Welcome to the community television Board of Directors regular meeting for October 22nd 2018 Will the secretary please call the roll? Chair Goodger. Here. Director Fisher. Director Hall. Director Rand. Here. Director Wade. Director Mannheim. Here. Director Lorenz. Here. Director Niziris. Director O'Driscoll. Here. Director Owen. Here. Thank you. We have a quorum This is oral communications. It's a time when anyone can address the board about items not on the agenda Seeing no one I will move on to consideration of late additions to the agenda or additions and deletions Are there any? Seeing none will move on the consent agenda. I believe that the minutes for one of the meeting is a request to make some small changes Yeah, I noticed a couple of spelling errors, and I want to have a little bit more information about the Application for an award that one of our members have submitted about his poetry show so that says the ACM awards and There was one other thing and I emailed you about Just a little little more explanation. Okay. I think it helps. So that's the September 24th. It's 25th It's June 25th or September 24th? Exactly. Which one? September. It's September one. I can make those changes. I'm agreeable. Okay, and then the packet included the minutes from the finance committee meeting a week ago And the August and September financial reports. That's the consent agenda Tom, did you want to say anything about the finance committee? The one thing I can say is we met And as always we looked at all of our finances. The one thing I liked seeing was that In terms of our revenue through satellite at this point through the satellite operation for the month of september we were 40 percent over what we budget. We brought in 40 percent more than we expected And year to date for the first quarter were over 25 percent ahead of what we projected So kudos to all of us Especially the people that put in the work, right? Yes Especially, yeah And that was it with a changeover of our community coordinator as well. Yeah Great. So is there a motion on the consent agenda? I move With the changes. With the changes specified. I'll second. Okay Then any other discussion? Seeing none all those in favor say aye. Aye. Opposed or abstentions? Seeing none we're going to move on to the oral report of the executive director For a second my computer was just black But it came around. Well, it's good we're into black. That's what we want. That's why some of us still bring hard copies Yeah Uh, so we'll start with financial as you just heard the co-working center is in profit for october And it's been steadily in profit for eight months at all. We're really excited about that Um, there continues to be a lot more activity in the cafe area and the parking lot is often full So we're pretty excited about that. We have a lot of people that are working in the cafe A lot of small businesses in the cafe, which is kind of fun. Um, we're doing Can I just for clarification for any viewers who might be interested in what the cafe is? Oh, yeah Yeah, lingo. Um, the cafe is the open seating area in the middle and it's it's surrounded by, um, Offices that are closed private offices and the reason it's called the cafe Is because it's like working in a cafe So you just go in and grab a table and there are a bunch of them there and we do have dedicated ones some people Stake out a claim on a particular table and then that's reserved for them But they call it the cafe just because it's full of a bunch of tables and chairs and you could set anyone at work Thanks. Yes, but and but the coffee in our cafe is free. How many members? I don't know members or are they a special member? Oh cafe membership Yeah, cafe membership is a different membership and our software doesn't break it out that way So I I actually have to count them if I want to know But we can also, you know, like I sometimes is coming for a day. Yeah. Yeah, we have a lot of people that just come in for this I just think it's interesting to see the utilization not sort of like a Exercise club membership. They can have thousands. It's only a hundred show up. Right. It's exactly just to see if the utilization versus the membership Makes sense, you know to to get more members of the cafe members Oh, yeah, and you can we have in our software the software tells us how much we have how much availability we have And we're not full yet. So we can definitely add on more we can grow a lot. So come on down Yes, come on down. There's plenty of room. There's room at many tables are empty. I'm waiting for you And an exciting place to work. It is fun. It is fun. Yeah, I like it Yeah, yeah, we're gonna we're doing a fun halloween party and there's a costume contest and it's just like if you had a real job at a place We have pumpkins to carve and And we do fun things we do fun things for holidays. So it's a good it's a good fun place to work We're we're working with a film producer right now who has he's made five films and he's about to make another He's shot the first half but the last half needs to be shot in a studio and he's talking to us about renting our studio and um the conference room and the edit suite and the audio booth and and a bunch of a bunch of different venues for uh for his crew to work and his producers to work and stuff for a short period of time likes, you know Two months maybe around january, which is kind of what we hoped when we built this was that we would get Companies that would want to come in and do something for a couple of months And it's all set up just for that they can do they can watch dailies in the conference room and edit stuff in the edit suites and record audio and of course This and they're also going to use our crane and our dolly. That's so exciting So I can't wait I know I bought the crane and dolly thinking okay. I hope we rent these and it looks like we're going to and and so Uh equipment rentals are kind of spiking up for a long time. It was just us running the equipment But um last uh month we did fifteen hundred and forty one dollars in outside rentals of equipment So I'm telling you that now because We are our advertising for the studio and the equipment is running on google now So I'm hoping that next month that number will be bigger But you know, it takes a while advertising is all about reach and frequency So it's not going to be instant, but it might be fun to watch that number now Will you be um as as people come in running equipment to you checked and find that how they heard about us Is that sort of part of yeah, we do it depends. I mean, uh, it's something that we ask the coordinator to do Sometimes they remember sometimes they don't but a lot of times they are able to tell us how they know Yeah, and that's good information to have. Yes, it is one thing we can tell We can see the google analytics for the studio website and we can know where they are So sometimes there are in other countries. I don't know So but um we can we can see if they're in this county here from san francisco Or that sort of thing that people that are attracted to the website at least Uh, we do have a new co-working coordinator. His name is Ian dairy and he's doing a great job He's caught on really fast and yet he got to spend four days with alana before she moved on to her next big adventure and um, he's doing great and um, he has a degree in filmmaking So he understands all our video equipment So wonderful. Yeah, it's really easy for him to and he knows other filmmakers and he is doing a really interesting thing I always let the co-working Coordinator figure out events that they would like to do and so he's doing movie nights So because he knows all about movies. So, um, he's got a whole bunch of um He's selected a whole bunch of public domain films that we can show on friday nights And we're going to start with first friday with a bunch of shorts kind of classic short films So people can come and go and um, uh, and he's contacted some filmmakers to see if they would lend us their films And they won't but I thought um, a good initiative That was great that he asked so but he's got you know, he's good film education He's got an eye for cool stuff And so he's getting he's amassing a bunch of things for us to do so we're we're getting a popcorn machine We're going to do movies on friday nights. It should be fun Um, we um the government meeting services. We're into paid services now. We're still under finances here Um We did 16 regular meetings and we'll end two special meetings in september And um, we had an interesting thing happen at at seamap. We had sort of a staff changeover And what I've done is outsourced the government meetings to victor So now he manages the staff there that do government meetings to video technicians And he does the schedule and the programming and so seamap will pay him for that because Um, well on the seamap side, it's really hard to find people that know how to do that That's not like as like there's not a lot of people around that know So um victor I asked victor what he would think of that idea and he said, you know, I've always wanted to do that I figured one day we probably would so Victor really doesn't like doing the documentation that we do we go out and shoot lectures and and people's Meetings and wrestling and and um, they he really that's not his favorite thing So, uh, I've hired a really good production person at seamap So seamap will do that part for victor and victor will do the other