Hi everyone, Joe for Jaspy's casebreaks.com coming at you with a box of 2022 Panini National Treasures Football. One box random team break number two, you can see the next one's already loaded up. But for break two, big thanks to this group for making it happen. Congrats to the people who won their spots and those two filler breaks, thanks to the people who bought their spots straight up. However you got in, I appreciate it. All 32 teams are in, let's roll it, let's randomize names in teams three and a five, eight times each, one, two, three, four, five, and a three, six, seven, and eight. Got Nicholas down to Steve, three and a five, eight times for the teams, one, two, three, four, five, six, seven, and eight in final time. Good luck. Matt Dallas down to Tampa Bay. All right, Nicholas with the Cowboys, Jose with the Chargers, Chris with the Viking, Steven with the Patriots, Douglas with the Saints, Jesse with the Colts, Logan with the Seahawks, Matt with the Texans, Jose with the Giants, Chris with the Jaguars, Steve H with the Raven, Steven, P with the Falcons, Bears, Bills, and Rams. Matt has the Broncos, Jose got my Raiders, Douglas with the Packers and Titan, Steven P with the Commanders, Matt with the Panthers, Josh with the Jets, Ron with the Steelers, Steven P with the Bengals, Allen with the Dolphins, Chris P with the Eagles, Douglas with the Lions, Arizona Cardinals going to Francis, Allen with the Niners, Matt with the Browns, Steve H with the other Super Bowl team, Kansas City Chiefs. They're your Super Bowl teams right down there, and then Steve H, Tampa Bay, Buccaneers. All right, we're going to pause the video just for a little bit. When we come back, we're going to see if there's any trades, then we'll have the break. You know the drill. Stick around. We'll be right back. All right, welcome back everybody. No deals are done, so that list right here remains the same here on Wednesday, the 31st, hump day, last day of the month, all sorts of stuff. Thanks everybody for making it happen. Appreciate you. Oh, we got someone in the Twitch stream asking, what's my favorite football team? It would be Liverpool Football Club. All right, so we did Box D already. We got one, two, three, four, five, six on the dice roll for this one box break, and it's four, one, two, three, four, middle box, box B. Next one box break is in the store, and good luck with this one. And they just beat Chelsea today, staying on top of the Premier League table. Put this around right here. Good luck everybody. We'll use this blank card right here to slow play the hits a little bit. We got a Brandon Cooks to 99, 85 out of 99. That's going to go to the Texans. That'll be for Matt. Got what time is it? Game time. Great loads. 35 out of 35. That'll be for Steve H. and the Ravens. Then we have our first hit. It's CD Lam, 19 out of 49. Next to the Jersey, going to Nicholas and the Dallas Cowboys. There's Geno Smith, three out of 25. I think the Seahawks just announced a new coaching hire. Let's see what they're going to do with Geno Smith. Seattle has to be for Logan and the Seahawks. Got a nice dual relic here, Tyquan Thornton, 17 out of 25. Stephen P with the Patriots. I feel like they're going to look for a change at quarterback. There you coach. We've got some John Randall, Treasures of the Hall dual relic. Minnesota Vikings, Chris with Minnesota. We have a Connor Hayward rookie autograph, two out of 25. That's going to be for the Steelers, Ron with Pittsburgh. Got a few more here, two out of 25, Antonio Freeman. Nice. Remember him? That's going to go to Green Bay. That's going to be for Douglas. There's the two out of 25. All right, a couple more here. Ooh, Nike Swoosh Tyquan Thornton, two out of two. That's a sharp-looking car. That's going to go to Stephen P and the Patriots. One that spot in the filler. Out of 5's and under, get the train whistle. Really cool-looking relic right here. Very nice. Stephen. All aboard the Big Head Express. Nice way to start the day. And the last one here is Breeze Hall. Nice rookie jersey, an autograph, 12 out of 99. For the J-E-T-S, Jets, Jets, Jets, that's Josh. With the Jets, one that spot in the filler. All right, there you go, gang. A nice box, but we still have not seen, not that it's guaranteed, but we've not seen a guy like Brock Purdy. And his R-P-A-J-S here. Any Brock Purdy would be nice at this point. Four boxes left in the case. Let's get after it. Next one's already in the store, jaskyscasebreaks.com. I'm Joe. I'll see you next time for the next break.


