Welcome to this lecture on digital communication using GNU radio. My name is Kumar Appaya and I belong to the department of electrical engineering IIT Bombay. In the previous lecture, you have got a taste of some impairments and how they affect communications system performance. In this lecture, we are going to look at frequency offsets and a basic idea of how you can measure frequency offsets in GNU radio and some of the blocks in GNU radio particularly the phase block loop blocks that can be used to figure out the frequencies. Of course, the PLL block is useful because even in the presence of noise, it is able to detect the frequencies. That is something which we will see as we start with GNU radio. Before we actually get into the details of a PLL, let us actually just do a simple conceptual exercise. Let us actually mix two sinusoid of different frequencies and check what we get. So, I am just going to double click this SAMP rate and make it 1, 9, 2, 0, 0, 0. And first, let us just get a signal source, CTRL F for CMD F, we will get a signal source and we will make the signal source a cosine, we will keep the frequency at let us say 1,000, that is fine but we will make it a float. Next we will grab another signal source, we will just CTRL C and CTRL V, CTRL V rather and I will make this into a sine and let us say that you know let us make this plus delta F and if you do plus delta F, then we will just have a range for this delta F, so CTRL F for CMD F, we will say range and we will double click this range, we will call this delta F and we will make this go from 0 to let us say we will make it go from minus 10 to 10 hertz, step 0.1 and just to make it more visually pleasing, let us make it 10,000, we will also make this 10,000 and we are now going to mix these, so let us first get a throttle, CTRL F for CMD F, we will get a throttle, we will make the throttle a float and we will connect this and we will then do a mixing which is multiplication CTRL F for CMD F, we will get a multiply block and the multiply block is going to be connected over here, connected over here and now let us visualize what we get if we have a delta F, so CTRL F for CMD F and of course we need to also do a low pass filtering to remove the 2fc component, so I will just get a low pass filter, CTRL F for CMD F, we will say low pass filter, we will make the low pass filter have real coefficients and have cutoff at exactly 10,000 hertz, transition width of 1000 should do and then let us visualize what we get CTRL F for CMD F and I will grab a time sync and we will view what we get in this time sync. So now you can see that if there is no frequency offset, you end up getting something like 0 because cos into sin and you know there is not nothing much to check but if we have a delta F you can see that there is a movement, in fact let us make this delta F something significant, you can see that it is moving up and down to actually visualize this better, let us actually increase the number of points here by 10 fold and now if you have a frequency offset, you can sort of see that you can get this cycle and by measuring the frequency of this sinusoid, you will be able to get the frequency offset, let us increase this by one more amount and then let us just check, let us set it to 10 hertz, let us actually do one thing, let us actually also view this in the frequency domain, so I will just set CTRL F for CMD F, I will add a frequency sync, we will increase the number of points for the frequency sync also, we will make it 32768 and let us see what we get, initially you get, essentially you get zero and these are, these can be ignored for the moment, if you increase this to 10 hertz then if you zoom in over here, you will see that you are getting a peak at 10 hertz, that is exactly corresponding to these, so it is 396496 you know and so on, so that is exactly 10 hertz, so the key idea is that this kind of approach to measure the frequency difference by mixing can allow you to construct a filter where you can start adjusting the frequency of this sign so that you match it along with the phase, now this has been implemented in a, this has been implemented in the PLL blocks in Blue Radio, so CTRL F for CMD F and say PLL, you have this PLL carrier tracking frequency detector and regeneration, in fact we will be looking at the PLL frequency detector that actually has a more sophisticated version of this and using it to generate a carrier at the receiver in the presence of noise as well, let us first begin by adding a few variables and making some simple changes, first we will make the sample rate a little more convenient, we will set this to 19200, then we will choose our FC as 40 kHz and we will just track nominal changes, so CTRL F for CMD F and say variable and grab a variable over here and double click this variable and we will call it FC and set it to 40,000, we will also add a range to add a frequency offset and ensure that we are able to track it, so CTRL F for CMD F, we will say range QTGY range, we will call this range Delta F, Delta underscore F and let's say that it's default zero, let it go from minus 100 to 100 hertz and let's say step by 0.1, now we are ready, let us create a signal source, a complex signal source CTRL F for CMD F, we'll type signal, we have a signal source over here, we will double click it and we can set the frequency to FC plus Delta F, amplitude is 1, we will not have any phase currently, we will add a throttle, CTRL F for CMD F and we will say throttle, we will add noise to this, let's first create a range for noise standard deviation, CTRL F for CMD F, say range, double click it and call it noise SDD and at the baseband, complex baseband, we will now add this noise, CTRL F for CMD F, we will say noise, CTRL F add and we will add this noise but we should change the amplitude to noise SDD, noise SDD should be a number which goes from 0 through 3 and let's say step 0.1, now the next thing that we need is actually a, we will use a PLL frequency detector, so CTRL F for CMD F, PLL, we'll say PLL frequency detector, of course we can also track it with the phase but we're just going to use a frequency detector to begin with, now a PLL frequency detector takes the input with three parameters and gives a float output, the float output is essentially corresponds to the frequency, let's set these values, the loop bandwidth is the loop filter bandwidth, we will set it to 6.28 upon 100 that is they recommended that a value between you know 0 and 2 pi by 100, the minimum phase per sample corresponds to the minimum frequency that you want to detect, since we are expecting about minus 100 to 100 hertz of frequency shifts, let's actually just write that carefully, so it's 2 pi times, so I write 6.28 times FC minus 100 divided by sampling rate, similarly the maximum we expect is a 100 hertz deviation 6.28 times FC plus 100 divided by sampling rate, now this essentially is going to give us our frequency detector, to verify that things are working, let us just add a QT GUI time sink, so I'll say CTRL F, I'll say QT GUI time sink and we'll add a real value time sink and we'll call this frequency detector, okay, so now let's just see what the output is in this case, if I execute this flow graph, so I have an output which is close to 0.86, now if I move this delta F, you will see that it varies ever so slightly, let's zoom in over here, by moving this you can see that this is essentially moving up and down, so what is essentially happening is this, the PLL is actually getting an estimate of this particular frequency and after estimating this frequency it is translating it into an amplitude or a voltage value, so as you can see this amplitude now can be used to generate a frequency, let's actually do that, so CTRL F for CMD F, we will say VCO stands for voltage control oscillator, we'll get a complex voltage control oscillator, we will specify the sampling rate, a SAM rate, now the sensitivity is basically going to convert the, it's a constant which takes care of converting the voltage to a frequency, so in this case the values are between 1.30 to 1.31 and we know that the midpoint that is something like 1.308 is going to correspond to 40 kHz, so let's actually try this, so I'm just going to say 2 pi times, we'll just do this calculation carefully, so 506, 116, so it's about 1.308, so then if we connect this over here, rather than inspect the frequency which we get, the CTRL F for CMD F and we'll say FREQ, we'll grab a QT GUI frequency sync, let's add two inputs and connect the generated frequency with this, now this sensitivity should actually correspond to, actually this is a slight change, this sensitivity should correspond to 40,000 Hz, so we'll say this is actually 6.28 times 40,000 divided by 1.30833, let's verify what we get, amplitude should be 1 and if we now execute this flow graph, you get a frequency close to 40 kHz and we see that these two essentially are matching because if you remove this you get the same, now if you increase or decrease this delta F, you will see that the change is essentially getting reflected, now in the presence of noise, you will see that this particular frequency which is the original one is a very good carrier but there is the noise is essentially affecting the generated carrier also, the reason is because your frequency measurement in this frequency detector has very very slight issues, one approach to handle it is to just smoothen this out with a low pass filter, for example, I'm just going to say CTRL F for CMD F, say low pass filter and we can actually either do this or we can actually just do something simpler with averaging, let's just remove this, let's actually just do some simpler approach with averaging, so CTRL F for CMD F and say interpolating, we'll grab an interpolating