part for seamap and I think that in the end it could be a wash, but I actually think ctb will make money at this So, um, I don't want to lose the documentation money. That's in my budget. So we'll make sure that it equals out um Under the equipment and facilities the only thing we really have going on now is we're bringing fiber to the building So, um, the process has begun We've got the paperwork signed and we had to get the line large sign off and he kindly signed the document and so they're now working on doing that and They're making some changes sometime this week with victor and then they'll be I don't they told me it would take a couple months to do So it's not around the corner, but it's coming and what was the bandwidth that we decided to go with? We went with 200 okay up and down so that and we can Upgrade if we want to and if it still if it keeps getting fuller of them, we probably will But um, yeah, so that's we'll see we'll be exciting Um, we are uh, I'm moving on to advertising our advertising agency is made they made a bunch of ads for us free So they could get them going so they've done that and uh, we should see the results of that pretty soon And uh, we're still working on that website. I've had a whole bunch of stuff happen that didn't I didn't have free time to work on it But it's out there. Well the um, uh, advertisements that that the Advertising company is doing the videos Those are for the web. Yeah, will we also be showing them on our air? Is there any reason why we couldn't? Oh, let me ask them that. Yeah, we probably could. Yeah. Yeah, I'll ask them I'll see if they mine that guess they made. Yeah, so like done at ct. You know produced by I think there are images and they're not like fancy, but uh, yeah, let me ask them If we could get parties and play them. Sure. Why not? That makes sense Okay, that's my that's my report for september Hey, thank you So we did that segues an item 10 with the consider approval of fiscal sponsorship Which you mentioned a little bit so back at it. It's in. It's your proposal Follows That format is just a rolls by it is hard to find where you want to be in there. Okay So I when I talked to this, um, we we've done fiscal sponsorships in the past We did for 20 years. We did the real Works works film festival and we we did their fiscal sponsorship So, um, I was talking to this producer about whether, you know, what he was going to do and what he could use and sort of Showing them our stuff and everything and then I mentioned to him. I said, well, you know We could do a fiscal sponsorship if you want and he was very excited about that So, um, I uh, this would be a bigger deal than the real works film festival. That was pretty That's short Time that was like a month long and and it wasn't nearly as much money But the idea is the same. So What it helps young filmmakers to have a Unestablished business behind them handling the money because then you feel safe giving, you know, people would be You know, if you if you don't have a track worker people people like to give money to real businesses They don't want to give it to independent filmmakers necessarily So this way we we used to do this at KQED and they they'd still do it. I think we would just partner with filmmakers And um, we do the money and they raise the money. We don't raise any money They do all the raising and the money just comes to us and we Take care of it We pay the bills the bills come to us and we pay the bills based on their Based on two things their budget and that the money is in the bank so It's a pretty um, it's a really good thing to do for it It promotes local filmmaking and it helps filmmakers who might not be able to realize their art if Someone didn't help them with the money. So That's what I think I would like us to kind of revisit that and really make it a little more robust program because we would charge for the The care of their money the management of it and so when a filmmaker would come to us we would get 10 percent of whatever they raise in order to manage it for them and All the projects that we would do would take place either in our building or with our equipment So they would be renting equipment or facilities from us as well and we would get a percentage of The money they make on it if there isn't so it's um, we get on-screen credit So we'd be known in the film world as a place where you can make a film So the and local producers get a really big benefit they get to you know, they when they ask for money they can they can assure the The donors that they have a third-party nonprofit company that's been established for a long time taking care of it and the supporters of the arts also benefit because they can They can give to our program. We'll establish a program. It's called the independent media initiative And they can earmark the money for a certain project in there So they can get a tax deduction by donating to a nonprofit to support films and then the films get funded so more films films are made people in in the The art of digital media get jobs and work on projects and get screen credits and we get content and When we rent a lot of our rental facilities and equipment So I think it's a really good thing to do I've I've talked to metal about it and she is up for it So I think it's a nice little revenue stream for us that we can build probably once we get started with it We get one done We can then go out and talk to filmmakers and go to film festivals and meet filmmakers and advertise in filmmaker places and Kind of it's a really nice target market So who is the person that has the financial credentials to actually manage the money? That people are going to entrust us to do and it's mel. She's a cpa Okay, you know she's our she's our accountant and you think one person can handle Coordinating budgets on multiple events or is this like well, we're gonna happen sporadically. Yeah It's not like there are 50 movies lined up for us right now We'll do one and and we can hire help for mel if we need to because we get 10 and if it's a big movie That's 20 30 40 50 thousand dollars. So it's a good it's a good amount. I mean that's not a big movie But it'd be a big movie for us So, yeah, there's plenty of money to pay for doing it and we should have where all these movie makers Do we have movie makers and stand up who's that are raising money and like how many do you think we have? Well, I know eric tearman and jeff done And this the the plume like you're right working with now those are three that I know But there are many others. I mean, there's lots of surf movie makers and there's all kinds of So I can't throw a rock right here or not. Yeah, somebody who thinks they're a movie Yeah, yeah Can we go outside the santa cruz footprint or is the goal to stay inside? No, we go outside out to the county I guess we could take it on a case-by-case basis if people from outside the county start asking us We could see we could see what it's a unique service. Maybe they would yeah Well, there's pbs stations do it too and there are so and then they partner with um I tv and They but they generally do larger Larger productions than we would do so I'm thinking that we're going to be talking to a lot of people that are making a small Movie, but you know, should we go talk to them about their experience running this kind of business and they're the pluses and minuses who You said other pbs stations Yeah, yeah, yeah, we did it there and that we there was a person in charge of it But and it wasn't me but I we had films going through kth used to do that That's what they did mostly was they got documentary filmmakers. They partner with them They'd make a film and the money would go through kqed And I made a bunch of television series where I was The line producer so it would be my job to watch that money And send it and make sure that I would work with the people that were the sponsors I mean is 10 percent. Is that a fairly Eight to 20 percent is the range. Yeah, and so we're doing 10 because It it's a nice round number It's easy to calculate. Yes. Yes. Is he calculating your heads? So yeah, and then we will also if if the movie makes money we get one more percent Right And you did speak to an attorney about yes. Yes, we went. Yeah. Yeah. Oh, yeah Well, by the way We went and talked to a non-profit attorney in Sam's story in capitol and told him what we were thinking of doing He was familiar with the concept and thought it it dovetailed with our mission And he gave us a list of little things that we needed to do to make it Work for us. So we're not just passing money through our non-profit And that's part of the things we need to do is make sure that we benefit And so we benefit by the percentage that we get when they When they make money we also They're required to use our facilities and equipment. Yeah, so we get money that way as well So it's more than just very exciting Are there any liabilities or any special insurance we have to have for You know fraud or anything like that like a bank. We're not a bank and maybe kqad has You know is bigger and can you know protect themselves? I would just say You know look at the financials, but also, you know, are there any liabilities that you're not set up to undertake? Not that i'm aware of I can look deeper into it. I think that they're the We're separating the money. It'll be in its own separate account And so that we'll just be and we're not going to we're not funding the film We're