Hello and welcome to Newsbreak. Today we are going to discuss mapping the elections with Seema Mustafa. Seema, all eyes are right now on UP and Vihar because this is the bulk of the seats from North India. And let us face it, it is a North Indian vote which is going to decide what is going to happen to BJP because they do not really have much of a presence in the South. How do you look at the first, the UP elections? 8 seats in Western UP are going into elections. So what do you think is the scenario in Western UP? Well, it is very interesting because this time, you know, there has been a very concerted effort by Ajit Singh and the Rashtri Lopthal to get back the Jat vote. And Ajit Singh actually told me that how they have worked very systematically over the last one year on that Jat vote because he has finally realized that he is losing that entire constituency. Yeah, the constituency which his father had sort of created for them. So he said that they went to the Jats and they said, look, you need to be powerful here and you cannot be powerful and have a say in who the government is or what government is formed unless you are a power vote and that you can only be with the Muslims. And you voted in the past for the Muslims. I mean, this is exactly how he was telling me. And now you guys should come together. They also work on your field. And you know, this whole fracturing of Muzaffar Nagar where incidentally he is contesting the election from should not happen and we should come back together. So he is now very sure that the Jat is returning and this Mahagat Bandhan rally that they had three days ago in Saharanpur, western UP, Dioband area, there was a huge response.  So it's very interesting and the Jats came out to listen. You know what you are saying also makes a different kind of sense because one is the unrest among the peasantry and that has affected the Jat peasantry as well. Sugarcane. Sugarcane and in fact, there's a bigger issue over there that they have gone into sugarcane in a larger way partly because of the threat of cows now the stray cattle menace which is now endangering their feed. And the cane is one crop which the cows find it more difficult shall we say and therefore it's less affected by the cow menace. So they have put in a lot of things on cane but unfortunately the sugar prices, both the international prices and the local prices, huge time takes for them to realize it. All of it is affected the Jat peasantry as well. It really is a part of the peasant unrest which you have seen. But it depends now to what extent the communalization is actually seeped in. The last 24 hours always you know is when this vote bank decides where it's going to go. I remember in the 2014 elections and I mean in the last elections that where are you going to vote after demonetization in the assembly elections and everybody in this belt came out and said we are very angry and they've ruined us and then they brought yogi in right. So you can't say what happens in the last 24 hours and much as we would like to underestimate communalization in UP given the fact that we all talking about how the elections campaigns are on issues and they being fought on real issues and economic livelihood. At the end in those 24 hours which is always crucial in the Hindi belt somehow these guys have the machinery and the organization to be able to flip things. Kind of hate propaganda which comes on WhatsApp and so on what it does. But you know this other thing that you talked about that Charan Singh had also built the alliance based on peasantry but also on the Muslims and the Jats peasantry and the workers, farm workers not being split. But he's been able to also project a secular constituency for himself as well as his party. That actually did fracture with Muzaffar Nagar and what the BJP has been doing for the last 20, 25 years in western UP. Yes and it was the Muzaffar Nagar was important because it moved away for the first time in this area from the towns into the villages. And it was communal violence. And the other thing was neighbor hit neighbor which doesn't happen. It doesn't happen. Usually the people who come in and you know these kind of things are usually outsiders in the village, in a village when you have this happening.  So it is a fractured sort of constituency. So while they've been working at it, have they worked enough? Is it actually mended fences? Are they actually coming back together? But what was very heartening on a positive note was the Gadbandhan rally in Sarampur because you had all the communities there including Dalits. And you had a very responsive, very enthusiastic crowd which was responding to all the three leaders, Mayavati, Kilesh Yadav and Ajit Singh. That's an interesting point because Jata when Jata is an old again tension. Yes. So while there was a secular constituency of Charan Singh it was a very casteist constituency of Charan Singh. Very anti Dalit and very anti Jata. Dalits were not allowed to vote. No. They kept out of the booths and even if they came to vote they faced violence later. Yes. And this time because of the Gadbandhan you will find that you know in these candidates who are say from not the BSP