FIR filter and let's make it float to float and interpolation can be 1, the taps we want to just average, so we'll just make it, let's say 1 times, let's say 0.1 times 10, this will give you a 10-fold averaging, it's just going to average, just a moving average of the last 10 samples and if we now connect the VCO through this filter, then you will see that even the presence of noise, it's going to be much more stable, so if you can make this even more, let's say let's make it 0.01 to 100, you'll find that it's even more sharp, okay, so by averaging, you're able to get the frequency back and let us actually view the frequencies, the sinusoid that are generated, so I'm just going to remove this, I'm going to remove this time sink and CTRL F for CMD F, add a time sink, this time sink we will add two inputs and the two inputs are the original and the generated one, and if you observe them, you will see that, let's observe only the real parts, you can see that they both have very, very similar frequencies, the very slight offset, okay, the offsets are of course, because of the fact that we have very minor, you know, differences in terms of the floating point and everything, the frequency domain you can see, but these kinds of offsets can easily be handled, so you can see that the PLL is tracking the frequency offsets very, very closely and this works even in the presence of noise, you can see that even if I increase noise, you're able to roughly see the tracking giving the same frequency, now if you add the PLL with the feedback and account for the phase offset also, the lock will be very, very good and you will not suffer from this issue, so in this way, a PLL can be used in order to track the frequency, of course we did not consider the case where there is a modulation on top of this carrier, that is something which you can learn from the references, but the concept is very, very similar. So in this lecture, you got a taste of how phase lock loops work in GNU radio, in particular, while it may be confusing to see how you are able to just get the frequency from, you know, you are able to get the frequency just from a pure carrier, the key idea is that even in the presence of noise, the phase lock loop essentially does a good job and in fact with a bit of filtering, the phase lock loop is able to track the frequency offsets as well. In the subsequent lecture, we are going to look at some other approaches where if we don't want to track the phase and frequency, how you can get away without having to use a phase lock loop. Thank you.


Hi, I'm Sal the TurboBonus. I'd like to welcome you to Sociology 2000, Global Social Problems. In this 2018 edition of the class, we'll be focusing on five major global social problems, economic development, refugee flows, political extremism, income inequality, and Earth's deteriorating environment. Along the way, we'll also touch on issues like sexual harassment, hunger, poor factory conditions, official corruption, and a lot more. The whole class will be delivered online, including the exams, but that doesn't mean you'll be all on your own. We'll be using video conferencing technology to organize students into six student tutorial teams. You'll do all your classwork for tutorials in these small groups, though of course, for your paper and your exams, you'll be individually marked. I'll be posting more information about the class as we get closer to class time, but if you have any questions or comments, please don't hesitate to be in touch by email. I hope you enjoy the class.


And we are off on another event. We're going to North Carolina North Carolina, I don't know why I have to say it like that. I always have to say it like that So I've been home for a long time now. It was another unscheduled. Well, this was more of a scheduled sort of thing we had fertility Early in the week and later on in the week we had more meetings and appointments and while I was at home We got a lot of work done.  I could probably spend another week at home It's a little bit overwhelming We're making it by but now I got to go make some money. I got to get on the road. I got to go to work You can't you can't stay home That doesn't profit anything Can't keep getting projects and I'd love to take like two weeks off just to work on that house and yard Just to get it nice, you know but alas We're truckers right diesel So since I'm running a little bit behind here, what I'm gonna do is I'm just gonna grab the truck Put diesel in it go and I got to go pick up a loaded trailer in Winnipeg Just up the road here and go pick up the loaded trailer Then I'm gonna come back to the yard and then load up all my stuff into the truck because I need to get that load I think that they close down there in like an hour So Little I'm cutting it a little bit close. Like I said, we need to get moving And it's very lovely to see that all of our friends on the windshield waited for us this whole time. They're still there That's dedication. They wanted to be a part of this So I'm in Winnipeg on the laser Mote a boulevard. I'm gonna go pick up a loaded trailer. I Can stress out a little bit less now because I thought I had to be there before one and it's already 1245 I called up dad And he says he picks up there all the time and they have a drop box for our paperwork So if they're gone already they leave our paperwork in a little mail slot for us So so I can still get it. It's not like I got to wait till Monday to get my load then, right? I Have an empty trailer a big empty box behind me.   I Get paid for each stop. So that's okay with me we now have our loaded trailer and we're headed back to the yard because We need to get some of the marker lights fixed on this trailer before we leave Because somebody parked it there with not all the lights working Or maybe it just sort of corroded and got all while it sat there. Who knows maybe use the people moving it around the yard there We as we have 10 stops on this load We're starting off in Streetsboro, Ohio ending off in North Carolina We got one stop even in Charleston, South Carolina Got a stop in Virginia We got a couple of stops in Pennsylvania. It'll be an interesting week. That's for sure Seeing some scenery we haven't seen in a couple of years Legendary people of North Dakota are about to welcome us with this very nice blue sign Welcome to North Dakota Legendary from the taxpayers of North Dakota. Thank you. Thank you very much. I like your sign It's a very nice shade of blue So we do have 10 stops and at the border they were warning me to make sure I'm stocked up on masks and gloves and the hand sanitizer because I got 10 stops on The East Coast my mask with me most are a lot of places already is mandatory Even it's time back now in my hometown. It's mandatory a Walmart.  We'll be okay. We'll be okay. I Refuse to live in fear. Okay. I will live in caution.   That's not that long. I don't got that life isn't that long I'm not gonna waste it hiding and shaking in a corner. And plus I like nice stuff To get nice stuff. I gotta work Out of the darkness emerges the Menominee rest area. Let's see if they got parking here for us Backwards wrong way, bud He's turning around Did he come in there?   That's a fancy tarp job Probably took him a while here. Actually, you know what there's another one available right over there Just had to avoid that. Oh, never like hit it anyway Just gonna avoid that pothole destroying potholes. How about that? Just gonna parallel park myself in here like a boss. Oh So I didn't have time to Finish my laundry at home. So I got it hanging all over the truck here again to dry I'm tired and sore from this long Long week of working at home So it's been nice to actually go back to work and relax De-stress a little bit just listen to some tunes and hold the steering wheel stare out the window Just like my teachers used to say that I would never never be successful staring out the window Proved them wrong, didn't I? Didn't we diesel Didn't No one can see you We'll see you all tomorrow. Uh, we've made it here to minamini, wisconsin made it just as far as I wanted to Got a long long day ahead of us tomorrow. So, uh Hope you join me. I'll need the company. It's gonna be a good stress-free day Just rolling. We'll see you then


welcome to module 46 of chemical kinetics and transition state theory. So, we will spend a little bit of time today on solving some of the problems with respect to RRK and RRKM theory today. So, let us get right to it. The first problem that I have put forward is for this Lenderman mechanism that we have been discussing for a unimolecular decay this is a back reaction as well. What exactly is A star? Is A star the same as transition state or not? So, take a moment, think about it and answer what you think is the right answer. So, hope you have paused the video and you have a answer for yourself yes or no with a clarification. The correct answer is no. A star is not the transition state. Transition state is a very specific structure. It is the maximum structure along the reaction coordinate and the minimum structure along all coordinates perpendicular to the reaction coordinate. A star does not need to satisfy all this criteria. So, if I again draw this kind of energy surfaces 1D energy surfaces this here is A and this here is B. This point is the transition state, but A star is any structure that is above the energy of transition state and it can actually have the same coordinates as a reactant coordinate just with a higher energy ok. So, A star is not the transition state. Let us look at the next question. This is a more mathematical question. So, we have looked at the RRK rate at constant energy in the micro canonical RRK rate. How is that rate related to the Arrhenius rate? There has to be some relation specifically when the