going to just pay the bills according to how much, you know, they'll have to raise the money. So there'll be Monthly reports and and that sort of thing and banks and all go through the bank. So there shouldn't And isn't it in the contract that you signed with the uh, I mean, I was involved. Yeah, there's an agreement. I mean, there's a very specific line Where we are not helped hold harmless. Yes. We're hold harmless and we're not helped Yeah, you're holding in a bank something happens money gone Not our liability. Yeah. Yeah, there's the whole We're paying the wrong people It's pretty pretty clear the fiscal and you know some story is very much aware of that Yeah, yeah sponsorship. Yeah, so he'll be if we do this he'll drop the um, the agreement Yeah, you might have to require them to have insurance because they're yeah, they would have to have the insurance And actually we do that in the chemical lab. We require them to be an entity that has insurance And naming us and have us as a yes, and we pull each hold each other harmless. Yeah. Yeah Good idea So we discussed this um A little bit and we thought it would be a good idea for the board to approve beca Going forward with a fiscal sponsorship as described in the document I would move That the board approved this and move forward and keep us posted on how it's going Thank you I would say it would be nice to know what some of the goals would be or and any potential expenses you may incur in order to set up You know the function whether it be at the bank or whatever Maybe a little mini business plan at the next meeting would be nice just to here's how i'm going to do it Sure I'll incorporate that into the motion I'll second that Any other discussion on this? None I'll ask for approval all those in favor say I Opposed or abstentions Seeing none we'll move on to a little Recap of the board retreat set today Oh, I guess I put myself first Why not since you so where we are on the technical end of things is I've Talked to my treya. He had an excellent suggestion for software that could run this simple studio And that I went to a place where he hasn't installed and we walked through what was required I already installed it on my own computer and started messing with it But it was really beneficial working with my treya seeing some of the tricks For instance Here we have cameras and the director selects a camera And this software You don't select the camera you select the scene and in a way it really makes a lot more sense But um, it was I didn't realize that so I couldn't figure out what I was doing at first A scene might include the camera and a lower third That kind of thing so when you switch between scenes you get more than just the camera Just why it's set up that way But like I said, I didn't figure that out So it was very helpful having my treya who's been using this for quite a while and has set it up on a couple of different computers To help me walk through it So where we are on that is I have a general idea what needs to be done software-wise to get something up and running I'm going to propose that I Do that I try and set that up I may Want to purchase a couple of simple pieces of gear like the foot pedal we talked about for instance So I could see how that's going to interface with it But we're not going to go far and spend a lot of money until we get a better feedback like we discussed last time Yeah, but the foot pedal could be used in here to run a prompter and all kinds of things To use it for all sorts of things. Yeah, that's a worthwhile buying anyway And so just to play around with it. I made a simple ps a for our Free co-working Wednesdays. Uh-huh. And if our director wants to show it, it's really really simple, but oh there it is The satellite Get right to work in a beautiful connected workspace with company chairs The satellite co-working space includes blazing fast internet From these staff and you know, no, you don't need an outdoor patio and free coffee to top it off Are you a professional or an entrepreneur who still has to check out what co-working can do for you? Stop by on wednesday and give it a try So Linda, can we run this again, but have audio person turn off the mics? The satellite Santa Cruz has free co-working every wednesday Get right to work in a beautiful connected workspace with comfortable chairs The satellite co-working space includes blazing fast internet Friendly staff and co-workers and outdoor patio and free coffee to top it off Are you a professional or entrepreneur who still hasn't to check out what co-working can do for you? Stop by on wednesday and give it a try free for the whole day Okay, so So what part of that was was the was the scene thing? Um, actually because there's not a picture with a camera on me. It was one scene It was a The slide show thing. Oh, okay, which was set up to automatically go through it to take exactly 30 seconds So all I had to do was hit one key to start it another key to stop it basically and then talk That's what I wanted to see is how if I could set it up to be basically one or two keys Cool to do it Um, but it did raise, you know as I go through it raises a lot of questions. So the committee needs to meet So I mean how many buttons are we willing to have someone do it is a good example Because you know start it change slides change camera back and forth You know have slides go automatic or not There's all kinds of things that we should discuss to see what makes sense In terms of how simple we want things or how flexible, you know, there's always that trade-off Cool That's fun. Yeah, so that was fun That's Then there's the venues equipments of committee and I believe that uh, my treya was mostly going out Yes, and I only know what I've done. I don't know what my treya has done uh, I've been pursuing the kawamba jazz center and and They were quite open to having further discussion their executive director and uh, she was going to talk to her on Person in charge of venues and and content and executive their artistic director and Wanted to meet at the end of october So they were going to come back to us with a couple of dates But they love the idea of the wish list, you know they tell us what they are envisioning for themselves to use in the lab and then some of the ideas that we pitched to them Which are why don't you permanently attach some video equipment with audio equipment? And therefore you can run or maybe we can run for you A photo shoot maybe even of the venue that's going on at the kawamba And They like that they they thought that's interesting I wonder you know, I said and is there some commercial viability for them To use this capability maybe offer it to the performer to cut a cd The three hours before you know or a few hours after their show They can go in and actually do a cd of the event. It would be nice beforehand. So they have something to distribute So it could turn into create something or create content for advertising the kawamba and or the entertainment venue itself could be Recording itself so that they can post a little commercial on their own website And commission us to do it or request us to do it for them In conjunction with the kawamba and we can share the revenues. They can probably usually artists will give you Three minutes or something that you can record of something So even if it isn't something that they could record totally they could probably record a clip Yeah, and then the kawamba can use it in just actually running it on our channel Is to advertise themselves by giving free You know snapshot And maybe all it takes for us to get that is to actually put the name of the artist and the date that it was taken So if we do that then they'll allow us to run it as this was what happened at the kawamba that day Yeah, maybe get three songs or something. Yeah, put those up. Yeah, that'd be cool. Yeah. Well done. Good thinking And I know there's other venues people are pursuing but i'm not up to date on them I don't I metrey has been leading this and so I think they're the next step that we've talked about internally is is the three of us getting together to sort of get a sense of what what How we'd structured on our end And if we sort of do the kawamba then we know how to pitch it to other people too So we could come up with a little prototype of what we're pitching Great And janice is here. So i'll ask you okay. Well, I've been on vacation. Yes And uh, so I just got back yesterday afternoon and so now i'm Going to be setting up a meeting between Our ctb stuff committee and the library staff would be involved. Great. So hopefully I will have a great deal more to say next meeting Thanks And next up is I have 12 the oral report from the volunteer advisory committee. Okay So as I mentioned last time we are starting up our orientation and and Camera class and the studio and in the fields and the audio class. So that's all coming up November 14th is the first orientation You know the remodeled reversed Orientation where we have a little bit more hands-on stuff for people that are actually coming in And but that's something in process that eventually they will be Like observing we will do the orientation before a program and then they get observing How things work. So but that's the one that works You know, we need to get the producer involved and we need to get people to To guide our new people through that. So but that's in the works Then also the Linda who's on the volunteer advisory committee. She