Hi, I'm Zor. Welcome to Unizor education. I would like to continue talking about mysteries of light. In this case, we are talking about quantum properties of light, light as quants. We were talking about corpuscular theory, about wave theory of light. Now it's a quantum theory of light. They're all related in some way or another and this lecture basically is about common properties of On one hand, we will have corpuscular theory. On the other hand, we have wave theory and the light has properties of corpuscles and and the waves and this particular quantum theory is kind of getting things together it combines basically all the known properties of light into one theory which seems to correspond to all the experiments known to us at the time. So we think that this theory is better explaining actually the nature of light. Okay, so this lecture is part of the course called physics for teens presented on Unizor.com. I suggest you to watch this lecture from the website. You just go to physics for teen course on the website and then to energy and energy of light in this particular case. There you will find this particular lecture. There are also benefits to use the website because it has exams for those people who want to take them. Now this course has prerequisite course, which is math for teens also on the same website, which I do recommend you to take before you go to into physics because physics is really based on mathematics, especially calculus and vector algebra. And the website is completely free. There are no advertisements, so it's just for everybody free for all for free. Okay, let's talk about light. By the end of 19th century physicists more or less switched from corpuscular theory of light into the wave theory. Because the wave theory was able to explain everything which was in the domain of corpuscles and at the same time it was able to explain certain other phenomena like interference of light. So the wave theory actually took over by the end of this time. At the same time there was development in the field of electricity and primarily the very very important discovery was by Sir Thompson in 1897, if I'm not mistaken, the discovery of electrons as carriers of electricity of electric charge basically. So it was possible to talk about electric charge, positively charge, negatively charge. They're connecting. There is a spark between them, etc. So there were certain experiments related to electricity. Which uncovered a very interesting effect where electricity and light are related to each other. The experiment was very simple. If you have charge two poles, negative pole and positive pole, and they are relatively close to each other, at some point you are accumulating the charge, well, you're accumulating the number of electrons in the negative pole and decreasing the number of electrons in the positive pole. So there is an axis and deficiency of electrons. And at a certain time there is a spark between them. So everybody knows, everybody saw the spark, everybody saw the lightning, for instance, which is basically the same thing. It's a spark, giant spark. So the spark is basically a flow of electrons from the negative pole to the positive pole. So wherever it's an axis of electrons these electrons are going to the positive, where there is a deficiency, basically neutralizing them both. Now the experiments were conducted with the light, which is actually directed towards the negative pole. And what had been discovered is that the spark appears earlier if the negative pole, negative electrode, is lit with the intense light. So basically it's a very simple thing. So if this is negative electron and this is a negative pole and this is positive, negative positive. So there is an axis of electrons here. So when the axis of electrons is really significant, then they just travel from here to here. But if there is a light, directed towards this negatively charged plate, the spark appears faster, like easier. So you don't have as much charge to have the spark as if you do without the light. And obviously by that time the experiments were sophisticated enough to measure basically how much electrons are moving, even the speed of the electrons, which are moving from one plate to another. So experiments were quite precise. And first, they have explained basically this effect very simply in the framework of the wave theory. If light is the electromagnetic field oscillations, the oscillations carry the energy with it. So this energy is transferred into the electrons. They are agitated more. And if they are agitated more, they're moving more intensely. They are easier going from negative to positive poles and the spark comes earlier because the electrons not only they have their own ability to basically arrange a spark, but also they are agitated, they're moving much faster. And that's what makes the spark easier. Good enough. However, there were certain properties of this effect, which is called photoreffect. Photoreffect of electricity. So there are certain properties which are not exactly fall well into this particular explanation. There are three major properties which physicists observed in the photoreffect. Okay, the property number one is if photoreffect is present, then the number of electrons depends on intensity of light. So the more intense light causes more intense flow of electrons from negative to positive. Well, you can say great. It falls into the contemporary wave theory, the classical, contemporary at the time, the classical wave theory, very nicely because obviously the intensity is basically an amplitude of oscillations. So it's more energetic because the amplitude is basically the measure of the energy of light and so the more energy goes into the electrons and obviously more electrons are flying across. Okay. But now there is another property. Speed of electrons does not depend on intensity, but depends on frequency of light. Now, this is a very, very important thing. So no matter how intense the light is, the speed of electrons and therefore their kinetic energy of each electron is the same. So they measured somehow, I don't know how they measured the speed of electrons or their energy, but whatever the way they did it and what's important is that the energy of each electron does not depend on intensity. With increasing intensity, you have increasing number of electrons, but not their kinetic energy. The kinetic energy of each electron was exactly the same regardless of intensity, which doesn't seem to be, you know, nicely falling into this picture of classical wave theory. In a classical wave theory, the more energy you pump in, yes, obviously the more electrons you bump out, but at the same time, their speed probably also should go because the speed is basically the measure of energy. Energy is coming and therefore energy is supposed to go out somehow. Not that it completely contradicts. You can always say, well, maybe the speed of electrons is the same, but their number is greater and that's why the more energy, the more electrons are coming, but with the same speed. But how would you explain the dependency of the frequency of light? So a certain frequency produces certain speed. The greater frequency produces greater, of light, produces greater speed of the electrons. The lesser produce lesser. But this dependency on the frequency doesn't really fall well into this classical wave theory. And then there is a third property, which is completely unexplainable for each type of material, this electrode, this pole is made of, there is certain minimum frequency of light below which light does not affect at all the number of electrons, no matter how intense the light is. So if the frequency is less than certain level, which is specific for each material, like it's a steel or copper or something else, I don't know. Depending on the material, there is some minimum frequency below which light does not affect the flow of electrons between them, between the electrons. This is completely unexplainable by this classical wave theory because, well, even the lower frequency, if you compensate the lower frequency with a higher intensity of the light, then it should actually produce exactly the same effect, which means electrons should be bumped out from the surface of this plate, negative plate. So what do we do? Classical wave theory does not really explain this. Well, if you remember, the whole wave theory appeared from certain experiments which could not be explained by corpuscular theory, so they switched the wave. Now the wave theory doesn't explain certain experiments, we have to switch to a new theory. New theory was first suggested by Planck, famous physicist, but then it was developed significantly further for the specifics of the Potter Electric by Einstein, who actually, he has received the Nobel Prize in 1921, primarily for his research of the Potter Electric, not for theory of relativity. In any case, so what Einstein has suggested was the following. Yes, light is electromagnetic oscillation, electromagnetic field oscillations, that's right. What he suggested was that it's not just a continuous oscillation, but light comes in certain groups of oscillations, like one, then something, there is a pause, then another, and then another. So these pieces of oscillations, they are called quants or photons. Now, what also was important, that each particular quant, each particular photon of light carries a certain amount of energy which depends on the frequency. So energy is the frequency. So there is no such thing as amplitude of a classical wave theory. The concept of amplitude of oscillation doesn't really exist in the same sense in the quantum mechanics, in the quantum explanation of lights. Well, you can imagine that they all have exactly the same amplitude and just different frequencies. And the more frequency is related to more energy, which particular photon actually carries. So mentally I have imagined it myself as oscillation, then no oscillation. Oscillation, no oscillation. So this is photon. This is a photon. Whether it's really like this, I'm not trying to impose this particular model on you, but you can actually think about light as a sequence of individual quants of light or photons, and each one carries a certain amount of energy which depends on the frequency of oscillations of