energy is large. So, when I give you this condition that the energy is much much greater than S minus 1 into Ea and the activation energy is also large much greater than kT. Then can you work out a relation between this RRK rate compared to the Arrhenius rate and identify what this A is going to come out. So, again take a pause this is a slightly harder question this kind of maths we have not usually worked out in this course, but it is still an important conceptual question how are how is micro canonical rate related to canonical rate. So, take a pause work out to the best of your capability on how to even approach this problem and then we will discuss it together. So, hopefully you have taken a pause this is a very important concept how to go between micro canonical and canonical rate constant and you have worked out a solution for yourself. Let us try to work this out together now. So, k RRK at a constant energy is given by this formula where k dagger is a constant. So, let us first do our mathematics and then we can analyze it what it means. This is k dagger let me write this as 1 minus Ea over E to the power of S minus 1. Now, I will use a relation that is the relation that we have not used very often in this course is approximately equal to 1 minus Nx if Nx is much much less than 1. So, this really comes from Taylor expansion you can think of this and open this whole fact this power series. So, the higher orders that you will get in x square and x cube that I can ignore if Nx is much much less than 1 that is all I am saying. So, here you see that we have given this relation to you here. So, what we have is that S minus 1 into Ea over E is much much less than 1. So, I can approximate this as k dagger into 1 minus S minus 1 into Ea over E ok. Now, the energy I am replacing with the thermal energy where does this thermal energy come from? So, I am assuming I have a lot of energy with me ok I have a big system with me with a lot of energy in it with a lot of oscillators. If that is the case on average each oscillator will have kT of energy that is what actually thermodynamics gives you. Again something we have not shown in this course, but you can get to your thermodynamics course and show that very easily. This is called equipartition theorem that each harmonic oscillator gets a kT of energy I have S harmonic oscillators. So, I have roughly S kT of energy. So, here we are talking of large numbers anyway. So, I am going to cancel S and S minus 1 S is some large number we have a lot of oscillators with us ok. So, they are approximately equal. So, I get something like 1 minus Ea over kT, but you notice what is in the Arrhenius relation Arrhenius relation let me get to Arrhenius relation here. This is a into e to the power of minus beta Ea. Let me just write it more clearly in terms of kT, but we also have given that the activation energy is also much larger than kT ok. So, I can approximate this as a into 1 minus Ea over kT which you see is very similar to what we have here. So, this is in the limit when kT is much much greater than Ea. So, this number is small I can do a Taylor expansion again and show this result. So, you see these results are similar with the identification that k dagger is a. So, when you have a lot of energy when you have a large temperature what you will get is essentially the canonical rate constant out from micro canonical rate constant. This is the basic analysis that we are doing here ok. Let us move to the next question. So, this is a more numerical question now and these are the kind of questions you should be able to do with the formulas and the development that we have done throughout this course. This is a very normal question for a given reaction at a given energy you have to find the RRK rate constant and of course, you know the formula. So, the trick is to finding k dagger correctly you have to identify all the parameters of RRK what do you put for k dagger E, Ea and S. So, take a moment pause the video and get a number out final number out with proper units. These are the kind of questions you will see in your assignments and exams. So, you should be able to do this question. So, take a pause ok. Hopefully we have taken a pause. So, let us work out these numbers now. So, we have to basically identify each of these numbers E is easy is 500 kilojoules per mole. Ea is easy that is 400 kilojoules per mole. This is the dissociation energy. Remember that the reaction that we are studying looks will look something like this along some kind of reaction coordinate and this energy is 400 and so, this is effectively your activation energy. This is the minimum energy you require for the bond to break. So, we will take that. Let us look at S. So, we are testing S to be the total number of vibrational degrees of CH4. Vibrational degrees of freedom is 3 N minus 6 for a non-linear molecule methane of course, is non-linear. Here N is the total number of atoms which is equal to 5 for methane 4 hydrogen plus 1 carbon. So, we have S as well. I must add a comment for the sake of problem we have taken S to be this total number of vibrational degrees of freedom. But that is not always the case for a good experimental answer. S usually is smaller than the total vibrational degrees of freedom. If you want to match experimental data and that we have discussed a little bit in our previous modules, S is somewhat ad hoc in RRK theory and that is a limitation of RRK theory itself. How to get S is not very clear. So, this is just a starting point. Let us take S to be that maximum number of vibrational coordinates. The final number is K dagger. Now, if you remember we discussed how we calculate K dagger. This K dagger is nothing but the limit of A going to infinite of your K RRK into e to the power of minus beta E a. So, this you can go back and this is the way we calculate K dagger one of the ways we calculate K daggers. And what we have given is that the high pressure pre-exponential to the rate constant is this. K dagger is the pre-exponential to the rate constant. So, K dagger is then 10 to the power of 16 second inverse. So, finally, we put it all together is 10 to the power of 16 into 500 minus 400 divided by 400. Here note that the units will cancel. This is in kilojoules per mole, this is in kilojoules per mole and this is also in kilojoules per mole. So, both numerator and denominator are in kilojoules per mole. So, my units are canceling that is why I am not doing any conversion of units here to the power of s minus 1 which is 8. After that you can simply plug it on a calculator and calculate this number out and that number I calculated and I got 2.56 into 10 to the power of 10. So, that is the RRK estimate for the rate constant at 500 kilojoules per. The final problems I want to discuss are much more application based. For the perspectives of the exams, these problems I can only give in part, but if you are a researcher who actually wants to understand how to calculate rate constants for real problems, then you should pay focus. Because when you are doing research, you will get problems which do not have a clear cut analytical answer and you have to make assumptions and estimates in between and that is the art of science. So, take a little moment we are here doing a very very famous problem. This is the claim of fame for RRK theory calculating rate constant for isomerization of cyclopropane as a function of pressure of cyclopropane. This was a major hurdle in early 1910s and 20s and RRK theory had the major breakthrough in getting it exactly right. So, I have provided you a little bit of parameters that people worked out over very tedious work over a decade of work. So, for this problem we are looking at 764 Kelvin at which the experiment was done. We will assume S equal to 12. Let us just discuss S equal to 12 we have cyclopropane. Cyclopropane is how many atoms? It has 3 carbons and 6 hydrogens that is a total of 9 atoms. So, 3 and minus 6 the total vibrational coordinates is much more than 12. You can work it out that is 3 into 9 minus 6 which is equal to how much it is I think equal to 19 or 18 I think my bad. You can work it out it is much more than 12. But if you choose that higher number you simply do not get the right experimental answer. So, S equal to 12 is really chosen to get the right answer and that is of course a limitation of RRK theory. If you want to improve it then we do RRKM theory. But now let us look at how RRK does it. What is the way of doing RRK? And S is a parameter we fit. One thing I should point out we use the same set of parameters for all pressures. What we will not do is for a different pressure we choose a different S that is GT. We have calculated this S for all values of pressures. So, there is some decency. There is some confidence we have in the model that for this parameter we get it for all possible pressures you can calculate and all possible temperatures. Even as a function of temperature we are not going to vary S. Barrier height is of course a fixed number that is not fitted to anything. K dagger you can calculate as in the last calculation we did for high pressure. So, that is coming from experiment. And collision diameter is actually also done as a best fit for all pressures and all temperatures one constant number. And this happens to be the number that gives you the best fit. So, both collision diameter and S are best fit parameters nothing more can be done about them in RRK theory. So, we will start out by first calculating K minus 1 in RRK theory as the pre-exponential factor in units of liter mole inverse second inverse. So, take a pause get your pens out get your papers out and do this maps it is extremely important for the purposes of this course. This K minus 1 you will see as exam questions. The next thing we will discuss