is doing the director and producers workshops The first one that's coming up is on the 18th of November Where that's a sunday Where we're doing the green screen and it's total hands-on. So all the directors and producers that we have here Are invited and they'll be setting up the green screen Keith is going to so chroma keying and And daniel and ron have some specific things also on how to set things up So this should be very exciting and we should be more versed in making As you say, you know go to the board meeting and we are sitting here in paris or something like that, you know things like that and And then of course we have A new studio supervisor training that's going to happen on the 17th of november It's going to be very busy month Because every time we have a program here in the studio There has to be a studio supervisor because as board, of course You want to make sure that our studio and our equipment is being treated well And you know the last long time So we're training some new people sherry who's here and jim who's here They're going to take the training about six people on the training and ian is going to take the training as far as I know So that's kind of what we're doing And i already mentioned last time that jim entered his poetry program For the acm awards, which is the the western states Video tv film Awards program from what's acm stand for you and alliance for community media. Yeah, it's alliance for community media So that's exciting and we'll hear maybe next time Those awards are a big deal when you go you go to the event They're like they have a whole party and people are gowns and they have a big event to the shirts lights I never went I went twice, but I never went Yeah, they make it are really they do a really good event It's really fun for filmmakers or video makers that that are Nominated But anyway, so that's my report Next item is the aura report the board chair The main thing I wanted to mention is that there's a new Board chair of seamap and I've had discussions with him And he's sent me a proposed new contract We approve a contract for starting december 1st every year for Becca's help here And I have that contract and we plan to have it Ready for this board at the next important meeting The only changes are a slight Change in the amount of money and the dates. So it's not like the previous year where we changed a bunch of stuff So I was not planning to have a separate committee review it It'll just most likely be in the next board packet I'll probably bring it to the finance committee first And then bring it to the board Before before you move on I wasn't sure if you're going to say that that you still are working with the non-profits on the PSA's that's that's very successful and And also that that you and Becca are submitting the elected spotlight for the new radio station k-squid and It's exciting. I mean, you know, we'll do tv on the radio, which of course That's what people have to imagine what they may be hearing But maybe they'll be hearing even more so what being said But we thought it would be a good idea because it's such, you know, the the elected spotlight is such an important Yes Service to the community where people in elected offices get to freely speak with With Becca who, you know poses really good questions To pull out, you know, what is it really that you're doing? So we thought, you know, it was No, it is interesting. And so we thought it would be good to also, you know, have it just the audio on the radio so So that's another undertaking for spreading the word So are there any other items special requests for items appear on the next meeting agenda We'll continue to get summaries from the subcommittees Um, and then announcements. I don't know if anyone else has announcements I wanted to thank the crew that helped produce tonight's board meeting nick kirk and ball jim ruso sherry ross John james lunaticos and karen scott. Thank you. Thank you And If that's it, we will adjourn to close session Okay, but can I just yes Before we do that. Can I just close it then say Move to adjourn and eat it or do we do that after we do that after We're you can we're well do we need to have a move a motion to adjourn to close session If so, I'll move. So I'm not sure I don't have a clue. I think it is probably a good idea. Yeah. Yeah. All right. So I'll move to adjourn To exactly snow. I moved to adjourn to close session to close session. There we go


So write down next heading, production of amplitude modulated wave, okay.  What we will do?  And then you put here carrier wave, this is c t, okay. This is a c sin omega c t. See, the way the amplitude modulation should done, should be done, will be in such a way that it should create three waves of frequency omega c minus omega m, omega c and omega c plus omega m. So if these three waves are present, no matter how you create am wave, you know, that it is fine. So it has, it should have these three frequencies, okay. So there can be multiple ways of creating these three frequencies. So this is what one of the ways is, okay, which we are going to discuss here. Then these two signals get added up, these two signals get added up and they become x t. So what is basically x t? x t is actually m t plus c t, okay. And then whatever x you are getting, you are putting it in a square law device. This is called square law device. So whatever goes in here, whatever goes in there will come out as a quadratic, okay. You will get y t, which is actually b times x t plus c times x t square, fine. So you are not directly squaring x t. What you are doing?  This is the square law device, fine. And then you are putting under band pass filter, right down band pass filter centered at omega c. So what does it mean actually band pass filter? What it will do is, it will actually pass those frequencies which are near about omega c. It will not allow frequencies which are far different from omega c frequency, okay. It can only pass the frequency which are near about omega c, okay. So once you have this band pass filter, you will get the amplitude modulated wave, okay. So this is called am wave, fine. Now what I want all of you to do is, this is the value of m t and this is the value of c t. Now follow this procedure and tell me what is the equation of am wave you are getting on this side. All of you please try this. What is the equation of am wave you are getting at the end? So x t will be equal to m t which is am sin omega m t plus c t which is ac sin omega c t, okay. This is x t, okay. Now we have to follow the square law here. So this will be b times x t which is b times am sin omega m t plus ac sin omega c t plus c times this am sin. So guys this expression may look very big, okay. But then you have to try yourself until unless you try it yourself you will never be able to reproduce it when it is asked in the exam, okay. Now what I want you is to open up all the brackets and tell me how many frequencies you get. You get two frequencies, four frequencies, five frequencies or six frequencies. Quickly open up the brackets and tell me how many frequencies you have. Type in two, four, five or six. How many frequencies you have in this particular wave? I will just try and then I will wait. So this will be b am sin omega m t plus b times ac sin of omega c t, okay plus c into am square sin square omega m t, okay. Plus c times ac square sin square omega c t, okay. Then plus two times c times am into ac sin of omega c t into sin of omega m t, okay. Now if you look at this sin square omega m, sin square omega m can be written as one minus cos of two omega m t by two. Yes or no? This you can write down like that and this one, you can write down like one minus cos two omega c by two, okay. And when you open up this, when you open up this, you will get two frequencies omega c minus omega m and you will get what omega c plus omega m, okay. So this entire thing can be expanded as now I have to make some space over here. So y t will come out to be, all of you please write down b am minus b ac minus c ac square by two. See I can understand it is little overwhelming but then you know it flows. There is a connection from one step to the other step. So you can easily write down if you are sincerely doing it, you will get what I am writing here, okay. So you should actually do it with me here. Otherwise then you know before the exam you have to anyway do it and if you practice with me here then you will have to make lot less effort later on. Otherwise you have to do it from scratch once you start doing it. Okay this is what I will get.  