electromagnetic field. Now, what does it explain better than the previous model? Well, let's just think about explanation of these particular qualities, whether they, whether this particular model explains or it doesn't explain them all. Well, with the first one it's easy because the first one is basically depends on the intensity. Now, what is intensity in this particular case? Well, intensity in this particular case is the number of quants of light, the number of photons per unit of time falling on this particular surface. So the more photons are coming, not the greater amplitude of these, but the more individual photons. So it's not like a classical energy carrier waves. The energy is carried by one particular photon and the energy depends only on its frequency. So each particular photon has certain energy and intensity of light is the number of photons which are crossing whatever falling on this surface per unit of time. And obviously this particular dependency is explainable by this because if there is a photoelectric effect, obviously the more intensity of the light is, which means the more photons are falling per unit of time, the more electrons are bumped out. So the first one is great. Second one, speed of electrons does not depend on the intensity, but only on frequency. Here's what happens. One particular photon falls onto this plate and since the energy of this particular photon is transferred to an electron, which it falls onto, this energy it goes to electron and obviously the more energy it carries, which is the frequency, the more energy is absorbed by electron and this energy is released as a kinetic energy of photoelectrons, those electrons which are bumped out, the more kinetic energy they have. So they're faster, speed is more greater. So the second one really explains quite well why it doesn't depend on intensity, because intensity is just the number of photons and the number of photons will correspond to the number of electrons which are bumped out, but not to their individual speed, because each particular photon is capable of hitting a particular electron and bump it out from from the surface and the amount of energy depends only on the frequency of this photon. The more photons, the more intense is the light, the more electrons will go out, but each electron will have exactly the same speed which depends only on the frequency of the light. So intensity does not contribute to the speed of electrons, intensity of light, only the frequency of light, because the frequency defines the energy which is carried by individual photons. So one photon with certain amount of energy which is determined by its frequency hits the electron and gives this electron certain amount of energy which depends on the frequency and that energy is, if it bumped out, it goes out as a kinetic energy. So the second one is also explainable. How about this one? There is a minimum frequency below which electrons are not affected. The flow of electrons are not affected. Again, very simply. There is certain energy which is needed to leave the surface. It's like we need certain amount of energy, certain amount of speed, if you wish, but speed is actually energy. If you will throw a stone from the from the ground to go all the way into the space and leave the gravitational field of the Earth, right? So there is certain minimum speed which is needed. Otherwise it will return back. If we will throw the stone up and the speed is not sufficient, then something like 11.2 kilometers per second, then the stone will fall back. We did some calculations when we were talking about gravitational field. Same thing here. There are certain ties which need to be broken for electron to go out. So it needs certain minimum amount of energy to leave the surface and travel all the way to another pole, another positive pole. Which means, since our energy is basically measured by the frequency, it means that unless our frequency is sufficient enough to supply this minimum amount of energy for an electron to leave the surface of the negative pole, there is no photo effect. And that's what actually an explanation for the third property. So there is always certain amount of minimum frequency, which means certain amount of energy which each photon carries with itself, which is needed to make the photo effect happening. So basically this particular explanation, again as I was saying it was developed mostly by Einstein and he got the Nobel Prize for it, is a contemporary view onto the light. And what's important is that this division of the electromagnetic waves which basically light is, into individual photons binds together corpuscular theory which we used to have in the very, very beginning and the wave theory. So it's still waves, but the waves divide it into certain quants, into certain photons. And the energy of light depends only on the frequency of oscillation of individual photon. Intensity of light depends on the number of these photons per unit of time, crossing certain border, whatever. Well, okay, so this is contemporary view onto the light, which is basically as I was saying developed in the beginning of the 20th century, primarily by Einstein. And this is what we are currently thinking about the nature of light. Now I presented it in this particular schema. I'm not really trying to impose this scheme on you, but it's really difficult to understand how the whole thing is happening and why. Nobody knows actually that. But it presents a model like everything else. I was saying it many times. We are not really finding out what's really, how it's really done in nature. We are building a model which corresponds to whatever observation we are making. We first build the corpuscular theory of light and it corresponded to certain things. Then we build the wave theory to explain certain things which were not explainable by the corpuscular theory. Then we build right now the quantum theory of light based on photons, which explains basically everything, whatever we observe right now, which means that as of today this model seems to be corresponding to whatever we observe in the nature. And that's probably as much as we can do basically. Again, we don't know how it's done, but we do know that these principles produce certain results which correspond to our experiment, which means we consider them as a true model of the nature of the light in this particular case as of today. But we'll be tomorrow, I don't know. But as of today this seems to be the front end of our understanding of what light actually is. And on this I basically finish my lectures on light. There will be an exam for those people who want to take it. And I wish you good luck. Thank you very much.


St. Lucia and the University of Vermont proudly recognized two decades of a strong and mutually beneficial partnership that had significantly impacted various sectors within the island nation. A project's presentation and closing ceremony was held recently and was attended by key officials, stakeholders, students and other representatives from both St. Lucia and the University of Vermont. The Deputy Permanent Secretary within the Ministry of Commerce, Manufacturing, Business Development, Cooperatives and Consumer Affairs, Mrs. Shamin Louis Justin, highlighted the substantial advantages that St. Lucia has gained from this enduring collaboration. She expressed her gratitude for the support and the positive impact it has had on the country over the years. I am acutely aware of the impact that this long-standing relationship with the University of Vermont has had and continues to have on not only the work and sharpen skill set of our department but on the wider community as well. From the commissioning of the computer labs and school gardening to the undertaking of useful data-driven impact surveys, thanks to the collaboration with the UVM, our staff have received valuable training in areas relevant to the department's function, including consumer law, research techniques and methods and report writing. One of the key achievements mentioned by Mrs. Louis Justin was the marked improvement in the quality of work among the ministry's staff who have received specialized training through the partnership. Moreover, Mrs. Louis Justin emphasized the tangible benefits witnessed in the current year alone, showcasing the ongoing commitment of both parties to making a real and lasting impact on St. Lucia's development. This year, we collaborate with the University of Vermont team to facilitate key projects in areas such as quantitative and qualitative surveys to assess the impact of inflation on local consumers, to establish the establishment of a school garden at the Camille Henry Memorial School, an interactive mapping project with the St. Lucia National Trust, and a social network analysis examining possible linkages among St. Lucia's non-profit organizations. Professor Thomas DeSisto from the University of Vermont underscored the resilience of the partnership, especially in the face of global challenges such as the COVID-19 pandemic. Professor DeSisto expressed his admiration for St. Lucia's commitment to maintaining and preserving the programs established through the collaboration, even during the difficult post-pandemic period. The University of Vermont and the Department of Community Development and Applied Economics prior to the pandemic had programs in St. Lucia, but also in Belize, Honduras, Peru, Kenya, Dominica, Brazil, and several other places. And after 2020, this is the only one that still exists. I mentioned that. Hopefully in the coming years, we'll be able to reignite several of those programs. But I think it just speaks to the resilience and strength of this relationship, knowing that we have partners here that we can work with, knowing that there are people who are here to, you know, who recognize the work that the students have done and that we can learn and grow with. The University of Vermont has been a steadfast ally in St. Lucia's pursuit of development and growth, and both parties expressed their optimism for the future. As they celebrate 20 years of collaboration, St. Lucia and the University of Vermont are looking forward to continuing this fruitful partnership with the hope that it will continue to bring about positive change and advancements for many more years to come.