is harder to put it in the exam. But this K minus 1 by now you should be able to calculate precisely in terms of a number in a given units. So, take a pause do this calculation. So, hopefully you have taken a pause it is extremely important that you should be able to do this calculation now. But let us do it together now. So, K minus 1 from collision theory here I have not even provided you the formula this time. You should be able to go ahead look back into your notes go back to your modules go on the internet whatever you need to do and get this formula what the correct formula you should use. Here K minus 1 is used for an atom colliding with itself. Remember for that we use a slightly different formula when we have a plus a we have a factor of half do not forget this factor. Once we have the formula all that matters is plugging in the numbers correctly in proper units that takes time without practicing you will not be able to get the units right I can promise you the first time you do it you will do mistakes. So, do not make your first attempt in the exam directly you must do these calculations on your own ok. So, let us look at all the different parameters first let us look at mu. So, this is the reduced mass ma into ma I have only one molecule. So, this is equal to ma over 2 where this is mass of cyclopropane. Now, cyclopropane is what this molecule with each carbon having 2 hydrogens. So, this is C3 at 6. So, the mass is carbon is 12 hydrogen is 1. So, 12 into 3 is 36 plus 6 is 42 grams per mole. But what is the unit I want mu in I have to put mu here I want it in kilograms not grams per mole. So, I have to be careful with that let us change our units half into 42 grams per mole we did it these calculations a lot when we were discussing collision theory. So, if you are confused you can go back 1 kilogram in 1000 grams also remember to convert moles into atoms we have to use Aragadro number here. So, this you can plug in and I got 7. So, remaining let us plug it in I have half pi D is given to be 3.9 angstroms angstrom is 10 to the power of minus 10 meters square KB is 1.38 into 10 to the power of minus 23 kilogram meter square per second square Kelvin. Remember your units or temperature is 764 Kelvin pi and mu we just calculated Kelvin cancels with Kelvin kilogram cancels with K kilogram. So, if I plug all of these numbers in right now it is just a matter of simply punching it into a calculator. Now, what is the current unit if I look here I will get meter square from here from this square root I will get root of meter square per second square which is nothing but meter per second. So, if I multiply them together I get meter cube per second note the units I want it in. So, I do 1000 liter in 1 meter cube into I finally want put in the Aragadro number 6.02 into 10 to the power of 23 per mole. So, this I will get in liter mole inverse second inverse. So, once I punch these numbers in I get and again a sanity check you see that the order of magnitude is more or less right what we did before you get usually 10 to the power of 9 to 10, but also see that the temperature is very hot right now 764 earlier we were looking at room temperature. So, it is natural that we have gotten a slightly higher number reasonable enough right and the d is also large cyclopropane is a big molecule. So, you have a large 4 angstrom diameter fine or I mean it is not that we are getting 10 to the power of 20 or 10 to the power of 2. So, that sanity check you should always do once you get the final number you should have a sense of what these numbers look like and by the way these are I mean I am not making up these numbers these calculations were done in 20s and 30s and these are the results they had actually got. So, these parameters that I am putting here are actually from papers I am not making up these numbers. You can find these parameters actually in this paper in this this is a paper in 50s, but this paper is actually taking parameters from older papers and tabulating up the data. So, you can look at this paper it is very well written that is the way of reason I have cited this one and it gives a very nice overview on how this RRK calculation was done and how its success was. So, now let us do the final thing we are not interested really in K minus 1 we are interested in the final RRK rate in the rate of cyclopropane isomerizing and this is the formula we had derived for RRK at the end of the day. You can go back into the module and look at it we have gotten K minus 1 only so far 1 parameter. S was chosen to be 12 this we already know what about K2? K2 is this for this K dagger is already calculated and I have given it to you again the way to calculate it is another problem we discussed in the last problem you look at the infinite pressure result and from that you extract the pre-exponential factor. So, that is the way of calculating K dagger. So, what remains we have everything here. So, we basically plug these numbers into this exponential e to the power of s minus 1 let me just write this one beta also you know as temperature K2 let me just plug in the numerator one term actually cancels out. So, that is the reason I am putting it in and you notice I have a denominator e to the power of s minus 1 so this term will cancel out. So, this thing will cancel out so I am not writing that in here you cannot do much better. How do I get concentration of a see experimentally they are not monitoring concentration at all they are monitoring pressure that is the way experimentalist behave you are a theoretician you have they have experimental data with them and they have came to you and asked whether you can fit it or not. So, what we will do and this is basically a rough estimate we will use ideal gas law and that is what you have to do as a theoretician you have to make reasonable approximations. So, pressure is n over v into RT which is nothing but concentration of a into RT. So, concentration of a is nothing but p over RT. So, instead of this concentration of a in my formula I will write p over RT I have a lot of fractions, but hopefully it makes sense at the end of the day you have to be careful we have reached this point. Now what this integration actually cannot be done analytically it is not possible. So, now we take help from a computer against that is the reason it is beyond the full per view of this course because we are not telling you how to do be able to do these integrals numerically what I did is to write a little FORTRAN code for myself. Okay and I will share this FORTRAN code with you this we will upload as a file, but I know many of you are much smarter than FORTRAN is perhaps an outdated language you can write your own Python code you can write your own Mathematica code or MATLAB code or you can go to the internet and the internet now provides these you can put an integral and do the calculation so you can do that as well. So, you do it however you want in fact I encourage you to do it your way and email me your program you do it by Mathematica, MATLAB, Python or whatever way and teach me because I do not know how to do that actually. So, right now it is your turn to become the teacher and need to become the student and show me how it is done beyond FORTRAN whatever way is your favorite way to do this integral okay and once that integral was done I got the following result you do it yourself and this is proper research now okay we had started with a particular reaction the S now when you have a code you can actually vary this S and collision diameter there is no reason to believe S to be the following and a collision diameter to be the following the actually the result that you get out here matches extremely well to the experiment I have not even drawn the experimental result for that reason but you can see how the result varies with S that is the homework for you how the result varies with collision diameter the for this result was obtained for that I mean so that we get this result for this you can take this to be the experimental answer basically and it turns out for this particular collision diameter and S you will get this particular graph. So, now the ball is in your coat you can twigle your parameters and see what you get okay we will end with one final problem this again is meant more for people who are doing research and get actual numbers out okay one way or another you are free to make reasonable approximations okay. So, let us look at an organic reaction okay and what I want to emphasize is from this course is have you actually gained anything so let us look at this reaction you have this D as an isotope of hydrogen and you can have two possible reactions either HCl can dissociate out or DCl can dissociate out. So, you are organic chemists can work out right possible mechanisms draw arrows and all that and here is my gauntlet to the organic chemists here in my audience I have given you the activation energy how will you predict which goes faster well of course you organic chemist will tell me that they can do the experiment and figure it out good that is one way of doing it I am asking can I also predict it mathematically is there a reason I can give which is faster and at the end of this course you should be in a position to do it. So, I want you to if you can make an educated guess guess whether K1 is greater than so this rate constant let us say is K1 and this rate constant is K2 can you make an educated guess based use your intuition and tell me which is faster I am not going to answer that that is on you you make an answer and you email me what you what you think what is your reasoning this is an open-ended question this is not have a right or wrong answer. What I will do is make use our theories now and calculate this rate. So, we know that RRKM is a better theory than RRK