam right now and I think you'll continue to see those other two outpace on a relative basis the Dow and the S&P because they've got some catching up to do and I think you'll see them in record high ground as well in the not too distant future the transports are up one and a half percent as you and I talk that is a big move in the transportation that's for sure that's really a big as this bull market evolves there you see a push pull you see some components of the big five lead like the Dow and the S&P and you see the others lag and then at other times you've got other components leading so over the long haul they tend to make new highs together as the bull market evolves and my theory is we're still in a secular bull market at least for another three and a half years I posted a chart here we speak it's a NASDAQ composite and we gapped above those old highs last Friday and boy that is a really powerful signal and of course we've continued to go higher so I have to agree that Mr. Gann is certainly spot on as we look at it today that's for sure and he's got the news at his back because they're saying that the Chinese deal is a done deal and as we know when they say it it must be so right Stan it must be so Stan what's your feeling on the gold here I know you do do some work on it but what are you looking at I'm bearish on the metals complex I think a couple of months ago we saw a significant high that high was part and parcel of a cycle that averages about oh 96 months also about 40 weeks both of those cycles I think mark that high and I think the metal complex are heading south that's what I think in the very short term we might get a little bounce but no I think overall the dominant trend is southbound okay now one other question and that is about the old Bondolis they've had one hell of a correction here now since September the third are we due for a bounce in these bonds are they finished well I think a couple of months ago we might have seen a significant high in the bonds as well long long term I think bonds are heading higher but I think that high from a couple of months ago might stand for a while okay hey Stan thanks for joining us my friend my pleasure okay buddy Stan Harley this Harley stock market letter you can Google it and you'll see the man himself we'll be right back folks if you're in the CD market and looking for a secure investment the Tiger first mortgage program may work for you the security for these first mortgages are building lots in the tax opportunity zone in St. Petersburg Florida the tax act of 2018 set up tax free zones across the country where you can build and hold for 10 years and pay no tax on the profits which makes these lots valuable the investment is anywhere from 30,000 to 75,000 the interest paid is 7% yearly paid on a monthly basis according to bankrate.com the best rate for a foyer CD in the country as of February 20th is 3.1% a $50,000 investment at a normal foyer CD rate of 3.1% would give you income of $1,550 per year or $6,200 over the foyer period that same $50,000 investment in the Tiger first mortgage program would give you $3,500 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LLC the bull bear trading hour with Tom and Tommy O'Brien next folks and we're still rocking and rolling we got the Dow Jones up two and a half now and we got the NASDAQ is still not making a new high we've almost 3100 in the S&P that is a very interesting number two so we're going to have lots of buying early this morning and of course that will continue all through the day as we know the bonds have gone down quite a bit and now they're bouncing a little bit here and there we made a low of 157-10 that low we made two months ago was at 157-17 so we haven't exactly collapsed from there watch the time frame of 10 o'clock folks 10 o'clock is going to be a really interesting time here in the bonds 10 and 1130 both of those times are very very interesting and in the stock market I would be looking pretty close to now that's what it would be looking at if this is going to happen but we'll have to wait and see we've had a small rally in the gold market 1482 up to 1489 that's just nothing more than a little small ABCD pattern so that's neither here nor there so we'll pay a close play close attention to that one. Regarding the hogs Ruby they didn't open anywhere near limit up and they're almost down on the day now so I hope you got out on the open because they're not acting well the corn is not acting well the beans are up a few cents, wheat's not acting well so those things if you believe the grain trade the grain trade is saying this is not going to happen right away in this stuff with the thing so I don't know but you know we have really bullish news for the grains today folks this is about as bullish as you can get no more tariffs you know free trade that's what they're looking for and this market's not acting well stock market's acting well but not the grain markets and not the hog market so I don't know if that means anything or not but that's just just wait and see well just be careful and put your stop in because if we break below that 78 percent level at once at 64 they're not going to look very good and last price I saw was just about 65 and change so just be careful because if you don't use a stop you're telling the market that I know more than you do and that's not the way it is let's take a quick look here at the chart that was sent to us by our good friend Dennis Gartman and I wanted to bring it up this shows you the relationship between the Chinese stock market i.e. Shanghai and also the the Dow excuse me the S&P 500 you notice that we're making these big patterns up here and the S&P 500 but now we'll have to wait and see we're just in a holding pattern here in the Chinese market so there's not really much going on at that point so if you have any questions it's<PHONE_NUMBER> if you have any questions please be be kind enough to let me know that I'll answer for you and if I can't I'll try to find somebody that knows the answer to it so that's neither here nor there we had a question this morning about the gold folks we really believe that that gold market we talked about it many many times I've talked about it this morning already we hit that 82 level and that's that same pattern that we were looking at in the gold just look at it again you'll be able to see it now the key here is yesterday when we hit it this is a good example here's a good example yesterday when we hit that low at 1483 we rallied up to 1495 that was a 382 retracement off of point B that's all that was and then when it came down today hasn't made a new low that's actually a good sign that could be really good and all we've been able to do is to rally what nine dollars back just about $7 back which is