but our RLD or even Samajwadi they are actually moving to seek the Dalit vote. Now that whether it gets transferred or not will depend but obviously Mayavati has made it very clear and the chemistry between the three was rehearsed, it was good. They didn't say anything which was wrong because they were really on show and a lot of voters of that region had said that we want to see how they are in this rally before we make up our mind. That's an interesting point because this issue of chemistry between the SP and BSP has been discussed a number of times that it's almost impossible for these two parties to come together but it was not so much the SP, BSP per se. It was also the muleim and the old guard who when the incident happened in the guest house if you remember the Dag Bangalore and that violence which was unleashed physically against Mayavati and the response of muleim after that not even an apology but a brazen justification that was really what fractured the relation so it's in that sense helped that the SP is no longer headed by muleim and he's really become a kind of... A patriarch sort of. Patriarch who is given respect but not listened to. Not listened to, yes, exactly. And I think Akhilesh Yadav's personality really contributes to this because he's very soft, he's quiet, he's very, you know he's sort of really very generous in the way he discusses or, you know, the alliances and it's a soft spoken, very sort of whatever you want, Mayavati Ji, Behendi kind of attitude that has really worked for him. Though he's a very firm guy, he knows exactly what he wants. He never moved back, he isolated that other uncle of his, Shivpali Yadav he made it very clear that muleim's saying you're my father but it's got to be the way I want to run the party running it. Well, you know this is of course the larger issue of dynastic politics which we won't discuss today but Congress is it going to be a spoiler in UP or at least in Western UP? That's what the fear, I think we did discuss it on one of our programs but it's becoming very real and apparently it's going to have a lot of considerable impact on several seats in Western UP which is going to polls tomorrow which is on the 11th and other seats also which are going to follow like for instance Muradabad. I mean that's you know something which you the Congress had one percent seats one percent of the vote share in the last election and they have brought in a very strong candidate from Pratapgarh, Imran Pratapgarhi while he is strong is he's like a rock star amongst the Muslims. He's sort of into you know this churns out poetry gets emotional, weeps, cries and yet keeps secular you know his language is very secular but he's the guy who's been brought in now he's very popular, he's a household name and if the Muslim vote splits over there then the BJP comes in. So there are lots of these seats where they have actually fielded candidates to contest the Mahogad Bandai which is which is just absurd. Well that we have discussed last time that the Congress seems to be thinking that it should be the key opposition it is not thinking of defeating the BJP at the moment and that's also seems to be the calculations that we cannot vacate the opposition space in states like that. I know and if that's going to be your calculation then you should have prepared for it for the last five years and maybe today you've been in a position to do it but you can't do it two months before the polls because you know it's you've got no organization in UP which is capable of mopping the votes. So at the most you will be a spoiler you won't win the seat but now will the Mahogad Bandai. Coming back to BJP to Bihar and I'm not sure we should call it the Mahogad Bandai at the most we can call it really the Gad Bandai. So Bihar is a little more like Mahogad Bandai except the left has really not come into it left has some pockets of influence I think there's only an adjustment over Ara as of now but no other seat including Begusarai. What do you think first? What are the broad picture you see in Bihar? Because we take the last election arithmetic into account unless there is a significant swing away from Nitesh BJP assuming that it still remains a sort of stable voting block of uppercast sections which don't see any other party in Bihar except the Congress which is of course there with the Gad Bandai. So what do you think that it is like? Do you think Lalu who is going to lose some support amongst his vote base? Well you know the reports are conflicting we yet have to go in and really look at the whole thing. From Ara it seems ML candidate is doing fairly well. Begusarai there's of course the CPI candidate who didn't leave the seat for him so he's contesting. Now it all depends on whether he gets the Bhoomiar vote and whether he gets the Muslim vote away in which case he'll have a winning target because in Bihar you know it's not that you come in in these states as national leaders you also come in against the local factors that all ranged against you. I mean there is a popular RJD candidate who is very strong he's the old socialist of the Lohia kind he's got a very strong support amongst the Muslims Bhoomiar of course there is