The lineup gets a boost in the return of Luke Voight. He's been limited to just 12 games so far this year, but he is back from the oblique strain that forced him on to the injured list in late May. Meredith Murakovitz caught up with him a little while ago. Luke, just how excited are you to be back here at the stadium and in the lineup tonight? Static. It's been way too long. Obviously got some good at Badstown in summer, said which is a great complex for the double A guys. And I can't wait to bring some energy and bring some fun stuff to this team. And just get the guys going and just have fun and be able to go again. How did you feel throughout that rehab stint from a health perspective? When did you know that the oblique was good to go? I was trying to find my way to get back in the lineup over the weekend, but I get it. They wanted me to obviously get as many as possible. So I was good tossing Vila down there. And I had to run the base to do a couple first, third score from second. And hit some different pitches, which was great. And it was fun playing down there. Obviously having Julio, who was with us last year as a coach, too, was a nice quote to him. And yeah, glad to be back as much as it was fun double A. Big League's a lot of funner. I know a lot of times it's not about results down there. But how were you seeing the ball? Good. I was telling the joke with the guys. I think I made the All-Star team. I had so many other guys. I felt good. Had a couple extra base hits. Swinging to strikes, so it was all good. So hoping that translates into the day. You mentioned Julio. I know some of the other guys down there. Typically, the veteran guy, the major league guy that's rehabbing has to buy dinner a few nights. What did you get him over this course of the rehab assignment?  Because obviously it's different now. A lot of these teams are paying for their teams of foods. And so they're getting nice food. And I was like, these guys probably just want pizza and just to crush pizza. And there's nothing better than that after post game, especially when you got a long road trip up the main like they did. So yeah, pizza. Taking you back to baseball. How long do you think it'll take you to get back to the swing of things up here? I'm hoping tonight. Obviously, I've never faced Brady Singer who's pitching tonight. But that's why we have a video. I've done some research on him. So I'm hoping it translates right away. But obviously, I know it might take a little bit of time. But can't get too frustrated. Can't look up the scoreboard, look at my stats. And obviously, I'm way behind on everyone. But just playing my game, and obviously stay healthy. Is that difficult to not try to do too much immediately when you get back? Because you want to be in there and contribute so badly? Yeah. I mean, I think I've matured over the last couple of years, too, to where I don't feel like I have to do too much. And I'm not going to lose my spot. And you have to come up here and prove to myself again. So that part, not too much. But yeah, I mean, obviously, I'm here to do damage. And I want to do damage tonight. And before I let you go, I know you're going to have a very special guest here tonight, your first-time dad. So happy belated Father's Day. And I understand your daughter will be here, right? Yeah. So Kennedy gets to come tonight. It'll be great. Can't wait for her to come to the first game. She probably has no idea what's going on.   And I can't wait.


Katrina remains in a place of clothing shops. There is a place where money comes from from their local businesses. It does not matter here. Realistically, it does matter that 3 lakhs of 100 children have to walk on 1000, 2000, 2000ęd. Tomorrow everybody will mostly normal.  случа  망 稱                              這                ,.


There's nothing about masturbation in these 1600 plus pages and yet kids are swatted for exploring their body.  Second, the Bible says this, flee from sexual immorality every other sin a person commits is outside the body but the sexually immoral person sins against their own body. Masturbation is a form of sexual immorality. Sexual fulfillment is only acceptable in the context of marriage. In this context we're called to think of the needs of our spouse first which is in stark contrast to the selfish sexual fulfillment in masturbation. Though we all have a tendency towards sinful desires God said that when we put our faith in him he will make us into a new creation. That doesn't mean that all our temptations are going to go away but it does mean that he has provided us with his power and his presence to overcome the temptations that we do experience.


Thank you for the introduction. Thank you for the invitation to talk here. I'll, okay, the title's here. The subject of my talk, my own interest to this subject grows after the paper by Oleg Glysovy, Kolya Yorgov and Sasha Gamayul, who shows that tau function for Penderbae equations, for example, for the most generic Penderbae six equation can be, has explicit expression in terms of conformal blocks for the rasora algebra, or if you want negrasa partition function first due to theory, and this fact has main generalization. So this is why I came to this subject. And I was a beginner in this Penderbae theory and I stopped my talk with some facts about Penderbae theory. And the subject of my talk is a Q deformation of the conjecture of Gamayul Yorgov and Glysovy. The subject, the main result, Q deformation of conjectures, and other conjecture. Okay, we'll stay here. Okay, I start from the Penderbae equations. It is known that there are six Penderbae equations, but it is convenient to decompose one of them into three. So we have Penderbae six, five, three versions, Penderbae three equation, Penderbae four, Penderbae two and Penderbae five, one. And in this diagram, each arrow stands for degenerations, confluence for this equation. And it is easy to see the level of parameters. So the most generic one, Penderbae six has four parameters, Penderbae five has three complex parameters and so on. And the most degenerate ones, Penderbae three, three, Penderbae one has both of them have no parameters. For each Penderbae equation, one can assign a certain rational surface. So this is a geometric approach to Penderbae equation. Originally they were introduced as a second order differential equation without movable branching points. But there's another approach to them as a geometrically due to a commota for each Penderbae equation we assign rational surfaces written here. And for such rational surface, we have so-called inaccessible divisor, in other terms, vertical leaves. And intersection form of the components of this inaccessible divisor is the same as intersection form on the scalar product on the affine root lattice. So to each Penderbae equation, one can assign affine root lattice. And they are written here in the color magenta. The arrows here, in terms of root lattice, arrows are very simple, we just add one node to the corresponding root, not affine root lattice. And good news, that today I will pick about very concrete example. One of the most degenerate, of two more degenerate Penderbae equation, Penderbae three, which assign to the root lattice D eight. Here I put it in the box. So this somehow general picture. And if you want, you can forgot it. Exceptional series, maybe we'll explain the equation, but after talking, maybe I'll say more, but probably the same answer, I don't know. Okay, so as I said, I will concentrate on this degenerate equation. So let's proceed. First of all, this is a second order on linear differential equation, which has no parameters. This is one of the conventional forms of it. Of course, it's not necessary to remember, but just to be explicit, I put it here. Another form, which is much more easy to remember, it is a Bollinia form of this equation. It is convenient to rewrite this equation as a system of two, I said, totally like Bollinia equations. On two functions, two tau function tau, and another I do not know by tau one. There's two equations. D2 is the usual second heriot operator with respect to logarithm. I admit formula how to write tau in terms of w, formula in opposite direction is w of z is equal to this ratio. For this equation, we also have a symmetry. In the last six equations, the group of background transformations is very interesting. This is an extended affine real group of D4. But here, this group is finite, just group of 42. We have only one until your transformation, which I do not by pi, such that pi squared is equal to one. And this transformation acts in terms of tau functions, very simple, manning maps tau to tau one and vice versa. And in terms of w, this is just, w goes to zero with w. And this is clear from this formula. Probably I also mentioned, so this equation has algebraic solution. So, genetic solution of this equation cannot be expressed in terms of any sort of another elementary function. Solutions of Penileva