So there are how many frequencies? We have one, two, three, total six frequencies are there. Total six frequencies are there and if I write down the frequencies omega m, omega c, two omega m, all of you please write down this omega c minus omega m and omega c plus omega m. Okay now what I am doing here I am putting these six frequencies through a band pass filter which is centered at omega c. So since it is a band pass filter it will only send the signal which are closer to omega c. So omega c will go definitely, omega c will cross the band. This band will not allow frequency which is far away from omega c. Okay now tell me are these two frequencies, these one, one and two are these two frequencies they are near omega c or they are very far from omega c, far or near please message one and two these two frequencies they are far away from omega very far okay right so they are far. So band pass filter will not allow these two frequencies this is not allowed this is not allowed and even two times omega c is far even this is far away. So if omega c is 10 kilo hertz two omega c will be 20 kilo hertz so even two times omega c is very far now tell me omega c plus omega m and omega c minus omega m three and four are they very far or near they are near okay because omega m the message frequency is very less so you are subtracting or adding a very less frequency with a very high frequency which is omega c. So the band pass will only allow omega c omega c minus m and omega c plus omega m. So that's how you generate these bands okay so I hope you have understood this particular thing and this is what transmitter does transmitter will take the message signal do some sort of modulation okay amplify the power and then send it through the transmitting antenna. So if I draw a block diagram of the transmitter this is how transmitter will look like this is a block diagram of the transmitter it's a block diagram of transmitter so you have message signal this is message signal you have carrier wave okay and this is amplitude modulation that is going on here inside the transmitter okay so how much gap sir so how much gap is allowed see r n it depends on what bandwidth you want to occupy so you can like depending on you know your message and omega c the band will become fixed so if you want to occupy higher bandwidth then you know accordingly you will see what message signal you have to transmit okay so there is no fixed answer to it because the the gap is different for different thing but then it should be it should not be very large the gap should not be very large it will have the gap will have two times the frequency of the message right because you have omega c minus omega m and omega c plus omega m the difference in these two frequencies is two times omega m so this is what the gap is so two times the frequency of the message this is what the gap will be okay so coming back to this block diagram of the transmitter so this is amplitude modulation and here what you do you amplify you use that amplifier transistor amplifier that we have learned so you have power amplifier here which amplifies the power of this modulated signal and then this is transmitting antenna okay so such is the complicated communication that happens inside our phone transmitting antenna so transmitter inside our phone does all of this whatever you speak on your phone that get transmitted okay now this is with respect to transmitter now our focus is on the detection part of it so at the receiver end what happens this is what is our next focus so this is the last topic of this chapter so this is after this the part the chapter gets over write down detection of am waves fine now the way the amp see the thing is transmitter modulates the signal and this then it throws it through the channel okay now the modulated signal although it contains the message but modulated signal is not the message okay so receiver will receive the modulated signal okay and once the receiver receives the modulated signal it has to extract the message from the modulated signal then only it can play at the receiver end like when you speak on your phone the message whatever you speak it get transmitted and the person who receives it on his mobile phone on his or her mobile phone there will be receiver who will be demodulating the signal which it is receiving okay so the focus is on what happens at the receiver end now okay so we are talking about the amplitude modulated wave okay the way amplitude modulated wave is received so we have here a block what it will do it will amplify the received signal this is amplifier okay and this time in the receiver the antenna comes first in the transmitter the antenna comes the last because you have to do all the processing and then throw it through the channel fine so antenna comes the last in transmitter but in receiver it should first receive so that is why the antenna coming first when we talk about the receiver so this is the amplifier the message the modulated message goes to the amplifier and then you have this block is called if stage okay we will not discuss too much about how this if a stage is getting constructed or how the amplifier get constructed okay what is the antenna what is the construction of antenna all that is a very involved topic this you will learn in your engineering the basic construction of antenna itself will take couple of months to understand this is detector and then again we have amplifier okay this is amplifier and here is the output this is what you receive or this is what you hear through your speaker this is what you hear okay so before hearing the message gets amplified what detector that does it detects the message after if stage okay let's see all of it how it happens okay so you have suppose amplitude modulated wave which comes like this this is the amplitude modulated wave this amplitude modulated wave comes okay then what you do you put it through a rectifier there is a rectifier what rectifier will do it will convert this alternating signal into direct signal so you are using a full wave rectifier here so what you'll get is this this one remains the lower one is gone okay then what we are doing here this is envelope detector envelope detector will detect the variation of the amplitude and reject everything else okay so at the end only this will remain okay and this is the shape of the message signal fine so I hope you have understood this particular thing the if stage is actually rectifier and this envelope detector is this okay and before if and detect before if and after detector you have amplified okay so if you want to draw a block diagram on how it is done you can do that also so here we have rectifier and then it goes to envelope detector okay before the output comes in so in this block diagram we haven't drawn the amplifier but amplifier is required because the at times signals are very feeble all right so this is what the entire chapter is all about I hope you have you know understood the entire thing and in case you have any doubt please message me right away anything with respect to this chapter okay you have any doubt please message or if you don't have a doubt then also please message that no doubts so that I can proceed further okay so I'll take that answer for everyone no doubts


Hi friends, welcome back to my channel.


Thank you very much for inviting me. I'm very happy to participate in the celebration of the anniversary of Professor Shadash Srilay. Many of his achievements were mentioned earlier in the conference. Today I want to emphasize the role of Samson in Integrability and specifically in Birthday Gauge Correspondence. I think this photo was not shown before. This is a new one. I'm just taking pictures. Well, but new for the conference. Your sister Nana is like Georgia Got Talent. So let's start with non-linear Schrodinger equation. First of all, the model has many, many different names. It's called Leap-Leninger, non-linear Schrodinger, Bosie-Gas, with delta interaction, and some people call it Tung-Schirard-Do-Gas. So there are also several different ways to write down Hamiltonian. This is the representation in terms of many quantum mechanics. Kinetic energy and delta potential, coupling constant will be positive for this lecture. Later I will write it in terms of the quantum field, Bosie field, like by Bosie field Kappa, standard Bosie commutation relation, delta is the positive number, which I will interpret later the step of the latest. So at first the model was solved by coordinate batanzas and stayed that way for a long time. Many interesting physical properties were extracted from coordinate batanzas, but later it was reformulated in terms of quantum inverse scattering method. That's our matrix, which is i squared of minus one, permutation, and this is lambda and mu, we call spectral parameters. So this is a l-operator, and somehow in the original paper it was written approximately in the sense of the step of the latest. Step of the latest was supposed to be small, and the l-operator was written approximately with this precision delta squared. But later we were able to restore all the next orders in the step of the latest, and this is exact l-operator on the latest, I mean no corrections. So the step of the latest, and under the square root, rho is the square root of this one, coupling constant, side by side, number of particles in the latest side number j, all the way index. And that's mainly modification of off diagonal elements by the square root, but also some correction on the diagonal, this number of particles. So this is exact l-operator, this is latest non-linear Schrodinger, l-operator for latest non-linear Schrodinger. It has involution, it has involution, so sigma x is off diagonal matrix with identities on the off diagonal, and then this is dagger is a conjugation of quantum operators. And lambda, later I will argue that lambda can be kept real for the purposes of this lecture. Excuse me, what is lambda? Oh, the coupling constant. No, no, no, no, no, no, no, no. This is coupling constant which enter Hamiltonian. Lambda is a spectral parameter which is a new parameter which was not in the Hamiltonian. This is like artificial new parameter designed in order to solve the model. model. There's something new which was not in the Hamiltonian, but appear, you know, the