exactly 618 of the last rally and here again that number that we hit last night at 1496 that was a you know a 382 of that move and then we came down and tested it again so it's trying to hold on but you know anything below that 1479 it's going to make Stan Harley's idea of much lower prices in gold you know really good and if people you know if everybody is going to be buying stocks I guess gold's going to go back down a lot lower all I know is that it's at a real critical level here because below that is going to be some serious selling that's the way it looks like from the cheap seats here in Tucson Arizona as I mentioned when we were on with Stan Harley Douglas Arizona's where that family was killed there's a Mormon commune there and I've heard of it before I've never been that area but Douglas is where the copper mines are it's about 70 miles do east of me here in Tucson and then about 70 miles south into Mexico in the northern Sonera desert is where this stuff happened and that's that's the area where a lot of these things happen folks they don't come through Nogales and Tia 1 anymore because it's too heavily you know guarded and now so they go into the other areas and that's where the problem is all drug related there you know these drugs are big big profit items and you see in the news they have their own 50 caliber machine guns they've got rockets and all this other stuff so it's basically a war but we have to protect ourselves folks do you realize that people came in from 147 different countries tried to get into our country this past year I saw that on Bloomberg last night I believe from 147 different countries so it's not just from El Salvador and all these other places it's coming from you know just about everywhere so we need to do something about that actually where I am here I mean we don't hear much about it or anything so we watch it on the news the good news from our standpoint was yesterday the city of Tucson actually overwhelmingly discarded the chance of being a sanctuary city so that was that was good news so we will see how that works out as we look at some of these things we still screaming in the market yes we are we've had a new high in the S&P up at 3094 and we're looking at the we're up to 200 250 in the Dow Jones industrial average so that's going to be a real interesting one and what else oh the Euro the Euro is still holding yesterday's low at that 153 but it looks like it wants to break below it all we were able to do last night was to rally 40 pips and then it sold off sold off dramatic we're just making new highs now in the Dow Jones industrial average so that's a that's another one that looks really interesting so we'll keep a close eye we're up 200 and what 240 now they're really moving today this is what we like to see like to see this early in the morning this is what we like to see okay let's get back to the old program here and what else do we want to cover the hogs still not doing much I I would be really careful of these hogs we're trading we had a low of 6505 we're trading a 6537 I just see on the Bloomberg terminal so if we get below down on the day I would be really suspect that's the that's the main thing to look at we've got just be careful that's all I can these markets are just not acting very bullish I mean we've got beans up two cents we've got corn down we've got wheat down that this is not bullish news for the for the grain people folks and that's the biggest you know it's biggest export that we have I think you know maybe be big I'm pretty sure it's bigger than Otto's anyway we'll take a little break here when we come back and then we'll see what's going on with the program so let's see any other questions and anybody oh the crude oil the rallying pretty nicely in the crude oil we had a pretty nice little rally up here this morning so we're going to see if it's it's going to do anything we just made a interesting spot here at 57 I'm certain you are or strive to be one of the best of the best at everything you do in life it's the most common trait that we tigers and tigers share if you're looking to become the best when it comes to managing your money let me teach you to do what most wealth managers tell you can't be done which is how to time the markets I'm Steve Rhodes author of mastery probability and for the last 12 months timer digest has been tracking my newsletter signals which have earned me the ranking as their number one 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will be of importance heading into 2020 for all the details check out the opening call on the front page of tfnn.com this segment is brought to you by think or swim for more information just click the think or swim banner on the front page of tfnn.com today we're back folks and we're going to wrap up the show with the price of the Dow Jones e-mini is trading at 27 660 almost a 27 700 another groundbreaking day so far and we got the S&P trading at 30 92 we had a high of 30 94 last act is up sharply just like all the other things the bonds are making new lows down in here I'm going to go ahead and speak at 15709 watch those folks at 10 o'clock and also at 1130 because I will share this with you whether it means anything or not I don't know but sometimes these patterns work better than others but let's just get it up here so you can see what this is our AI program of what we're looking at here is for kicks and giggles we'll get this up here so you can take a quick look at it you won't have to risk much I can tell you about the coffee is if it's above I haven't checked it in a few days Ruby but let me just get it up here I know that it's it's got a really bullish pattern and I don't know if it broke out above that let's just get get it up here if you can tell me if we're above that 105 level roofie it's going to look pretty good because the next level is 108 so I don't know where it's trading right now but that 105 was a really strong resistance and if we get above there it looks good you did a great job on that I know Mr. Z was really helpful there you go 10870 there we're back up to that 61% retrace and we owe that one to you and Mr. Z they were both talking about that and that's really been a heck of a move so we'll watch this really really closely here to keep an eye on these things as we're watching over here this morning okay let's sit they're almost every day in an attitude of gratitude and may God bless and try to do something nice for somebody that doesn't have very much folks and we will see you on the flip flop tomorrow we will have Dr. David Paul on Tom will not be with us tomorrow he has to do some family things but he will be back with us next Friday and David David will be back with us next Friday they were hoping we're going to have them as a regular very very