equations are some sort of transcendental function, which are not equal to anything else. I mean, now we know that they are very related to conformal books, but they're not hypergeometric, not elliptic, and so on, so on. And I think this equation don't have hypergeometric solution, this don't have elliptic solution, but have one, or even better to say two, algebraic solution, just w is equal to square root of z plus minus. And the corresponding tau function is exponent, up to some simple factor. Appearance of square roots has, of course, certain geometric origin. So, you see, there's no square roots in the original equation, but we have them in the solution. Probably I also commented that the solution is a, okay, the reason here is invariant on the background transformation, general, some kind of general. Okay, it was a very short course of this equation. Now, I come to the relation between this kind of equations and conformal books. So, this formula, which was conjectured by Comay-Unior-Gofflin III in 2011, that's the tau function of this of this equation has this explicit formula. Now, what is written here? We have two variables, two parameters, s and sigma, which are integration constants in terms of the original Pindov equation. Recall that this equation has afforded two, so, a generic solution should depend on two complex parameters, s and sigma. s appears here, this formula has very clear predictive property with respect to s, with respect to sigma. If we shift sigma by sigma plus one, then tau function applies by the number. And as usual, tau function is defined up to constant multiple, so constant with respect to the multiple, so, this factor is not essential. This is the power, and this function c is the explicit function given in this form. Given this form, one over product of two bar g functions, and bar g function, I recall, satisfies this functional equation, and there's a special solution of this functional equation. This is about the red part of the formula. Now, I don't know whether it's visible, about green part of this formula. This function f of delta z, either we take a limit of verisorac and formal block. Delta is the highest weight of the corresponding representation, in which we calculate conformal block, if you want conformal dimension. And the central charge is not written here, since during my talk, central charge will be equal to one. So, this explicit formula. And this formula relates one sort of, one sort of transcendental functions, namely tau function of many equations, to another sort of transcendental functions, conformal blocks. And there, more or less, this space of function, so more or less, this is the meaning of this formula. Okay, it was a conjecture, five years ago. They have certain motivation from conformal field theory, certain explanation, in terms of conformal field theory, based on fermionic realization of the c equal ones can be represented in terms of fermions. And also they represent, not in the way, but correspond to either monodromy problem, in terms of fermions. But this is some sort of speculation. There was some sort of speculation. Another motivation was that this series was not known, but first terms were known due to Jimbo. And then they calculated the next terms and realized that this is actually conformal block. I don't have a short answer about motivation, you see. They have some motivation. Another comment is this function is the necrata partition function for pure SU2 theory due to a GT relation. So thanks, necrata partition function is given by explicit combinatorial formulas, summation of the partitions, and so on. So in this sense, this is explicit combinatorial formula for tau function. Okay, this conjecture was proven two years ago, two independent papers, one of your presentation and another is, myself is Anton Shchetskin. Now I'm going to relate generic story about Penilever equation, which I mentioned before, back home transformation, algebraic solution to this formula. So as I said before, there's a back home transformation which acts on the solution of the Penilever tau functions. And in terms of this formula, it's just a transformation which maps sigma to sigma plus one over two. I mentioned before that this back home transformation have order two. So pi squared maps sigma to sigma plus one, and this is okay due to periodicity. So this formula is consistent. Using this formula, we can rewrite Balini relation, totally like Balini relation. As a one equation on the function tau, and this equation will be differential, second order differential equation on that, and second order derivative equation on sigma. So we have one equation on one function, which is differential on that, second order derivative on sigma. Algebraic solution, which corresponds to special parameters, sigma and s. And using this formula, it's easy to find them. Given by this formula, it means that we have an identity. So if you substitute corresponding algebraic tau function, we give the formula of, we give that this exponent is a linear combination of conformal blocks with certain coefficients, which in this case can be made rational. We can factor out something, this is very simple, and get this. And this is interesting because this conformal blocks itself do not have a simple formula, or at least nobody knows it. And it looks like there's not hypergeometric functions, I think not elliptic, so there are some transcendence, and in this form, this identity is not trivial. Also, I mentioned that conformal dimensions, which appeared here, are probably now called as conformal dimension twist fields. I mentioned two papers about this twist field, but there are a lot of them. In this formula, okay, yes, depending on normalization, probably I put it here to conformal blocks, or just for good, I don't know what is that. They should be here, so we have some. So algebraic solution means that we have certain special relation between conformal blocks and an exponent, and means that the corresponding fields are somehow special. In this case, they're known as twist fields, whatever. This twist is responsible to appearance of the square root of z here. Okay, so probably we are almost done. We are ready to go to the main subject of my talk, is a Q deformation. Is there any question about what I have called? Good point to ask. Okay, now we are going to, now Q deformation, and okay, we follow a so-called geometric approach to the deformity of different Penileva equations, which was introduced by Sakai. So if I understand correctly, history, so in 90s, there are many different equations, different analogues of Penileva equations, integrable different analogues were introduced by many people, Jimba Sakai, Grammatikas, Vramani, I think I forgot several names. And then in 2001, Sakai invented certain unified geometric approach to all of them. It is some sort of clever different analogues of the original Penileva property, that we study different, Penileva property means that we study differential equation without movable branching points. And Sakai introduced some sort of different analogues, different analogues of this property. So to go to the answer, then to each Sakai sign difference equation to the rational surface, which obtained by blow up of nine points in CP2. Here cheating a little bit, so these nine points don't mean that all are line CP2. Maybe we take one blow up and then take another blow up on the pre-image of the, on the additional exceptional divisor and so on. Morally, nine blow ups of CP2. Then for each such surface, Sakai signed certain combinatorial data, latest, which is generated by reducible components of the anti-canonical device. And this latest is called surface latest as, and as before in Kamot approach to differential equation, the intersection form on this latest, coincide with the form on the certain affine root latest. And this is the table of all possible intersection forms on all of R, so all possible R's, so corresponding all all possible rational surfaces, all possible different different equations. So you see after Q deformation, so before we have say eight, before Q deformation we have eight equations. Now we have I think like twice more. So this part was the same was for differential equation, but that means that it is the same for each of D, for example, for this D81, okay, for this D41 we can set both differential or difference equation. So really we have more equations for Q deformation. And maybe I should comment that this fill A part of this diagram correspond to Q difference equation and this part correspond to D difference equations. Since I want to study Q deformation, I will leave in the first row. Difference is that you have function on Z and for Q difference Z belongs to C star, not equal to zero. And for D difference Z belongs to C. So for example, it depends on what kind of singularities. So for example, you can look for the meromorphic solution on C star or on C, so this is some sort of difference. Yes, yeah, exactly. For