trick of solution. Also, the dimension 2 by 2 of the operator was not mentioned in the Hamiltonian. This is yet another auxiliary object, you know, designed to solve the model. Okay, so this is entries of this operator. This is two of diagonal and diagonal, and I can calculate the commutation relation. This is SU2 algebra, representation of SU2 algebra. But spin is negative. Spin is minus 2, kappa divided by delta, and I'm very happy to present this in the presence of Professor Karchemski, who's somewhere here because he likes negative spin, minus 1. So I mentioned minus 1 specifically. Complex even better. Well, for the purpose of this lecture, it will be negative spin. So once again, kappa is positive. Okay, SU2 representation was negative spin. Then quantum inverse scattering method works very similar to the continuous case. So I can multiply elliperes in the auxiliary space. I mean like matrices 2 by 2, row by column, and then the entries, the quantum operators in different letters such commute with one another. We call it ultra-locality. So this product I can write as explicit matrix 2 by 2 in the auxiliary space. But a, d and b and c are complicated combination of quantum operators, all of these s plus minus in all of these letters sides from 1 to l. I'm sorry, for the degeneration of notation. I mean, length of the letters is also l. Trace of one of the matrix, a plus d, is important, and the Hamiltonian will be extracted later from this trace of monodimetric by means of tracer densities. This involution still works for the monodimetric. So dagger means Hermitian conjugation of quantum operators. Zero means this is an explicit matrix in this auxiliary space of 2 by 2 and sigma s is of diagonal matrix 2 by 2 and multiplication that auxiliary space. So it's easy to invert this matrix. I kind of can use Kramer's formula, but with some shift of spectral parameter. So here, I mean, I can divide t inverse and, I mean, can multiply by t inverse and t inverse will be given by Kramer's formula almost with some shift of spectral parameter. And the determinant also given like ad minus bc with some shift of spectral parameter. So it's like we call it quantum determinant. It's the center of the algebra. It can be used with all other operators actually equal to some function of spectral parameter with quadratic function. So algebraic betanzot works in the form which was designed by Professor Tartajan with quarters. And then it leads to betanzot equation which we shall analyze in a moment. The equation, so lambda is those spectral parameters. Later, they will play the role of momentum. Momentum is a simple function of this spectral parameter. And then they're even more convenient than momentum because if I write two-body scattering matrix as a function of momentum, it will depend on both momentum of two colliding particles. But if I write this in the terms of spectral parameters, then scattering matrix will depend on the difference of spectral parameters. It's like more convenient parameterization from the point of view of study of two-body scattering. So, and then next we have to design Hamiltonian starting from a leperator. There are several different ways to construct Hamiltonian on the letters. The most popular was constructed by Tarasov, Tartajan and Fajiev. Later, I will mention other Hamiltonians. So, this one, TTF, people call it F, well, TTF. The Hamiltonian is written in terms of the logarithmic derivative of gamma function. And this J, depending on the local spins, here is, here is this, I mean, this is spinning one letter side, spinning the neighboring letter side. And then in this equation, everything commutes in this equation. So, I can, this quadratic equation, which I can solve by, you know, standard formula. And then, substitute this into here. So, this is famous, Tarasov, Tartajan. Hamiltonian, which we shall study for a while, and then later we shall switch to another Hamiltonian. So, for spin minus one, specification for Professor Karczemski, and then spin minus one, this is better than this equation and this is expression for the energy. Let's study better than this equations for a while. We can prove three different theorems for this better equation. So, let's prove the theorems. Do I have time for proof of the theorems? Okay, 15 minutes. Theorem number one, this system of equations, first of all, I have n variables and lambdas and also an equation. So, for K here, supposed to run through one to n, so it's not one equation, system of equations. So, theorem number one, if solutions of the system exist, all of them have to be real numbers. So, how can possibly prove this statement? Well, I have to study these factors in the right-hand side. So, in the right-hand side, I can simple elementary calculation show that the models of each and every factor in the right-hand side is larger than one only if imaginary part of this lambda is greater than zero. If it's smaller than zero, then it's smaller than one. In the left-hand side, it's the other way. So, if imaginary part of this lambda, of this lambda is greater than zero, then smaller than one and the other way around. So, how I can prove it? First of all, let's, I mean, consider this set of lambdas. Maybe they're imaginary. Let's pick the lambda with the maximal value of imaginary part. If there are several of them, I pick one of them. And then, I plug this in the right-hand side. So, in the right-hand side, I will have this difference. This lambda has a largest imaginary part. So, the difference actually will have a positive imaginary part, this one. So, the models of the right-hand side is larger than one, as well as the left-hand side. So, left-hand side of imaginary part, I mean, is larger than one. Then, this means that imaginary part is smaller than zero. So, all of this show that maximum lambda with the maximal imaginary part, it's imaginary part is smaller than zero. So, all others, lambdas also have imaginary part smaller than zero. So, all lambdas has imaginary part smaller than zero. Then, I can go through similar consideration, can pick up lambda with the minimal imaginary part. And then, I can prove that all of the imaginary part is greater than zero. So, this means that they're equal to zero. So, that's like real, right? Okay. So, I proved is that... George Poirier was using same arguments in 1918 in his break on Riemann-Zieterfams. Poirier, 1918. I will have reference for 1856 later. But for the different subject. Not about this, some other stuff. Okay, so, we proved that it's the solution. If they exist, they're real. Do they exist? So, take logarithm. Take a logarithm of this equation. So, L is the length of the letters. Theta is this. The logarithm of what was left-hand side. And theta is of the difference is this logarithm of the former right-hand side. So, built equations, famous. So, how I can possibly prove this solution? So, I want to prove next theorem that solution exists and unique. So, after I choose integer numbers. So, first I pick set of integer numbers, which is the subject of the third theorem. Well, the second, let's pick set of integer numbers, this N. And then, after we do that, solution exists and unique. So, how can I possibly prove this? Actually, this equation has young action, has action. So, that's action was suggested by young and young. So, theta 1 is integral of the theta of the previous transference integral. And then, this is integer numbers. And this is theta integral of those scattering phase. So, if I consider extremum of this action, that derivative of S with respect to lambda, I will come back to this equations, to this equation. So, this equation has action, which was used in many papers by Professor Shadashvili. So, let's prove that this is, it's convex. So, let's prove that it's convex, then it has unique minimum, then solution exists and unique. So, let's calculate the second derivative. Second derivative of this is diagonal element K. It's positive, right? Because K is small, coupling content is positive. And this is of diagonal element, which is also with a minus sign. So, let's calculate quadratic form. So, V is some vector, a real vector with real components. So, after some massaging, it's equal to L, this K multiplied by the square. And this of diagonal will be combined to this square of the difference, square of the difference. So, anyway, it's positive for, if V is real. So, the young action is convex. So, unique minimum. Nice. So, theorem number two, solution exist and unique, given by the set of integer numbers. By the way, the determinant of this play will pop up again later, when we shall construct eigenvectors of this Hamiltonian, which was mentioned in the beginning, then the square of the norm of the better way function is actually given by determinant of this matrix, determinant. It was conjectured here first by Michel Godin from Sacle and then I proved it ten years later. So, now the third theorem, which I promised, Pauli principle, Pauli principle. Let me come back to this equation. So, Pauli principle, the third theorem about this equation. So, third theorem is the following. I can prove that if all ends are different, then all lambdas are different, which solutions exist. But if two ends coincide, then corresponding lambdas, corresponding means with the same index, also coincide. This is not good. If two lambdas coincide, that construction of algebraic betanzots will have this B square, and then all these