theory. So, we will use the RRKM theory and calculate these rates now and we will see what we get and I will solve it only partially this is the end of the course you also should be able to do this kind of calculations and make your own estimates. So, you should not become dependent on being given being spoon fed on everything. So, the first question I will ask you is what are the parameters you need if you are doing RRKM theory well you need frequencies. So, for now at least for this discussion I will limit only to frequencies and not rotations. But you should I am limiting but you should not be limited you should try to think how will you include by rotations as well in your calculation. So, my first question to you is well how many frequencies do you need? So, let us say you have a theoretical friend with you whom you can go who will do the electronic structure calculation. How many frequencies you expect your theoretician friend to give you he is going to give you some numbers you have to cross check whether your theoretical friend is doing the right job or not maybe he is making mistakes maybe he is fooling you it is your research you have to get it right. So, you make an estimate on the number of vibrational frequencies you need for the reaction and transition state take a pause and calculate it. Hopefully you have done a calculation this is not a hard calculation. So, I will it is essentially counting the number of atoms frequencies equal to 3n-6 here n is 1, 2, 3, 4, 5, 6, 7, 8 and it is of course a non-linear molecule. So, 3 into 8 minus 6 is 18. This is for reactant. Remember transition state will have one frequency less. Now your theoretician friend will actually give you frequencies in wave numbers any electronic structure package gives out number in wave numbers it is your job now to figure out these activation energy therefore in wave numbers. Once you are doing these calculations you will need to do these answers in wave numbers then. So, that is your next job take a pause and calculate convert both of these activation energies in wave numbers. So, hopefully you have taken a pause and actually done this if you do not do it on your own and only listen to me once you start doing it on your own once you get a problem like this you will not be able to do it I guarantee you unless you try it on once on your own. So, this is a golden opportunity for you I am also going to solve it and then you can match whether I have done it correctly or not. So, EA equal to let us say 232.7 kilo joules per mol how do I go to wave numbers this is equal to HC into nu bar where nu bar is in wave numbers that is how I convert. So, nu bar is 232.7 divided by HC. So, I have to be very careful of units. So, I will write this as 232.7 into 1000 joules divided by 6.02 into 10 to the power of 23 for converting moles. So, I have a number in joules H I write as this C I write as remember I am not reading writing in meters per second because why want the answer in centimeter inverse that is why it is 10 to the power of 10 be very careful with your units. This is supposed to be joules in 2 seconds my mistake there joules cancels with joules seconds cancel with second and if I plug it in I will get 19452 centimeter inverse. So, you can cross check your calculation if you do not plug in the exact numbers here actually I get this with putting an exact value of C not 3, but 2.998 whatever it is. So, you might get a number that is slightly off here and there, but close by for 237 the other one I get 19886 wave numbers. So, now let us actually calculate these rate constants using RRKM theory. So, your theoretician friend comes in you ask him to have asked him to do the calculations and these are the frequencies he has provided you at the reactant which is this he has given you all these set of frequencies with degeneracies. So, there are frequencies multiple frequencies appear with the same value. So, first thing let us add these numbers together and see if we get 18 or not 18 is what we had calculated. So, 4 plus 1 5 plus 4 9 11 14 15 16 17 18 good your theoretician friend is not completely wrong he is making some sense. You have two transition states one for this reaction and one for this reaction he has done his job and given you these frequencies. Let us add these together and get 17 or not 3 plus 2 5 7 8 13 14 15 16 17 perfect let us add these numbers together 4 5 6 7 3 10 14 15 16 17. So, never blindly trust your theoretician friends that is a bad idea make sure these numbers add up together. So, that is fine, but how do I get this K 1 and K 2 your experimental friend has simply given you this big table what now. So, now we will have to well RRKM formula is given by this we derived how do I get W and G are what do we do with them. Here is when we have to use our intuition first thing note that your these these energies are very large. So, I have just chosen a few energies above the barrier height.  So, I have chosen energies above 20,000 and a few sample points you can calculate more why not what limits you you can write it and draw it actually make a plot of K 1 and K 2 as a function of this energy and then do a thermal average. So, here I am limited I am doing you a little bit less for what and you are a researcher you are free you are you have the open sky with you fly as high as you want, but how do you get W dagger and G are that is what I am trying to get to here G I will calculate classically that is fine because G is for the reactant at this energy which is much more than K T. Okay. So, G it is absolutely fine to use the classical formula. So, at 25,000 wave numbers I would write 25,000 to the power of 18 minus 1 divided by 17 factorial into a product of all these frequencies. Okay. So, it will be 2940 to the power of 4 because 2940 is appearing 4 times into 2160 into 1340 to the power of 4 into dot dot dot. Okay. So, I am not going to plug these numbers for you it is your job you do it. Okay. You do it for different values of this as well. So, I will calculate it at 35,000 has been or whatever energy you are interested in I have put these energies out of the blue you choose your energies. Finally, how do I calculate this W? W also have a classical answer, but that is a bad idea why because W is calculated at E minus EA. So, let us look at 25,000 minus EA for 19,000 roughly 500 wave numbers let us say that is roughly my barrier height. So, you see this number is not very large this number is roughly is how much 5,500 wave numbers much smaller. So, doing much smaller compared to what compared to your frequencies your frequencies are in the order of 23,000 wave numbers here. And this is also in the order of I mean a little bit more this is not very large. So, that is the sense you have to get now if you are doing actual research. Okay. So, here we have to actually manually calculate W. W set of quantas n i such that the total energy is less than your E minus EA. Okay. How many possible n i's I can construct such that this holds and omega i's for transition state 1 you will choose this one and for transition state 2 you will choose this one. So, you will get 2 different set of W's for the 2 different calculations. Okay. So, that again I am leaving it to you you can do it manually or you can write a code. I have written a code for myself in FORTRAN I am old fashioned. Okay. So, you can write a code in Python perhaps. So, that is another exercise for you. Finally, these are the numbers I get. So, this is a benchmark for you you can calculate it for yourself. One thing I just want to point out the first question I asked whether k1 is greater than k2 or k1 less than k2 there is no clear answer to it actually the correct answer. At different energies you will get different answer at lower energies you can get k1 is greater than k2 at higher energies you get k1 less than k2 and you should be able to actually rationalize this the point is that smaller energies it is the barrier height that matters and the barrier height of 1 is smaller. So, you get that to be a faster rate, but when your energy is large the small difference in barrier height of 5 kilo joules per mole does not really matter and entropy takes over and as it turns out the second one is entropically favored. So, therefore, you get a rate of k2 larger than k1. So, that you could also have reasoned out using your intuition and now you have the capability to do it. Here I am not solving the full thing intentionally because I want you to do it on your own and I am not putting it as an assignment problem because it goes a little bit beyond the scope of the course because you have to write programs to calculate these kind of things. So, I do not want to do that as an assignment which is graded. But if you are a researcher you should absolutely attempt this problem and see if your number matches. If they are not matching email me maybe I have made a mistake it is very possible. So, with that I will stop this was a slightly longer module and this is the end of the course. Now, hopefully you have you have gained abilities to be able to calculate rate constants. You can as you have seen a little bit of intuition goes in all of this. You should never plug in formulas blindly. You have to think what formulas to use when? When should I use classical answer? When should I use quantum answer? When is rotation important? Here by the way I have not included rotations for example. Of course, they are important. So, you should make an attempt at including them and once you have included them email me. Let us have a conversation. So, hopefully by this course you have learnt how to use transition state theory, RRK theory, RRKM theory and a bit of molecular dynamics of rolling surfaces on these energy surfaces to get rate constants, to get dynamics out. Thank you very much.