each D I can assign differential equation, I can set difference equation. If I take any of A, say this, and take this limit, then in the limit I can have differential equation assigned to this D. Different equations A and D, for example, two different equations can have the same limit. So theoretically speaking, there are infinitely many ways to invent difference equation, which has the same limit. But we are looking for good ones which should satisfy some sort of difference when they were proper, it should be. If I understand correctly, the limit of this equation is not Pen-Levers, it should be something elementary. So differential Pen-Levers equation lives here. So from A3 we can go to D4. This is called Q Pen-Levers 6 equation, which is invented by Jim Ben-Zakaya. Any more questions? Okay, there's another part of Sakaya story which I want to mention. To each surface, one can assign so-called some sense dual data, which I denote the R-Togonal to the Togonal complement to the lattice R, which I mentioned before. And here is a picture of the corresponding R's. I don't have time to explain details of such notation or such or even this notation, but it's just a paper, but I will sometimes use one of the table and sometimes another. The only thing which I can say is that we have two lattices, R and R-Togonal, and the rank of this group is 10, since we have nine blow-ups. So the sum of the ranks of R and R-Togonal is also 10. Such lattice R-Togonal is useful not to describe the group of discrete dynamics of the corresponding plane-level equations or whole group of discrete group which acts, which form our equation. And this group, roughly speaking, has a form. We take a while group of the corresponding affine root lattice, affine, yes, affine root system and take also semi-direct product of the external automorphism of the corresponding affine root system. And this is the whole symmetry group. Therefore, the lattice R-Togonal is called symmetry lattice. So R is called surface lattice and R-Togonal is called symmetry lattice. Just, okay, and on the next slide, I put both lattices R and R-Togonal, both tables. You see here, for example, that here's rank two, here's rank eight, so sum of the rank is equal to 10, everywhere. And again, I will speak about very concrete equation. So differential equation lives here. It's D-8-1. So the corresponding difference equation should be connected by arrow with this equation. So, and I want to study Q-deformed in scientist. I want to Q-deformed conformal blocks. So my choice will be this, A-7-1 write for the box and draw the notation. So as before, this is some sort of broad picture. And now in the next slide, I will say you in some details, what is the mean of this equation, what is the mean of this, at least of this notation. So you can forget all the reason about this very large table. But we have, so as I said, so difference equation is assigned to a rational surface. In this case, we have several, in any case, we have not one surface, but certain model space of such surfaces. And this, we can choose certain coordinates of this space, which I forgot, I omit the exact definition, but I don't know them by z and q below. And on each surface, I have its own coordinates, which I denote by f and g. Now, as I said before, group of disk transformation is a semi-direct product of the, while group of the symmetry lattice of the root system of symmetry lattice and external automorphism, which is now is the de-hedral group, group of symmetries of square. I also put here presentation of this group using generators and relations, as 0 and S1 are reflections of while group. So they have relations, they both are square equal to one and no other. And P1 and P2 are generators of de-hedral group. P2 is a rotation of 90 degrees, and P1 is a reflection. So this satisfies this equation. And here is the action of the de-hedral group of the while group is written. So actually, external automorphism of this group, of this root lattice, this root system, is the two, which we can permute to root, to simple roots. And P1, here should be this one. P1 should, I think, permute them. Oh, no, no, no, no. P2 permutes to roots as permute to the corresponding reflection as 0 and S1. And P2 squared and P1 commutes with this affine. And the action of W is given by the following formulas. This, these formulas come from geometry of this rational surface, but I don't have time to explain what is the definition of such surface and how to use its geometry not to write these formulas, just to give an answer. And all this done by Sakaya, this is how a formula looks like. The most non-trivial parts of the formulas are certain rational functions. For one can check that transformation defined by this formula satisfies these relations. So for such formulas, more or less clear, but for such rational functions, this, it looks for me non-trivial, but it is okay. So this trial group acts both on coordinates on the modular space of surface and coordinates on the surface, so on the total space of the point of the bundle. Accelerational surface, it's a blow-up of CP2 in nine points. And, but such a combinatorial data, these nine points are not generic, so some of them lie on the premise of another one and so on. And the sort of the generation is encoded some, we have some, there is some combinatorial description of the sort of the generation which corresponds to this surface. So actually we have only four points on CP2 and so on, then three points in the premise of one of them and so on and so on. This lattice, so this coordinate prime regime Q, prime tries, this is the generation. So combinatorial data is the same. Maybe I'm answering the wrong question now. Okay, thank you. Okay, let's proceed further. I also introduced element T in this group. This element of an infant order, translation W. And in order to, I use standard notation for different equations, I denote by X upper, by T of X and X down, T inverse of X, then you see T shift Z to QZ and T inverse shift Z to Q inverse Z. These formulas are obtained from this formulas. It is impossible to check this on the different slides, but it remains to believe. And for function F and G, we have sort of national function and using this formula, we have this, we can write one equation, function G. And I will say, next slide, but I can say it even now, that this equation is actually Q deformation of the original second order differential Pendevere equation. So in the limit Q goes to one, in the leading order, this equation goes to Pendevere three, three equation. Of course, this limit should be arranged. So Q goes to one, it goes with G and Z, so Z goes to zero in certain speed, G also goes to zero, so there's this sort of regime under which this equation goes to this Pendevere equation. In another regime, it can go to something, elementary and so on. Okay, now I want to write formula for tau function in order to Q deform original conjection. I want to write formula for tau function and the first question is, what is the definition of the tau function? And for differential equation, Akamoto gave the original definition using Hamiltonian formalism and so on. And for difference equation, at least as I understand, situation is not so simple. For example, for our concrete equation, we haven't find in the literature the definition, so actually we invented the definition of the tau function but following the Tudda approach. And I mentioned there are, probably there is no convenient definition of the tau function for such equation, but there are several approaches. So I mentioned last paper by Naomi about this. There are several papers of Naomi and his co-authors. And I also want to mention paper by Rinke and Borodin who defined the tau function not for the Pen-Lever equation, but for linear difference equations. And differential Pen-Lever equations arises as another problem for linear differential equation. So there should exist relation between Q deform Pen-Lever equation and Q difference problem. So problems there is a relation between their definition and definition which we need, but this is not done. So this I just mentioned, actually we follow somehow Tudda approach, but it is not necessary to know what is his approach. I put it as a theorem here. So we can introduce for tau function. Is there some reason why for tau functions looks to be good choice and define action of the transformation P1, P2, S1, S0 on them by the following formulas. Those will then find action of the T. So these four columns are already given below, given above in the previous slides. And these formulas are our definition. And one can check that all relations are satisfied. All relations of the group are satisfied. Moreover, one can check that if F and G are expressed in terms of tau function by this formula, which are look very similar to formula which expressed differential function. Solution of the differential Pen-Lever equation in terms of tau function. So if F and