the CPI base but the Bhoomiar is also with the BJP so Kanhaiya will have to whip up a certain kind of campaign which he seems to be doing pretty well but in Bihar you know the conflicting story is between whether Nitesh has lost to what extent has he lost and to what extent has that vote moved away from him and the other report is that Bandhan is doing very well or the Mahagat Bandhan is doing very well because they managed to get some of those parties which were last time in alliance with the BJP so the shift is obviously towards them and there is this Yadam, Muslim, Dalit kind of a consolidation that is making itself felt in Bihar. So you think that there could be some shift away from particularly Nitesh's vote base because Nitesh in Bihar had a non shall we say Yadam but a OBC vote base and a little bit of the uppercase and others talking also among the Muslims he was regarded as a secular force in the last election and before the last election even when he did go with the BJP his secular image was not really that dented but this election after the polarization we have seen in the country the kind of hatred that is being sort of served on a platter everywhere I think the Muslim has no choice but to move away from him because he is seen as the grand betrayer he betrayed a vote the Yadams also look upon him by the way as a grand betrayer because they came out of Lalu in the last election parliamentary election and for them it is Lalu all the way now particularly so there is this big vote bank which things that they've been done against and I don't think in terms of development what he did earlier in the last year or two it's not been tremendous development plus the polarization so interestingly I always feel that Bihar is less communal and more casteist than UP or not more equally casteist but somehow less communal than UP in the sense it's very difficult it's not easy to polarise people on Hindu Muslim lines there because it's cut so deeply by caste and maybe the BJP hasn't been able to work there with the same focus and intent as it has been able to in UP well UP the BJP old Jansung base if you remember goes much deeper and then you have this Adityanath sitting there but apart from that it's a much deeper communal base if you take Bihar there is a strong socialist base I don't forget there was to be a strong left CPI later on you know it splits but even liberation CPI and it's got a percentage of votes that you see I mean even in Begusarai the CPI had 19% of the votes which is good for a party which doesn't have any organisation there so in this sense the people therefore have seen socialist and left politics in a big way in Bihar in 60s what we remember the CPI was a big force in Bihar and Eastern UP and Eastern UP but Bihar was really significantly higher than Eastern UP so what I'm saying is BJP or Jansung at that time its communal politics was contested by both socialist and communist not only the congress in fact congress as you said used to be a casteist formation in Bihar and that legacy still continues both with the BJP and with the congress in fact everybody you know over the last year absolutely right and they played really deep communal politics I mean if it came from the Ramandir and then it came with Rajiv Gandhi's Ramrajya and then the whole thing it's been the laboratory the playground not even the laboratory the playground of polarizing divisive politics of hate so it's come a long way which is why now when I speak of UP I speak with the rider of how the communal element or that virus that has been fed into that state is going to react in the last 24 hours before election before polling yes I think if the communal virus is bitten most deeply it will be Gujarat and followed by UP these I think are the two states where it has really gone very deep and the countervading forces have in that sense have been more shall we say community based in terms of caste formations and not really secular formations who can really contest therefore not identity politics but really with secular politics which always you know is the really the counter counter point of the antipodes so to say it's secular versus communal the minute you get into caste versus caste then engineering caste alliances becomes also a game which the BJP seems to have learned pretty well very well and I think what in Gujarat the polarization the fracturing is complete you know I mean you have different colonies people stay separately it's like you've actually and you will you know when you cover the elections or move around Gujarat you will find the Muslims carrying the identity on a sleeve and being ignored they're not there they're not they don't have a say in most issues they just have to be happy that they are not being targeted UP hasn't yet come to that point of complete segregation it's in the process and another five years will complete it I think if we don't manage to reverse it exactly so things are interesting very we are living in interesting times as a Chinese and fluid you know which is why it's probably being reflected in what we are saying because we really don't know we can just tap the broad parameters it's all very fluid lots of things are at play in UP and Bihar but one thing I think is almost certain the BJP is not going to be able to repeat the same amazing performance it had the 2014 election so that is a gain for the other side that those numbers cannot be replicated today thank you very much Sima for being with us mapping the elections not only in terms of seats constituencies but also in terms of what are the voting blocks what are the kind of issues from which the votes are likely to take place it's difficult to hold a crystal ball and predict this elections particularly this time because we have the recent incidents in Pulwama followed by Balakot so all of this is also shall we say a volatile mix at the moment this is all the time we have the news click today do keep watching news click