calculations of algebraic betanzots will lead to one additional extra equation. So, the system of betanzots equation will be overfilled, will be too much equations. And this is the third equation, looks like positive number equal to zero. So, there is no solution. So, if two ends coincide, there is no corresponding eigenvector. It does not exist. So, it means that all ends has to be different. So, that's the end of the theorems, and the implication for physics means that the ground state of the hemispheres will look like a thermosphere. It will look like interacting electrons. So, all ends will, at zero temperature, will feel some interval, and this will minimize the energy. So, I started with bisonic theory, but in the momentum space, it looks like fermions because of the Pauli principle. So, let's move further. Maybe something interesting. So, this is thermodynamic limit. I have this length of the box, total length of the length, which I assume go to infinity right now, and also number of particles also go to infinity. So, number of particles go to infinity, length of the box goes to infinity, ratio is fixed, density, and then it can be this lambda's solution to bet equations. They distributed along some curve. Curve described by Roa, and Roa is a solution of integral equation. Q is a value of spectral parameter on the thermosphere, which people sometimes call it thermosphere. And as long as Q is finite, then one can prove that this linear integral operator, I mean I can move this in the left-hand side, is not degenerated. So, there's a unique solution of this equation. It's somewhat similar to a Leap-Leninger equation. For a Leap-Leninger equation, I have a similar equation, but instead of this one, I have one divided by two pi. So, this is kind of Q deformation of Leap-Leninger, because I moved to the lattice. So, in the continuous, I had this equation, but this K was one divided by two pi, and now in the lattice, I have this K. So, these equations, I mean we cannot solve it analytically. We don't have an analytical expression. There is very simple decomposition. When coupling constant kappa go to infinity, the integral becomes small. But at small kappa, this is very, very singular. And I mean Leap-Leninger are studied right now for small values of coupling constant and the coefficient given in terms of our own Riemann z-ade odd arguments, which further Smirnov likes so much. This is even more singular at small kappa, which we didn't study it yet. Okay. So, in thermodynamic limits, there's no bound states, right? Because all lambda's are real, no bound states. And any energy level can be interpreted at a scattering state of several elementary excitations. So, elementary excitation can be described, well, it has some energy and momentum. So, the energy of elementary excitation is, this is original energy. This is chemical potential. And this is integral equation, which we already saw. Later, I mean, as I said that lambda is not really momentum. This is formal spectral parameter. So, momentum as a function of lambda, I will write later, a little bit later. So, this is the picture of this elementary excitation. This is my firm sphere. So, meaning that all the states here are filled in. So, I cannot put any more particles into here because of Pauli principle, but I can make a hole. So, here I have excitation, which is a hole, and this is like energy. And out of this interval, there is no particle, so I can put particle into here. And then, this is my dispersion curve, dependence of energy on spectral parameter of this elementary excitation. My momentum will come momentarily. So, it's gapless, the energy of vanish. And then, later, we shall see that the velocity of sound, sound velocity, is given by the slope of this curve. Well, I have to differentiate with respect to momentum, but we'll do this later. Okay, this is formula for momentum, like physical momentum. This P0 is a log, this is log of the left-hand side of mybert equations. Theta is a logarithm of the right-hand side. And the rho is something which we saw before. So, this is momentum of the particle. This is momentum of the hole. But all of this together describe elementary excitation, give the dependence of energy on the momentum of this elementary excitation. This is scattering symmetric, these two elementary excitation. This scatter, and the scattering is elastic. The resultant transition and phase shift is given by the similar integral equation. In the right-hand side, I put this theta. Theta actually has a physical meaning of the phase shift in the bare vacuum, zero density. And then, when I have non-zero density, I have to dress up this phase by this integral equation. So, phase shift. V is a derivative of energy with respect to momentum of that elementary excitation on the Fermi H. And it describes, well, by now, it's called quench velocity. Quench velocity means many different things. Among other things, if I make some local quantum mechanical measurement in one latest site, then it will cause the entropy wave. And entropy wave will spread with this velocity, quench velocity. In a moment, I will go to, we'll describe thermodynamics, young and young thermodynamics. Thermodynamics has an entropy, thermal entropy. But before that, at zero temperature, I have another entropy, which is entanglement entropy, which should not be confused. So, first I talk about entanglement entropy, and then we close up zero temperature and move to the positive temperature. Entanglement entropy behaves standardly. So, ground state is unique. So, entropy of the whole ground state is zero. But there is some entropy in the block of spins. This is quantum mechanical phenomena, right? Because in classical, if I can see the classical random variable, if the total entropy of the classical random variable is zero, then there is no entropy in any subsystem. One can prove the theorem. Quantum k is not so. Total entropy can be equal to zero, but there is entropy in subsystem. Quantum fluctuations, entanglement entropy. And then, of course, entropy is a complicated function of the size of this block of spins. But for large size of the spin, it's logarithmic dependence with a coefficient one-third, and it agrees with safety. It agrees with quantum field, conformal field theory, because central chair is equal to one. Rainy entropy. So, rho is a density symmetric of block of that spin. So, alpha is some fractional number from zero to one. And then, I take this density matrix, raise in the power, alpha, take trace, log. This is a rainy entropy. Rainy entropy also depends logarithmically on the size of the block, but coefficient in front of the log depends on that alpha. So, this is entanglement entropy. I mentioned this. Well, Professor Verlinde mentioned this in his lecture. So, it might be appropriate. So, now, let's consider thermodynamics. In principle, for continuous nonlinear Schrodinger, thermodynamics was constructed by Young, seeing Young as Cp Young. In here, in the latest version, it's similar. Construction is similar. Also, equation is not different from the continuous case. Difference in here, in the homogeneous. In the continuous case, it was square of lambda square minus chemical potential. In here, I have this my bare energy. That's the one which I saw when I wrote that equation. This integral looks really, really similar to a Young-Young equation. So, this is famous Young equations. There's some notation. So, epsilon is the ratio of the density of the holes to the particles. I mean, at zero temperature, I have a concentration of particles for a small moment of minus q. There was no holes on the particle. But, at positive temperature, everything mixed up, particles and holes. So, the ratio is epsilon. Epsilon also has other meaning because this model is integrable. There's infinitely many conservation laws. This leads to consequences that even at positive temperature, there's stable excitations which does not decay. And then the energy, this epsilon is actually energy of this stable excitation which exists for positive temperature and does not decay. So, thermodynamics, free energy. Free energy can be described by, well, that sounds in terms of this epsilon. I wrote equation for the epsilon. This equation, the previous Young-Young equation was analyzed. I mean, the only one mathematical theorem which was proved that if I started erasing this, like in the first approximation, epsilon is given by this expression. And then I put this into here and keep it erasing. So, this iteration converts, so one of the solutions exists. But, it's probably unique, but it's not proven. There is no theorem that it's unique. But, one solution exists. So, this is free energy. This is pressure. And this is entropy. So, but this is thermo entropy, right? Thermo entropy of the whole bulk. So, it's not entanglement entropy. I mean, it's, thermal entropy also exists for classical thermodynamics. It doesn't describe quantum mechanics. So, while entanglement entropy is a difference between classical and quantum. So, it should not be confused. So, all of this can be done for other values of negative spin. So, here I decided to deviate for Professor Karchemsky and consider not necessarily minus one, but maybe some other number. Everything goes through. This is the basic equations. This is thermodynamics. Entropy. Everything works. Okay. So, this was so far analysis of the Hamiltonian of Tachtajan, Fadeev and Taras. So, there is other