G expressed in this formula, then the action on the tau function is consistent with the action on double on F and G. Which I mentioned before. The second order differential equation on G. In terms of tau function, this equation reduces to system of two, Bellinia again, like Toda equations on tau functions, tau, use two tau function, tau one, tau three. And last comment that we have made several checks that on the, and that is followed. So on the level tau function, all what I can get action of W is a Laurent, even no series, Laurent polynomial as here. So for G, it's not true. Here we have real, we have rational function, G minus Z is denominator G minus Z. But if I will act on tau functions, I will get only Laurent polynomials. And probably this fact could be explained using some relation to cluster algebras, but I don't know. But this looks like one more hint, that our definition of the tau function is good one. Now, I consider all my function which I introduce, F, G and tau as a function on the variable Z and also Q. So I write action of T as a shift on Z. So H up is H of Q Z and so on. Then equation on function G has this form and here I can take the limit Q goes to one and get differential in the equation. And for tau function, our goal will be the same as what was informed by gamma union of Lissa v to introduce only one function tau. Depend on two parameters, U and S. Here I use U, but U is, I can say that U is a Q in power of two sigma and sigma and S are direct analogs of sigma and S in continuous formula. And for this function, we set tau one given by this formula, tau three given by this formula, assume periodicity and we want to have such Balini relation. This Balini relation is equivalent to Balini relation on the previous slide, it works slowly, maybe. So this is my problem. To find function tau, which will satisfy this Balini relation, maybe also periodicity, also periodicity, then I will find a solution, I will find function G by formula, which was on previous slide. So in this sense, I will solve difference in the equation. Here, it's a type, here should be the inverse. Thank you. Probably this T looks different from this T and this is also type. And this T also looks different, this is also type. There are several types. More questions? Now we almost come to the main conclusion, main conjecture. So main conjecture will be on the next, main definition will be on the next slide, but before, in order to write it, I need to recall what is QD form conformal blocks. So I wrote this tau function in terms of the QD form conformal blocks, I will write it. But before I need to recall what is QD form conformal blocks. First, just in words, this square of the vector vector of the VeroStora algebra. So it has the same representational definition as usual conformal block. But for actual calculation, we use another definition or statement. This function is a Nekrasov and Stanton partition function for pure SU2 gauge theory, five dimension. So therefore, this function has an explicit combinatorial form. Summation of a pair of partitions, and here is the Nekrasov type product. So the function defined as a power series in Z. Here I used two parameters, U1 and U2, but actually this function depends only on the ratio of them, U1 over U2. So everywhere I will write just U. Also, during the, also today, my talk Q1 inverse will equal to Q2 will equal to Q. For the VeroStora case, it will correspond to the C equal one in terms of topological vertexes. Vertex, it means that our topological vertex is not refined, so that's very good. And this formula have maybe better say U2. When we take a limit, we don't have this U1 counterpart. To be honest, I not really understand the difference in this notation for SU2 and U2, maybe you will explain. In the representational definition, we do not use additional Heisenberg, we use just VeroStora. But if we take a limit, this is the same. For Heisenberg, we're taking the ones. Maybe this is not important. But, so this two is essential. So U1 is not, this is not fair. Okay, I would like to put as a lemma that this series is a series converge. As a series, as a series on Z. And converge for if absolute of value of Q is not equal to one. And U is also not Q in power n, so for such U we have poles. Last I mentioned this function is a topological string partition function for local p1 times p1 geometry. So this function up to simple factor, infinite program symbol squared is a topological string partition function. So this function F, which has three interpretation if you want, Q VeroStora conformal blocks, necroson string partition function and topological string partition function is main ingredient of the conjunction. Definition. The tau function will be given by the following form. What we have here? F is the same as before. Q deformant conformal block, necroson partition function of pure SU2 theory. The main, the new ingredient here is this function C. Also with this factor, and this function C if you remember in conformal formula we have Z in some power divided by the products of Barnes G function. This is some sort of analog of Barnes G function and this is some sort of analog of Z in some power. In order to state main conjecture that this tau function is solution of the Balinia different equations. We need to impose following conditions function C, system of three conditions. This condition can be viewed as a second order difference equations as a function two variables, U and Z. Here is a second order difference operators with respect to U, here with respect to Z and here with respect to both of them. Function R is not essential, I can state that R is equal to one no one can say that R satisfy homogeneous version of this equation where right side is equal to one. This is not necessary for Balinia equation but it is sometimes convenient to impose that functions U and R satisfy symmetry with respect to U to U inverse. I recall that conformal block satisfies symmetry and also this products satisfies as possess symmetry so maybe convenient but this is not necessary for Balinia equations. This is the definition. So the most material part here is of course function C. For example, after such formulas you can ask whether this function exists and the answer is positive. This function exists and there are a lot of such functions. Here I put two possible solutions. One of them is actually more or less the same suppose before Q deformation, something like Z in some power but now this power which is called sigma before now this is a logarithm Q over logarithm Q, logarithm U over logarithm Q therefore we have some such strange formula. And advantage of this formula is that in this case function will be miramorphic in Z, miramorphic in U. This function of course not. I don't know whether it is a good question what is the best answer for function C? This function is defined up to the multiplication periodic function in both U and Z or even of this multiplication by solution of the homogeneous equation which were on the previous slide. I don't know. At least such function exists. I have two rather random examples. I also noted from the definitions clear that our function satisfy periodicity condition with respect to U. So it's in here. And if C and R are a universal variant then the corresponding function will be also universal variant. Now conjecture that function tau defined on the previous slide satisfies this Boolean equation. As I said before this Boolean equation is actually equivalent to the corresponding Q difference in the equation. This main question. Q difference in the equation of the surface type A7 would seem to be right. One can rewrite this equation as a Boolean equation conformal block. I put it as a theorem but actually this was a long but straightforward calculation. I don't know proof of this. So this conjecture is equivalent but anyways you can say that this okay and this relation is conjecture. No, no, this conjecture is. What is proven that this relation is equivalent to this but it is not victimized. So if you introduce times it's basically a singular vector for Q-virus or it's essentially like Q-virus or constraints is it related to this state or isn't it related? So it has actually proven. No, no, I know the paper but I don't know if it's this relation. I don't know, I'm not sure this is related. My understanding, I don't know. I don't know if this is related. Okay, I just had two comments that first of all we of course we have checked this relation up to certain power of Z and second we checked this equation conformal limit of this equation and this additional check because up to certain power of Z we use only first say three or maybe five summits on the left side on the right side, but in conformal limit and limit where Q goes to one we have checked all terms. And everything's okay. Continuous limit is true. So I think this conjecture is true. Let me briefly mention two other parts of the of the differential pin lever equation and the