Here at the New York Times says four Saudis who participated in the 2018 killing of Washington Post journalist Jamal Khashoggi received paramilitary training in the United States the previous year under a contract approved by the State Department. The training was provided by Tier 1 Group, which is owned by the private equity firm Sabera's Capital Management, and was defensive in nature and devised to protect Saudi leaders. Sabera did not immediately respond to a request for comments. In response to the Times' report, State Department spokesman Ned Price said under the law the department cannot comment on any of the licensed defense-exports licensing activity alleged in media reporting. Prince Price rather also said U.S. policy towards Saudi Arabia would prioritize the rule of law and respect of human rights. Khashoggi, U.S. resident, who wrote opinion columns for the Washington Post, critical of Saudi crown prince Mohammed bin Salman was killed and dismembered by a team of operatives linked to the prince in the kingdom's consulate in Istanbul in October 2019.


Blizzard swept across swaths of Russia on December 15, carpeting Moscow on one of the biggest snowfalls in decades and sowing chaos on major roads where truck drivers battled with more than 20 cm of snow and strong winds.A cyclone brought more than a day of constant blizzards to the Russian capital and what could be one of the strongest snowstorms to hit Moscow in 60 years, according to meteorologists. More than one-fifth of the average snowfall for December was recorded over just. 24 hours at meteorological stations across Moscow where streets were blanketed in snow and motorists struggled to get their cars out of parking spaces, the justmedia weather websites said total December snowfall in Moscow could reach 50 cm, the highest recorded for that month, schools in some regions of European Russia were closed due to the snowfall, Russian television reported. A vast 10-kilometer traffic jam formed overnight on one of Russia's major roads, the M-4, to the south, trapping motorists in freezing temperatures.


Hello and welcome to the session. I am Deepika here. Let's discuss a question which says What cross sections do you get when you give up? number one vertical cut to horizontal cut to the following solids part A upper B around April C a die D a circular pie and E an ice cream cone Let us first understand the meaning of a cross section Now an object which is in 3d can be viewed in different ways One way to view an object is by cutting or slicing Now when a solid shape is cut or sliced vertically or horizontally The cut face is called the cross section of the solid Let us write the solution of this question in the form of a table Now in part A The given solid is a brick Now brick is like a cuboid with a rectangular face So when we will give a vertical cut to this brick the cross section is a rectangle Again when the cut is horizontal then the cross section is a rectangle Now in part B The given solid is a round apple Now a round apple is like a sphere Now when we will give a vertical cut to this round apple then the cross section is a circle Again when the cut is horizontal the cross section is a circle Now in part C The given solid is a die Now die is like a cube So when the cut is vertical then the cross section is a square Again when we will give a horizontal cut to this die the cross section is a square Now in part D The given solid is a circular pipe A circular pipe is like a cylinder So when the cut is vertical the cross section is a circle When the cut is horizontal then the cross section is a rectangle Now in part E The given solid is an ice cream cone So when the cut is vertical When the cross section is a rectangle When the cut is horizontal then the cross section is a circle So this completes our session I hope the solution is clear to you and you have enjoyed the session Bye and have a nice day