Hamiltonians of the latest non-linear Schrodinger. So, I keep our matrix. My matrix is the same like it was in continuous case. And for the latest, I never change it. Like it was discovered by Young actually. So, I keep Young for me. Eloperator is the one which was in the beginning. But by now, I want to change it a little bit. I want to make it different in the order and even latest sites. Well, the purpose of doing this to get some other Hamiltonian. So, this is the shift of the spectral parameter, which is a little bit different in the order and even latest sites. So, and I think it was J before. So, I'm sorry for changing notation. So, it was J. Now, it's N. And it's evidently different. All diagonal elements looks the same. But this in homogeneous, it also appears under the square root. And kappa now becomes size. So, I just copied from the other paper. So, and then later we shall see. Delta is still like step of the letters. And this is number of the total number of particles in the whole latest set. So, with this modification of Eloperator, we can design new Hamiltonian. This is expression in terms of trace identities. So, tau is a trace like a plus z of the product of all of this Eloperator. And this is a special value of spectral parameter where Eloperator become one dimensional projector. The quantum determinant vanish at this point. So, that's the reason I can write these Hamiltonians looks even more complicated than Fadi if Theras if it's an octogen. So, this T we express in terms of alpha. And alpha is relatively simple function of the local bosid field. So, this Eloperator actually describe interaction of eight latest sites. So, people might argue that Fadi if Theras of octogen is better. Okay. So, now I'm actually moving to form factors. Before that, well as I mentioned the square of the norm is given by this golden formula but the determinant. Form factors in the behaves similar in the continuous in the latest case. So, I will kind of explaining first I will remind what happens with form factors in the continuous case. I mean they don't exist. The answer is like negative. But, I mean the behavior is similar on the latest in the continuous case. So, this is some one of form factors. So, this J is the side I guess I for the continuous case. This is local density of particles in the X and T space standpoint. This is standard canonical bosid operator. And this Q is number of particles on the interval of zero X. So, I can take this Q and taken matrix element between two birth states. This is like one and this is another and normalize it. It's actually was long story. First, some determinants representation was written for this. And determinants representation I mentioned determinant of the matrix of a large size. The size of the matrix equal to n capital number for particles which goes to infinity. And later I will mention the similar determinant representation also exists for the latest non-linear Schrodinger. Not identical but similar. And then this determinant representation was studied and the answer was negative. Because when the lengths of the letters go to infinity this form factor decays goes to zero as some fractional power. So, f is some solution of integral equation. Actually, this is a phase scattering phase of those two elementary excitation divided by two pi. This is definition in terms of the lambdas. We call this shift function, but it also coincides with the phase shift of two scattering matrix. So, the form factor is vanish in the continuous. This is just other form factors also was analyzed. They also don't exist. This is the determinant representation, but maybe it's published somewhere. Maybe it's not interesting to the people right now. Okay. So, this last couple of transparencies. I was explaining problems with the form factor the continuous non-linear Schrodinger. Similar problems occur for latest and Takeshi Otto from Japan. He wrote the term and representation for some operator or for latest non-linear Schrodinger. The operator somehow has correct continuous limit and maybe I just come back. So, and then Karl Kazlovsky. Karl Kazlovsky here analyzed the thermodynamic limit of this determinant of Takeshi Otto and then it also goes to zero as a fractional power of the length of the latest actually the same power. So, this is more or less the end of what I was going to say about non-linear Schrodinger on the latest. Maybe the last transparency that similar calculation can be done for Sainte-Gordon. This is continuous Sainte-Gordon and then continuous Sainte-Gordon was sold by Aldi Bragg with Anzac in Quantum University, recommended by Professor Tahtajan and Fadeev. But we have our own latest version which is interesting by itself. But maybe, maybe it's a good time for me to stop my lecture and wish happy birthday to Professor Shatashvili again and here he was my best student. So, that's the end of my lecture. Any questions or comments? Maybe, maybe just some references. The main reference. Here, the main reference is this and this was our inspiration. This was Professor Shatashvili related to dimension topological gauge theories to non-linear Schrodinger to continuous non-linear Schrodinger. This was inspiration for our work. So, if you look at Sainte-Gordon do you, on the left, do you see something of the Kostel et Thales transition? Is your Aldi Bragg method? I didn't see that phase transition.  I mean, that answers for Sainte-Gordon, I mean, this is a relativistic model. There is one Feynman diagram in Divergent. For that answers, we have to learn how to make ultraviolet renormalization. And here, for Sainte-Gordon, for specific, like for rational values of coupling constants, there is an anisotropy parameter which is coupling constants. For the rational values, we can compactify the local Hilbert space. We don't have to have this infinite dimensional Hilbert space which we had for latest non-linear Schrodinger, but we have a finite dimension. I mean, dimension is equal to the denominator of this fraction, so we just use it more like for mathematical justification, everything is rigorous, but Schrodinger's is no to your question. There is another, I learned sometimes ago, Latis version of the delta function. Schrodinger operator? Ablovitz logic? There's two people in the United States, they live in the Midwest. One is Ablovitz, that's the name of a person. And Latik is another person. The author of that paper I was told is some Dutch person living in Brazil. That's the James. I don't know, well I don't know that paper, but Ablovitz-Ladik, you know Ablovitz-Ladik, so Ablovitz-Ladik has another discretization of non-linear Schrodinger. I mean, we kind of insist on ours because in their case, our matrix is different, so our matrix depends on the Latis step. And in our case, like going from continuous to Latis is like changing the representation of the same algebra, right? The algebra is given by our matrix, so we just keep our matrix, change the representation, so we think like this is an intelligent way to discretize. But I mean, Ablovitz-Ladik, they change our matrix. Sorry, and your question was? That one is actually this second order differential operator, delta function potentially replaced by some differential equation, which in the limit becomes that. Well, I mean, the way function there is what's called Hall-Litzwood polynomial. Yeah, I don't know, if I take non-linear Schrodinger, it replaces the second derivative by the difference, it won't be integrable, so one should be careful with this. I mean, it's just straightforward discretization would just keep, and then there will be problem because the phase transition will appear when I send the Latis step to zero, then it's not integrable, then it's not integrable, and this is kind of problematic. So it's not regularization, it's like falsification. Right, I think that at least this person. I don't know that paper, so maybe you show me the later. Well, maybe I should also mention that on the Latis non-linear Schrodinger, the model is equivalent to XRK with negative spin, which has multiple application to Latis gauge, you know, Professor Karchemski, and Lipatov, and Fadeev, but also Kazakov, in his fishnet, has this XRK with negative spin. So the Latis version has direct application to four-dimensional young males. We'll talk to him. Also, I have a question just about, you were saying that when, let's say, going to infinity, this land has become uniformly distributed with a certain density. Did young and young, or can it be proved rigorously? Oh, actually, yes, yes, yes, yes, yes. Sure, the answer is yes, because remember, well, maybe I can answer your question if you permit. Okay, so remember, when I wrote Bertrand's equations, I had three settings. The third, I kind of crumbled, you know, I didn't say clearly, but the third one was like this. I have logarithmic form of Bertrand's equation. I have this n, so I can subtract this equation, and I can estimate the difference between two neighboring lambdas in terms of the difference of n's from above and from below. So when l, total length of the way to go to infinity, I can prove that the difference between lambda go like one divided by l with some finite coefficient. So we can prove that the difference one divided by l, and then this is the basis of the proof that rho exists. So the answer is yes, it's not from young, young is like in my book. He didn't prove this. The idea, it's in the textbook. Thank you.