liquid deformation. First I told you that there is a background transformation for differential pin lever three equation and here we'll have also analog of this different of this background transformation. This analog permutes tau one and tau three and this claim which is the second which is not so clear it is a question on algebraic solutions. I recall that differential pin lever three equation has one two algebraic solution plus minus square root of Z. The same holds here and this is even simpler. You can start during my talk substitute this G of Z in this equation and get everything's okay. This equation is satisfied. I don't know whether this classification of algebraic solution of this equation but anyway, naïve analog is a solution. And therefore we can substitute this solution to the conjecture and get the following results. So if tau function is U inverse invariant then for special values of U and S S is before is plus minus one and U should be square root of Q here. This is essentially reduces to this double pagandar product. In terms of conformal blocks this formula is equivalent to the relation that this double pagandar product is equal to the sum of Q deform conformal blocks. This is a certain Q rational coefficients and here I have power Z. So probably I forgot it in the first slide. Let me make one more comment and about this pagandar product and then I go to the conclusion. That I said that algebraic solution for pin lever d8 is a exponent. Tau for correspondant function is exponent and this should be compared of the Nekrasov partition function for pure U1 C which is also exponent. Here algebraic solution is a double pagandar product and this also should be compared with the Nekrasov could be compared with Nekrasov partition function for pure U1 theory five dimension which is also one infinite product. So the fact that exponent the Q deformation of the exponent is such infinite product is known. Any infinite product can be viewed as a deformation of the exponent but I think this relation means that such infinite product is natural here. Also we have the same phenomenon here. We have exponent of Z and here is exponent of square root of Z and in terms of CFT it relates to the fact that we actually consider twist fields we need to take. And here we also have the same square roots of Z. Okay, I have three more slides and I don't know five more minutes. Okay, first comment is that the main statement is conjecture. So if I consider myself as a mathematician so some of my questions to prove. If at least try. If I, okay, if I forgot about this question then the next question is to generalize. And now I recall this big table here called symmetry table of the symmetry table for symmetry lettuces and I recall that we live here now. Naive conjecture is that for this line, for this point of the equation are related to five dimensional and cross-partition function with n fundamental multiplies. So here I discussed case where n is equal to zero. And naive conjecture that for any n at least here is this holds. So n is not less or equal to seven. This, for example, it is known that if n is less or equal than four then we can take to goes to one limit of this equation and get that there should be relation between corresponding differential and the equations and corresponding four dimension across a partition function. And this relation is actually known due to Gamayoun-Yorkov-Nissavi for this case, we know that there exists a limit. Another important or even no important relation is that 20 years ago, Cybert argued that this gauge series, so SU2 here should be SU2 somewhere. SU2 here, SU2 gauge series, or U2 I don't know, with n fundamental multiple has global symmetry E n plus one. And, but I don't know whether exist any, I don't think that this is coincidence, but I don't know any explicit relation between this fact that this gauge series has such global symmetry. And our desire that our hope that the corresponding, that two function of the corresponding Q-Panelier equations can be given in terms of the cross-partition function of this gauge series. And of course, I don't know here we have actual group of symmetries is a affine real group. So where, how affine part comes. So probably this affine part comes due to the fact that we have not only one across the partition function, there's a whole series, but this is a question, maybe more interesting than proof, but this one. So it is. Okay, second part of the discussion, and that I, from the, how if you look at the original, of the formula for this group, which you see that I use only part of this group, only shift t, and also p2 squared, which is, which goes to the background transformation of the corresponding differential equation. So this part is a, has clear meaning in the limit. But actual discrete group is larger. And so this actual group will look double, looks to be new phenomena, which arise after Q deformation. And it would be interesting to understand this in terms of our formula, of the tau function. So actually this symmetry is used in this, such simple case, to that transformation z to the inverse and Q to the Q inverse. And second transformation transparent, more or less, conformal blocks has such symmetry and also p-cum- functions has such symmetry and so on. But to z goes to the inverse. I don't know whether it's possible to say something about our formula for tau function and say some correct statement, which involves our formula for tau function and also such symmetry. Naive idea that this symmetry should, means, should be clear into certain symmetry of conformal blocks. And, okay, two comments, but first about this symmetry. So I recall that this, this Q-deformed conformal blocks is more or less equivalent to strain partition function for local p-1 times p-1 geometry. And for such geometries, there exists fiber-based duality, which intersects to interchange two factors of p-1. And in terms of this function, this duality has the form.  And if absolute value of Q is not equal to one, the series do not converge. So I don't know how to use it. So if I define this conformal blocks as I did before, as a power series on z, then as I stated before, the series converge, everything's okay. So for absolute value of Q not equal to one, left side is defined, right side is defined, but they are not equal. And as a formal power series, they are equal, but this not, but do not converge. So I don't know whether any relation between fiber-based duality and this question z goes to z inverse. And probably this question is more or less, is very related to the question on the previous slide, what is the relation between the affine group symmetry and symmetry from cyber paper. Okay, and my last remark will be more or less the same as on the previous talk. I mentioned another paper by Giulio Alessandro and Dalba, who constructed Q differ, also who also constructed Q deformation of the formula for the level three power function using this paper mentioned in the previous talk and many others. I just wrote here two sentences and maybe Alba will explain more. It's interesting to note they work in different regions so in their case, absolute value of Q is equal to one. And if I know correctly, this approach are not completely, our approach are not somehow related, but I don't know details and maybe Alba will say more in the next talk.


SCP-409 resembles a large quartz crystal, approximately 1.5 meters or 5 feet tall, and 0.6 meters or 2 feet wide. Any objects coming in contact with SCP-409 will begin to crystallize after 3 hours. This effect will occur in any material other than granite. The crystallization will spread by approximately 2.5 cm or 1 inch per minute, and will convert the entire object or organism. Subjects report this effect to be extremely painful and similar to frostbite. After complete crystallization, the object will begin to make snapping and creaking noises for approximately 20 minutes before bursting into thousands of fragments with great force. Anything touched by or touching a fragment will immediately begin to crystallize. Nothing at this time is able to reverse the effect in organic matter, including amputation of affected areas.


I'm going come on, man. Like I said, Google has been AI and there's been your calculator was AI. People used Abacus to do math and now people use complex artificial intelligence. Your airplane, you're going anywhere. This iPhone I'm shooting on. These are all examples. I mean, even, even I was thinking movies like Hollywood, the first movies were late 1800s, early 1900s. In a sense, that was artificial intelligence or artificial robotic because the human eye was replaced with the lens, the complex eye, and the human brain specifically the amygdala where we have our memory was replaced by stored film where they stored movies or tapes. So I mean, this has been going on for quite a while here since some level of industrial revolution. So in a sense, all this stuff you see about AI is overrated.