Well, hi there. It's Sandy Olnock and today I am doing a by-request video. I've had many people ask for some more tips on coloring people of color. As my longtime subscribers know, I've been coloring the human rainbow for maybe a decade or so. It's been a really long time. I have handouts that are for free. You can download these as well as blank ones to color yourself on my website. Link is in the doobly-doo.  She has a Leading Ladies and Leaning Gentlemen series. I have stamped them all onto one sheet so I can make one big picture with all of these people in it. Some of them are repeated because I want to show you that you can do the same stamp and color them in different ways. For the most part, I'm just not going to pay a whole lot of attention to the lines themselves. I know that is scary for some, but there are some of the people where I'm just going to change the shape of the face. Here on this little girl, I'm giving her rounded cheeks. On each one of these, I am going to be adding masks onto them. That is going to be something that you might want to try. I decided to do that in this video since we are going to be facing probably months of mask wearing at the least going forward, but it also makes coloring people a lot easier. These two little kids in the beginning are not going to be wearing a mask. Originally, I hadn't thought about doing that because I've also had people ask, well, how do I put a mask on a person because I want to do a card with a mask. After I finished these two, I realized I could have just done all that in one video. I'm going to add masks to the kids at the end. Stay tuned if you want to see how I do that at the end of the video. This little girl is going to have these really cool ponytail sticking out all different direction things. I looked for pictures on the web and of course right now there is a plethora of awesome people in masks if you want to go get some ideas and go look on Google and just put in the kind of person you're looking for, the kind of hairdo and you will find on the images tab a ton of different ideas. For most of these, I'm not going to be putting the colors in here, but for most of these, I start off with a warm gray. I add in a really dark cool gray or neutral type of gray in it like an eight or nine or ten and then kind of do something in between.  So that's where I'm creating some of those empty spaces in between to give it that sort of a look. Now this is a teeny tiny stamp so I'm not getting into a ton of detail there, but I colored right over top of all the stamp lines. It's one of the great things about doing no line coloring is you can change things up. I can still see just barely the stamp lines for where her eyes are and so I could draw them back in. You could draw them in with a sharp pen, but I would recommend trying it with your Copic markers and just see if you can make little teeny tiny dots and lines and those sorts of things. I'm also going to give her little beads on the ends of some of her little pigtails because they were so cute in the photo I found of her and then her face will be about done aside from the mask that I'll add later. Each one of these I'm coloring the clothing off the off camera because this would have been a mini hour video. This whole thing took me all day to do so I did not want to be doing that much footage so I'm just going to get the faces and we're also going to speed it up a little bit too. This little boy I gave him a higher forehead than he had on the stamp because a lot of times the scalp line is pushed back because a lot of African American folks don't have bangs. I'm used to like me having bangs and everybody in my world that I draw has bangs. Every stamp it seems. Lots of stamps have bangs but if you don't have bangs you see more of the forehead and for each one of these people that I'm coloring also watch where I put eye sockets in.  I didn't do that really well on this one but once I put his mask on him later he'll look nice and small and of course he looks small compared to the other stamps because he's a littler guy. Then for this lady I'm going to start with the mask. This is where I thought I'll begin and these smiles on these masks or under these masks are basically just horizontal lines so depending on the stamp you're using you may have lips that you'll have to deal with. That's why no line works really well so you may need to just put more color on the mask in order to add the mask on top or else before you stamp it just wipe the ink off of the mouth and nose area and then you can put your own mask in. With this one I'm also trying to shrink her head a little bit. She's the one stamp and I guess the guy stamp is a little bit bigger. You can see that the two stamps to the left of the one I'm coloring the one has a really smaller head the guy with the bun in the back.  I wanted to have these sort of raggedy curls I started making them originally with the gray too vertically and the picture that I was looking at I realized they needed to go more kind of sideways and sticking out in little groupings just the the way that the hair clusters in different ways just find pictures literally just look at the pictures and see which ways the hair goes and I'm just using grays and blacks and that's all you have to do to make it make different hair just follow along with what picture you see and I'll give you the warning to just be a little bit careful so that you don't end up with the hair getting too big but it's really easy to just add two eye sockets above the mask and then drop the eyes into that and you'll see me do that throughout this so next I'm going to go over to this lady and I wanted to give her more of a scarf around her head because I found a beautiful woman with an orange and orange white and black scarf and she had a mask on and then I just colored her face in in between and once you start getting used to doing this especially if you're doing with a lot of people like I'm doing it's going to become second nature to just create that face shape and ignore where the eyes are just add in your own your own eye sockets when you get there I'm going to add a little bit of a hairline sticking out from underneath the the scarf she's wearing soften it with some brown so that her scalp isn't really sharp and then add in the two eye sockets that kind of come in from the side a little bit a little shading under the neck and then I can go in with a black or a like a c10 or a c8 or something and add eyes well on her I just put sunglasses on her she's outside so she's wearing her sunglasses and I just painted them painted them with a marker colored them right over top she also had hair that was sticking out of the back so this was basically holding all the hair away from her face the scarf and this time I did the dark first since I had that marker in my hand and then added the light of the the gray color outside of it because the gray will be the areas where the light comes and hits the outside of her hair add a little detail to the mask and then put a few lines of depth into the scarf so now she is all ready to go with a little bit of sunny highlights on her sunglasses both of the kids were wearing jackets but the adults I'm trying to put them in some summer wear so I gave her more of a tank top dress and the the kids are wearing just normal clothing with with jackets and then the girl on the right is wearing a t-shirt and then we have another person we're gonna color over here and she is an elderly lady and I looked up elderly african-american person in order to find a picture of this beautiful woman she had the most gorgeous hair if I had her hair I would be so happy it was sort of a diamond shape around her head so the two sides went up in almost a kind of an angled triangle shape and had dark around the bottom edges there I blended that with some warm gray so that it would kind of go up into these really soft gray highlights on the top of her head and then ended up using some other grays in the middle to just get some transition colors going and I love her hair I just thought it was so beautiful had some of it hanging down across her face and then I added some shading onto her face so that I'd get a little more color in there and her eye sockets and things and blended it together and then added her eyes in there and eyebrows and I realized I hadn't added any eyebrows above sunglasses chick over there so she got some sunglasses as well and then I realized I could add some really dark colors in the shading on the elderly lady's hair and I just thought she came up beautiful and of course she has a yellow mask and a yellow sweater so that makes me happy there you go building this whole thing up little by little now let's talk about doing one of the guys because guys you can do the same crazy things with I'm going to do a really easy one first and this guy's just going to be wearing a baseball cap backwards this is something you can do on a lot of different stamps just you know color over top of the stamp itself and you know give him a mask if you're going to but the hat is the easiest thing in the world to do so make a little bridge shape for the back of the hat make it go across the whole top of the head and then a line across the middle and now he's got a hat on if he's got any hair sticking out you can put the hair on either side that sort of thing add the two eye sockets and then drop in some eyes for him I wanted to add glasses because the picture I was looking at he had glasses on so I just went over top of the eye areas over top of the mask as well with colorless blender for a little bit to lighten some of that up and then I took my Copic fountain pen yes there is such a thing and drew in the lines around it so that I could give him some glasses next up we have this this little person here is another one of the guys this is the same stamp so I'm going to change it up a little bit forgot to put his mask on so he gets a black mask and you could do the same thing here like I was trying to show you how you could draw a beard just leave the mouth open so if you're