We will now move on to First Minister's Questions. Question 1, Ruth Davidson. To ask the First Minister what engagement she has planned for the rest of the day. First Minister. First Minister, today is world aid day. Let me begin by saying that it is First Minister that I am determined to play my part in on-going efforts to challenge the stigma and myths associated with HIV. Later today, I will have engagements to take forward the Government's programme for Scotland. Ruth Davidson. Ruth Davidson. I associate myself and my party with the statement that was made by the First Minister regarding world age day. Does the First Minister have complete confidence in our education agencies? Well, as Ruth Davidson is aware, we are undertaking a governance review. Our education agencies bring real strengths and benefits to Scottish education and to the curriculum for excellence, Ond we are asking right now some fundamental questions about school education, and the best way to empower schools to improve. That is why we launched the governance review, which is looking at the roles not just of the main agencies, but also local government and of the Scottish Government. It is part of a wider set of reforms that we believe are needed in light of real and legitimate concerns that emerged last year from the SSLN findings. We're absolutely determined to raise standards for all and close the attainment gap for our poorest pupils and the reforms we're undertaking to the roles and functions of the different parts of the school system will be a crucial part in achieving that. The First Minister says that fundamental questions need to be asked about those agencies and I think it's hard to disagree with that, but she might want to reflect, just for a second, on who's actually been in charge for the last ten years. Over the last few days, the Parliament's education committee and education experts have begun to shine a light on that record. For example, it emerged yesterday that teachers are swamped with no fewer than 20,000 pages of guidance for curriculum for excellence. Parents' groups have pointed out that those documents are, and I quote, totally inaccessible to the average mum or dad. Worse of all, expert evidence has revealed that parents and teachers have no way of knowing if curriculum for excellence is even working or not, as Professor Lindsay Patterson put it this week, that failure is a dereliction of duty. Someone has to be held responsible for this failure, First Minister. Who should it be? First Minister. First, I don't accept the characterisation as failure, but for the avoidance of any doubt, I'm responsible for taking forward this Government's commitment when it comes to education, with, of course, the Deputy First Minister, the Education Secretary. In terms of the guidance that Ruth Davidson refers to, that is guidance that has built up over many, many years. One of the priorities that the Deputy First Minister has been working on is simplifying the whole landscape around education and reducing the unnecessary bureaucracy that teachers work with. I think that the efforts that he has been making have been broadly welcomed by the teaching profession. In terms of the wider thrust of Ruth Davidson's questions, I think that we were right to put in place curriculum for excellence, and I think that curriculum for excellence in its development had, broadly speaking, cross-party support. However, I am absolutely determined to ensure that, as we go forward, we are able to measure the success of our education system, and we're also able to highlight where things are not working as we would like. That's why we have published the national improvement framework. That's why we will start to publish more data about school performance than has ever been published before. I think that that is a sign of how seriously we take this issue and our determination to improve standards for all in Scottish education. Ruth Davidson. We keep hearing from the SNP about Jam tomorrow, but that's from a Government that's spent 10 years failing to sort out endemic failures in Scottish education. First Minister, the Scottish Qualifications Authority has a very important job of running our children's exams. At the Education Committee last week, those were just some of the views that were expressed by MSPs. The SQA exists in a parallel universe—that was Johann Lamont. There were in danger of sinking in a sea of jargon—that was Richard Lochhead. The MSPs have seldom come across evidence that is so compelling in its concerns from Liz Smith, and Tavish Scott, who ended up asking, please do not scare me anymore—a criticism and a loss of confidence from right across the chamber. I am absolutely sure that SQA staff are attempting to do the very best that they can in pretty trying circumstances, but my question to the Government is how have you allowed this to happen on your watch? I am sorry if that disappoints members. I do not think that I am prepared to make not scaring Tavish Scott a key priority of Scottish Government policy in education or any other matter. Ruth Davidson does a disservice to the work that is going on in education. The governance review is intended to take a critical look at the whole governance of Scottish education, not just agencies such as Education Scotland and the SQA, but also the role of local government and the role of the Scottish Government. I would hope that all MSPs, those who expressed the views quoted by Ruth Davidson and indeed every member of this Parliament and interested members of the public, would take the opportunity, because there still is an opportunity, to give views to that review. Of course, it closes in the first week of January, and the Government will