Mi tu mungi atusa, kwa zahizuri kahebo, kwa mi introduce yourself again for us. Asante. Mi nimza Yujimu Ridhi. One of the pastors in Life Church in Nguro and I bless God. Thank you Jaycee Sako family for having me once again. I'm a married man to one Miriam Nyambura and mi tu masalamuzaki. Piai ni mulu yaki blani. Nalawu ja blisatuna. Ameza matuwa chasa limi ane. Hewani. Ukuya hewani. Ukuya hewani. But I know she is watching. Amen. In the last week we began this series. Adi tukai yekai kwa series. Thanksgiving is a master key. Just a small recap maybe you can just tell people what Thanksgiving is and the importance. You go on it now mentioning those keys as you go. Thank you Miriam. Thank you Jaycee family. Jaycee Sako family. Last week we began on the matter Thanksgiving and indeed we learnt that Thanksgiving is a master key. When you read Psalms 100 and verse number 4 especially now for those of us who are students of the Bible the message Bible says a certain aspect of that word and it says enter with a password thank you and you know we are living in an age where everything has a password. Sayi ewezi yako what's up ya mutu ikona password. Password zime kwa kila mahali and we learnt last week yakua Thanksgiving is a password that gives us access not just to God but also to the things of God and also to people you've done things for them and they are not grateful what that does it cuts that access the next time you'll not be willing to do maybe a particular thing even to such people but Thanksgiving will give you access it will always open the door for the next and for the next and opportunities sometimes are cut off because of people refusing to be grateful and one of the points that we will learn today is that refusing to give thanks refusing to receive because once you are granted maybe an opportunity it could be something that is small today but that thing when you are thankful when you are grateful it will open up a door for another bigger thing greater thing and I believe Thanksgiving is so powerful and so that is where we begin or we start from today and I believe it will be a blessing. Yes now take it out your person today you have time today you have time today you have time higher 20.7 sasa your camera is usually on okay welcome and we continue to learn from where we stopped in fact people began to reach out through the week that send me the notes send me the remaining points and I had just to send them so na jo kuna watu wamba wakuna notes amen I want you to know that we began to read a story in the book of Luke chapter number 17 okay yes we began to read a story in the book of Luke chapter number 17 and when you read that story where Jesus interacts with 10 lepers and we understood or we discovered that when he sent them because they cry to him to heal them and so when he sent them and he said go and show yourself to the priest the Bible says when they were on their way when they were headed there the Bible says that they realized that they were already healed and upon discovering their healing one of them turned the Bible says that he turned because he realized that he was healed when you read from verse number 15 of Luke 17 it says and one of them when he saw that he was healed returned and with a loud voice glorified God and fell down on his face saying him thanks and the Bible says and he was a Samaritan so we realized that the rest were Jews but this particular one individual was a Samaritan and in verse number 17 it says that so Jesus answered were there not 10 cleansed but where are the nine and the Bible says were there not found any who returned to give glory to God except this foreigner verse number 19 and he said to him arise go your way your faith has made you whole listen to me when you don't know what is possible you end up settling for that which is valuable and thanksgiving gives us access to the possibilities that are in God the possibilities that are in people when people do small things for you and you return to say thank you it opens up that possibility for you even to be given more for you even to experience more to be added more and so today we will pick it up from because thanksgiving is a key is a master key and I know my points will not exhaust everything but today we will just try to pick the few keys and we say number seven is that thanksgiving is the key to maintaining peace in life the thanksgiving is the key to maintaining peace in life and when you read Colossians 3 and verse number 15 according to the NIV version it says let the peace of Christ rule in your hearts since as members of one body you are called to peace and be thankful we see that thanksgiving is a state of being is not just an action is a state of being be thankful that you can be thankful you can choose today to adopt a certain posture you can choose today to adopt a certain demeanor that you are thankful thanksgiving is a state of being Philippians chapter number four verse number six and verse number seven it says do not be anxious about anything but in every situation by prayer and petition with thanksgiving we see that thanksgiving is an accompaniment that thanksgiving is an accompaniment is not just enough to pray and I know even as we begin the year as the JC Sako family I know that we need to open and unlock this year and the possibilities that are in God even through thanksgiving we can pray we can bring our petitions as applications but thanksgiving will grant us peace and verse number seven is where I want to focus on it says and the peace of God the peace of God which transcends all understanding will guard your hearts and your minds in Christ Jesus I pray for you that is watching us today that through and by thanksgiving that you will locate the peace of God there is a key that opens unlocks peace in the lives of men that is called thanksgiving number eight is that thanksgiving is the key to submission and the authority we live in an age where people struggle to submit even in our workplace in our churches in our families in our marriages in our homes people are struggling with these subjects thanksgiving sorry submission why because we are not grateful for what people do today I sit here I'm grateful even for the small things that people do even in my hope I'm grateful for what my wife does for what my family does I am grateful and the day you discover the power that there is in thanksgiving we live in a world where people will lift placards and begin to say our rights our rights people are not grateful even for small things when was the last time you gave thanks to your boss to your employer for even giving you an opportunity to work at the end month if the salary delays we are big on saying our rights but we are not even big on saying thank you have you ever wondered how many people desire to have the opportunity you have and so thanksgiving is the key to submitting under authority and in the Bible in the book of 1 Timothy chapter number 2 and verse 1 and 2 it says I urge you then first of all that petitions prayers intercession and thanksgiving and thanksgiving be made for all people for kings and all those in authority today if you begin to thank God for the people above you let me tell you you will rise as fast as you can Leviticus 22 and verse 29 according to the NIV it says when you sacrifice a thank offering to God sacrifice it in such a way that it will be acceptable on your behalf and this will lead us to the next point which is point number 9 that we need to offer thanksgiving in a manna in a way that it is acceptable on our behalf or yes on our behalf number 9 thanksgiving is the key to living a sacrificial life yes I know sometimes things don't happen the way we want sometimes things will not happen the way we desire but thanksgiving is the key for living a sacrificial life living a sacrificial life and Psalms 107 in verse number 23 says let them it is corporate let them sacrifice thank offerings and tell his works with songs of joy sometimes when we sing praises we are offering thanksgiving offerings sometimes when we sing praises we are thanking God we are offering what is called we are declaring the works of God with songs of joy and we see that these are corporate call but also there is an individual call a personal call to this when you read Psalms 116 and verse number 17 it says I will I will sacrifice a thank offering to you and call on the name of the Lord Jonah chapter number 2 and verse number 9 the Bible says but I it is you need to cultivate that intention you need to become intentional with thanking God with thanking people with thanking those who are under you those who are above you you need to be intentional but I with shouts of grateful praise and with sacrifice sorry but I with shouts of grateful praise will sacrifice what I have vowed I will make good I will say salvation comes from God point number 10 it is that thanksgiving is the key to receiving from God and we saw this even when we began that thanksgiving does not just grant us access to God it also grants us access to the things of God it will not just grant you access to God but also to the things of God and so thanksgiving is the key from God first Timothy 4 and verse number 4 listen to this because this will change your life this will change your perspective about thanksgiving that for everything God created is good we see this in the book of Genesis chapter number 1 that every time God created he said it is good and so thanksgiving thanksgiving shows that we acknowledge that God is the creator of all things and everything that God created is good according to first Timothy 4 and verse number 4 and nothing is to be rejected or refused if it is received with thanksgiving I want you to know that refusing to give thanks is refusing to receive refusing to give thanks is refusing to receive and lastly I want you to understand that thanksgiving is the key to a rooted, a built up a strengthened and an established life in the faith what we call abounding faith what we call an overflowing kind of life it is a life of thanksgiving and I will repeat that point again that thanksgiving is the key to a rooted, a built up a strengthened and established life in the faith and I pray that today even as you learn this that your life will overflow with thanksgiving verse number 2 according to the NIV version the Bible says rooted and built up in him strengthened in the faith as you were taught and overflowing with thankfulness allow me to say this may your life begin to overflow in this year 2024 in this january where many are struggling where many are saying it is the first month and people have cast spells even over this month may your life overflow this is my prayer for you today may your life overflow with thanksgiving may God bless you and I pray that these points will transform your life and they will become like your life of faith amen thank you so much for saying that it was really powerful I hope you have been blessed I hope you have written enough notes come on and check out the notes there are 2 places one is MDM and the other is ZIPA if there is anything you need to understand follow it where Eugene Morady on Facebook or Sir Eugene Morady on Facebook I think this is me millennials but you are called Instagram you are called Instagram Saiido ni meanza kwa ingia tiktok ni kama bada tiktok nga ingia nga hizi kwa tu ni story kwa ingia ya wukuli tiktok ni kama bada Tiktok ni kama za kwa kwa ni kama bada terima kasih Operma kwa ingia kwa kufindwakia kwa kaka kipurama Ina mga ni kama Thank you Happy Kwa ni kama nga kwa Ina kama It is a good Give me some would say to give inspiration to kickstart the year starting with Dancegiving I know it would be a new year of dancegiving we cultivate that culture for being thankful this is a challenge I want to throw to everyone watching us today what is 30 days of fasting 50 days of fasting 20 days of fasting I know In fasting, suifanya kwa 2 thanksgiving Hallelujah Anyway, we're going to go to next Chesam zikimoja 1, 2, 3 and we'll be back with more Alright