trying to just add a beard on somebody you could do the same thing and I just filled it in to make it a mask and then put his scalp line his hairline you know high up because he doesn't have bangs and his hair goes straight up instead of coming down in bangs gave him some shading and some eye socket so that then I can give some eyes and eyebrows to him and as you can see these are not all that hard if you have the stamps to start with it gives you at least some proportions to begin with this gal I wanted to give her a higher forehead because again she doesn't have bangs coming down so I'm going to give her that higher forehead her hair is going to go up and she's got more of a pom-pom type of bun on her head than the girl in the stamp but since it is no line stamping and I'm just using the no line ink but you could use any light gray ink to achieve the same kind of a thing and then I'm adding some deeper shadows at the bottom of the pom-pom and then a little bit of lines for kind of some of the hair pulled back from her forehead toward the back of her her head and then add a little bit of shading for her including the nice little eye socket so that she can have her eyes set into something if you're coloring people of other races just use a lighter color of course don't make them you know look like they have sunken eyes but one of the nice things about using the the eye socket technique here in addition to that and the mask you don't have to worry about features much is that you just put those two in it gives you that general idea and then you're not trying to draw them into a blank void and figure out where the eyes would be so if you can get those looser eye socket shapes makes it a little easier. This gal I wanted to have with bigger hair because I found a beautiful woman with these long really this flowing hair that I just I'm telling you I have hair issues if you watched any of my Instagram live in the last two months I had more complaints about my hair than I had about anything during the whole quarantine period so yeah I still haven't had a haircut I am one of those who works at home so I'm going to let other people once we do open and I think we're supposed to open soon after the pandemic I think we're going to get to phase two eventually in my county and we will be able to have haircuts but I'm going to let other people have the first haircuts because I work at home I don't have to be in an office nobody has to see me so I will continue cutting my hair a little longer but who knows maybe I can grow my hair out long enough to get one of these hairdos so next up next vacant face that needs some coloring her I'm going to change and transform entirely so it may be an old lady's stamp a grandma stamp but it can also be anything else you want because you're just getting the basic face shape here so I'm going to create a gal with really long braids it's another hairdo that I always used to wish that I would have I used to have hair that was down to my rear end back in the day long long long time ago and I don't think I'm going to grow it that long before I start getting it cut but you know it might not be a bad idea I forgot her mask as well so she gets a dark mask on her face easy enough to do and then I'll start to put in some of the features including some shading on her face and the eye socket and with all of these I'm just following along what I see in some pictures to get some hairstyle ideas and looking for where the scalp line is and what the hair looks like what directions are all the hair is going and here she had these just long incredible braids trailing down across the front of her shirt down her shoulders and stuff absolutely beautiful long long features of her beautiful hair and with her she also had almost some you know some braids that started up at the top they started in her scalp so you saw almost lines in that top section I'm sure there's names for all these hairdos I don't know what they are since that's not my hair so my apologies if there are names that that I ought to know and now I'm going to do a bald guy because yes you can do a bald guy too bald is beautiful and for him I'm just going to add his his shading his eye sockets and his eyes and then he needs some more shading on his head so I'm going to add a little bit more color to him to give him a little bit more depth on there and then leave the rest of that face there just add his mask and then I'll do his his shirt coloring offline I'm glad I did that because this video is already long enough it would have been probably hours long even sped up so here is adding the masks onto the kids if you want to add masks onto a stamp you've already colored you can do that either they can wear a dark mask like this little boy would probably wear a mask with cool patterns on it and stuff on a dark mask and then a little girl is going to have to wear pink and yes you can color pink right over top of something you can start with a lighter pink and go with a darker color over it that sort of thing my finished piece is not only a tutorial on coloring different kinds of hair and adding masks to people but also serves as a reminder to get out and vote make sure you're registered if you already are registered double check that it's still good that you haven't fallen off of any roles because getting your voice out there and making it heard is important you can also download the colored and blank pages of the human rainbow series over on my website link in the doobly do and I will have some more voter registration information on my blog if you are interested if you're not registered and you need to learn how I will link to some sites that will give you all that information so thank you very much I will see you again very soon have a lovely lovely day


Hello everybody, Andrea Maesky here. So you guys have probably seen my post on Facebook. We are doing some major team training today, which is pretty exciting because we have a very large team. And they basically took the the highest earners, well not the highest earners, but those that have been doing this for a long time, which are typically the higher earners, and they and they all kind of took turns to explain different things to us about the company, about the products, they talked about marketing, they talked about how to build a team, and they talked about how to make money, you know, so it was a very inspiring team training. In fact, it's still going on right now, but I kind of wanted to hop on while it's still fresh in my mind to talk about some of the more the notes and things that they had had talked about. So I was literally actually I did a lot today. I had organized my closet, I was organizing the spare room in the basement, I was organizing my office and all at the same time I was listening to our live training on my iPad right here and then taking notes on my cell phone, like I have all of these notes here. Where are my notes? I have all of these like notes here that I want to share with everybody. So pretty much you guys, everybody asks number one, so what is this all about this working from home thing? What is it all about? Like what exactly do you have to do? How do you make money? But I'm also very interested because people can see that it does work, okay? Being a brand affiliate with pretty much any company, like it doesn't matter what company you are with, but being a brand affiliate, you have to like the products obviously. Think of any sales rep of any kind, whether they're selling toothpaste, whether they're a sales rep for a oral care company. They might be selling electro toothbrushes, they might be selling vacuums, they might be selling whatever. They have to like the product to sell it. Are they trying to scam you? No, they like the product.  They share ideas how to use it and then you go, oh wow, that looks awesome, like I just have to have that. Like when have you ever not watched the shopping network? You know, I see it every so often if I'm just sort of looking through things, right? I'm looking through the channels for something to watch and then I'm like, oh, there's the shopping network. I don't know how they do it, but I want every single product that they advertise because they just do such a good job and they show why the product is so amazing. So this is basically the same thing. Being a brand affiliate for New Skin, you are sharing your love for the product. We have a wide range of health oral care products. We have like cleansers, toners, moisturizers. We have lip balm. We have sunscreen. We have multivitamins. We have omega three. We have a lot. So have a look, you guys. You don't have to sell a little bit of everything. There are members of our team that pretty much only specifically sell our toothpaste and some like seasonal products, okay? So our toothpaste, our tanner is so, so hot right now. The multivitamins because everybody wants to be healthier. So it depends on what you want to sell. You don't have to sell everything or you can sell a little bit of everything. I like to try different things. So I sell things based on what I have tried. My toothpaste or the toothpaste and the mouthwash is probably my biggest sellers of all time. I just started selling the tanner like a week ago and that is, that is pretty much starting to become my biggest seller too. So what is a brand affiliate? You sell the products and it's really exciting because you know, even if you just post something as simple as you holding your cell phone like this, hey guys, and do a post about I am so lucky that I can work from home. That's all you have to do.  