set out its intentions thereafter. At the heart of the governance review is our commitment to ensure that as much power and responsibility in education lies with teachers in schools, because that is a key part in our views. I would have thought that this is an opportunity for Ruth Davidson and her party to feed into the governance review. I am not sure whether they have done so yet, but if they have not done so, I would encourage them to do so. Ruth Davidson. I hear again the First Minister talking about all the things that she plans to do in the future. Frankly, we have heard about reviews, commissions and listening exercises before. The evidence before this Parliament points to a system that is broken. Let us spell out what the consequences are of 10 years of inaction from this Government. We have a stubbornly wide attainment gap that is not closing. We have numeracy standards that are falling. We have inspections at a five-year low.  It is a generation of pupils that have been failed by the SNPs and teachers who are trying their best but are swamped by bureaucracy. The First Minister talks of a governance review, but it is clear that the issues are far more fundamental than just the area that that review tackles. My question is how many more pupils have to be failed before we get a routine branch review of everything and all of the changes that we actually need. First Minister. Let me touch on a few of the things that not surprisingly Ruth Davidson did not mention. The fact that over the last few years we have got record exam passes in Scotland, a credit to teachers and our young people. Let us also mention the fact that we have got a record number of young people going into positive destinations in Scotland, a credit to our teachers and to our young people. Let us also mention the fact that, yes, we have got an attainment gap that I have made very clear that we are determined to close, but we see signs of that already closing. Those are the positive things about education. It does not surprise me that Ruth Davidson wants to talk it down. As I said in my original answer, we are determined to ask the hard fundamental questions about how we make Scottish education better. That is why John Swinney has already taken steps to reduce the bureaucracy in our exam system, something that I would have thought Ruth Davidson would have welcomed. It is why we have established the governance review. It is why we are getting on in implementing the national improvement framework, so that shortly we will have more information to hold the Government and all parts of our education system to account about the performance of schools than we have ever had before. I think that those are the steps that parents around this country want to see us take, because we are determined that we will have a world-class education system, that we will have rising standards for all, and we will close that gap in attainment. Question 2, Kezia Dugdale. To ask the First Minister what engagement she has planned for the rest of the week. First Minister. Engagement is to take forward the Government's programme for Scotland. Kezia Dugdale. The treatment time guarantee will ensure that eligible patients start treatment within 12 weeks of the treatment being agreed. That is what we were told by Nicola Sturgeon when she introduced a legal right to treatment for patients. So can the First Minister tell us how many NHS patients were not seen within 12 weeks since this legal right was introduced in 2012? Well, since the legal right was introduced in 2012, there have been 53,257 who have waited longer than 12 weeks, but there have been 1,267,000 treated within 12 weeks. Waiting times are lower than they were when we took office, but we have worked to do because of rising demand in our health service. We continue to ensure that our health service has the investment and record numbers of staff so that we can continue to provide the best care and treatment for patients across the country. Kezia Dugdale. That is a legal guarantee to 53,000 people broken. In fact, over the last few months have been the worst on record. These are not just statistics. It is pensioners in need of a knee replacement having to wait for months or people waiting for eye surgery facing delay after delay. Each time I bring an individual case to this chamber, the First Minister promises to deal with it. It would take me centuries to work through each of these 53,000 cases. How bad do things have to get before she steps in to fix this mess? Kezia Dugdale talked about records when it came to waiting times. It is worth pointing out that, when this Government took office, there were only 85 per cent of patients treated within 18 weeks. Not only have we reduced waiting times from 18 weeks to 12 weeks, a higher percentage of patients are now being seen within that shorter waiting time. That is the progress that we are making. We also see record numbers of staff working in our health service, and we see record levels of investment in our health service. I know that Kezia Dugdale does not like me to point out that fact, but there is going to be more investment in our health service under this Government than there would have