You work from home? What, you know, people want to work from home right now because a lot of people can't work in their typical jobs. I have my own dental hygiene practice. I can't see patients. I am missing out on a lot of income. So thank goodness, I am a brand affiliate for new skin and I can work from home. People are still, they want something to purchase. They want something exciting. You might be thinking, well, nobody's buying right now. Everybody's buying right now because we need something else. We need something to do. We need something exciting and we are on social media like 24-7. I know I am because what else are you going to do? They had mentioned a statistic where most people are on social media four hours a day. Now it's more like eight hours a day. That's insane. So now is the perfect time to have a job where you work from home selling something. It is literally, you guys, that simple and the nicest thing is, is this company pays you every day. You don't have to wait two weeks. You do not have to wait a month. They pay you every day. I can make $30 a day. I can make two. My highest so far has been like 300 and something a day. From selling toothpaste, tanner, I sell the foot cream because it's amazing. The lip gloss, I love. I have sold that before. Basically everything you sell, you make a commission and it's not about like selling, selling, selling, selling. The best part is too, is that we train you guys. We show you exactly what to post, how to post, and then after you have more practice, you sort of know what to post. You can change things up a little bit. You can change things up a little bit. You do not have to follow the exact templates, but the exact templates are there because the system works. We have people, we have moms in this company who have been doing this for many, many years and now their children are doing the same thing. It's like, I have turned 21 now. This is an amazing business. How do I get started, mom? That's an excellent sign, you guys, when it's passed on because this is such an amazing business, you can work from home. What else did I want to say? I was actually, I was talking to a friend of mine and she does qualify for unemployment, but she won't get that for a couple of months. I actually don't qualify for unemployment because I have my own business, but anyways, but with new skin, I had said to her, well, we pay you every day. How about you come work for me?  Let me train you. Let us as a team train you and you can get paid tomorrow. You can start making money. It's that simple. People want to purchase from you. I have had so many people come to me and say, oh, I saw your post about the toothpaste. I would love to actually purchase some from you because we need toothpaste and I know you need the money because you're not working right now. You know, like people are hilarious, but they want to help you. So I had told her that and she said, oh my God, you get paid every day. We'll all do anything, like I'll do anything to make some money at this point because I'm the one making the income. She made money literally like two hours later. She posted about the toothpaste and she said, I wrote it down. She had six people order that toothpaste. Just as an example per tube of toothpaste, you make $10, $10 commission, six people. That's $60. She made $60 in two hours for basically doing that thing. You guys, this business works. I would not steer you in the wrong direction. If I can do it, you can do it. If she can do it, you can do it. Let's see here. So we did talk a lot about the different products at the training, but I can help you guys with that. And the nice thing is too is that our training that we did today is all online. It has been recorded. So you can see all of that. It's pretty much everything that you want to know about the company. They talk about that. They talk about how to market. They talk about how to advertise. They talked about the products, which is always nice to know. They talked about sort of like how to not sound like you're trying to sell something because that can be annoying. They talked about how to be organized in your business. They talked about some of the accounting features, like how to stay organized. They talked about how to make more money. They talked about sort of the best times to do your posts. So you guys, I left so many notes here. I can help you guys with that. So that's basically what it is. You are working from home and it's amazing. The system works. There are people making hundreds of dollars a day by posting and being on social media. Isn't that amazing? That's pretty amazing. So you guys, please let me know if you have any questions. Feel free to comment below. I'd like to do a live for my teammates, depending on how many new people sign up. It can be every couple of days, once a week, whatever. We have these trainings talks all the time. So there is no such thing as a dumb question. Please let me know if you have any questions. Anybody can sign up. It doesn't cost you anything. You have nothing to lose. Let me help you make you guys some money. It's that simple. I'm not even, it's that simple. Okay. So thank you guys. Let me know if you need anything and I hope to see you guys very soon inside our training. Talk to you soon.


Why the sudden halving every four years? I understand that the Bitcoin reward per block has to be a decreasing function, such that the sum of all rewards would be finite, like 21 million after 100 years. But why not choose a simple, decreasing function that would smoothly go to zero? Isn't it inconvenient that every four years the profitability of miners suddenly decreases, or otherwise fees suddenly have to increase in order to compensate? That is a question that has been asked many times, why Satoshi did it that way. Why not have a smoothly decreasing function instead of having a step function? Currently, the production of Bitcoin, the issuance of Bitcoin on the blockchain every ten minutes, is twelve and a half Bitcoin, so twelve and a half for four years. In 2020, boom, it goes down to six and a quarter, and gets divided by half, this halving function. Part of it is, that is the way Satoshi built it. Once it was built and in progress, there is very little incentive for miners to change that. There is very little desire for anyone to change that fundamental function. Obviously, by postponing the pain of a step function all of the four years up to that step decrease, you are getting the full amount, so you are not getting a gradual decrease. Which means that it does give an early advantage to those who are mining now versus in the future. One way to look at it is that, despite the fact that it is a step function, because it is broadly known that the profitability will drop by exactly half every four years, and because that is known well in advance, we know exactly how that step function is going to work out all the way to the year 2140. Miners effectively build their operational models to account for that. No one is surprised by this. The market already prices in that consideration years before it actually happens. From an operational perspective, miners are already adjusting for the profitability that is going to happen after the halving, up to a year before the halving. Investments in infrastructure, operational costs, electricity costs, etc. are all taken into consideration, knowing that this is going to happen. The market ends up pricing this in so that when it actually happens, not much changes, because the network was already ready for it. That is the fundamental difference between the halving of Bitcoin, for example, and a sudden change in the interest rate of a fiat currency, which is unexpected, and the market has to adjust. In that scenario, the market does not know there is a probability, and that probability is appropriately accounted for, in the pricing of a currency. In Bitcoin, it is not a probability, it is a certainty. It is a certainty that is known well in advance, and therefore people can plan for it. Why did it not happen this way? That is not how Satoshi did it. Once it was done, it was done. Could it have been better with a stepped decrease? Well, there are the blockchains where that is the case. It is a mixed bag. I do not know that this is a particularly big disadvantage of Bitcoin. So far, what we have seen is that the two halvings that have happened have been largely uneventful, if anything, they have caused an increase in the value of Bitcoin right after the halving. It does not seem to be a problem. Vladimir asks, what trends in the Bitcoin ecosphere do you think will be emerging in the long run? As the block reward will be getting smaller and smaller, will there be less miners? Will security be compromised as a result? Will transaction fees skyrocket to support miners? Honestly, none of the above. I think that as block rewards get smaller, as Satoshi predicted, in both the paper and many of his writings, fees are going to have to replace the reward. However, those fees may come from more transactions or bigger transactions that aggregate things on the second layer. The value of Bitcoin may be very different than it is today. That may mean that miners can be compensated through that. Quite honestly, if we have less mining than we have right now, if we have less proof of work, that does not make the system insecure. We have been growing at such a ridiculously exponential rate in terms of the total mining power, that Bitcoin was secure two years ago, and 90% of the mining we have today did not exist. We have been going at an order of magnitude increase every two years. At that rate, making the network ten times more secure does not mean that it was not secure before. If we did have a reduction of miners, there are levels of security with proof of work that we had in the past that are perfectly capable of maintaining the security of the network. I don't think we have any major problems. Historically, every time there has been a halving, that has affected the long-term price by increasing the price of Bitcoin. It has mostly been a non-event. The halving is something that you can predict with certainty, but not accuracy, years in advance, and with somewhat accuracy as you get closer and closer to the event. Then, of course, it does happen on the exact block you expect it to happen. The entire market prices that in with increasing level of accuracy as you get closer to the event, and so do the miners in their operating models and profit models. It becomes a non-event in the end. I think it will continue to do that.