been in the unlikely event that Labour had won the election. Labour promised the lowest increase in health funding of any party represented in this chamber. That is the reality. We have rising demand for our health service. That is why we continue to invest to build up the capacity of our health service so that we can continue to ensure that more and more patients get seen within these shorter waiting times. Kezia Dugdale goes again, bringing up a 10-year-old record of a Labour Government and pointing it out in England. It just does not cut it with patience. It does not cut it. The First Minister likes to remind the chamber that she is going to spend £500 million more over the lifetime of this Parliament, but what she did not tell us is that Audit Scotland told us last month that she has to cut £500 million out of health budgets in this year alone through her health boards. That is a fact that she cannot avoid. In fact, it sums out the priorities of this Government. Whilst Labour Party activists were out campaigning with NHS staff and patients at the weekend to protect the NHS, the SNP were out talking about independence. It is no surprise that the SNP does not want to campaign on the NHS, because here is their record. Local services face enclosure, missed targets and a growing workforce crisis. Is not it the case that, under the SNP, the NHS is stuck in the waiting room, while the First Minister plots a second referendum? The reason I—Kezia Dugdale rightly asked about the performance of this Government, and when you are talking about the performance of this Government, it is perfectly reasonable to look at the situation that we inherited and the progress that has been made since. Kezia Dugdale wants to quote Audit Scotland. Here is what Audit Scotland said in its recent report. Overall, staff levels are at the highest level ever in NHS Scotland. When we took office, as I said, 85 per cent of patients in Scotland—this is quarter one 2007—85 per cent of patients in patients in day cases were being seen within 18 weeks at that time. Now there are almost 90 per cent of patients being seen within 12 weeks. The waiting time is shorter and the percentage of patients being seen within it is larger. That is progress in anybody's language, but it is not enough progress. That is why we are committed to continuing to increase investment, not by £500 million over this Parliament, but by £500 million more than inflation over this Parliament. Labour simply committed to inflationary increases for the national health service. More investment, more members of staff reforming our health service so that we get more investment into social care as well. Those are the actions that patients across the country want to see, and those are the actions that we will continue to take. On Monday evening, over 200 people attended a public meeting to express their opposition to the proposed closure of the Vale of Leven Maternity unit. One of those attendings said, and I quote, If the Cabinet Secretary for Health is not doing her job, then I am going to tell her and hold her to account. She has said that she is committed to the Vale. The problem is that we have got to make sure that she sticks to that. Those were the words of the SNP group leader on Westumbartonshire council. Does the First Minister agree with him? Will she make sure that the Cabinet Secretary for Health sticks to the vision for the Vale? The Government is committed to the vision for the Vale, and it is worth pointing out, I think, because people perhaps have longer memories than Labour would like them to have. If Labour had won the election in 2007, it is highly unlikely that the Vale of Leven hospital would even be open today. That is the reality. That Government, step 10, we saved the Vale of Leven hospital just as we saved accident emergency services at Monklands and at Eire. We will continue to stand up for local services, because that is what people expect of this Government. People know that it is not what they got when that lot were last in Government. Question 3, Willie Rennie. To ask the First Minister what issues have we discussed at the next meeting of the Cabinet. Matters of importance to the people of Scotland? Even though her chancellor is in Scotland today to talk about Brexit with the First Minister, Ruth Davidson is obviously too embarrassed to raise it in here. In June, Ruth Davidson said that her priority was the EU single market. But this week, her five tests on Brexit adopt the language of Nigel Farage about rekindling trade with the British Empire instead. It is clear that they will sign up to anything on Brexit, no matter how bad the deal. It is a blank check Brexit. The Scottish Conservatives may have given up, but we have not. When the First Minister meets the chancellor today, will she make the case for a UK-wide Brexit deal referendum so that the public can have a say on the final Brexit deal? First Minister. First, I have to say to hear Willie Rennie talk about the benefits of referendums for a change in this chamber. I agree with the broad thrust of Willie Rennie's question. Increasingly, it is very difficult to distinguish between the Conservatives and UKIP and anybody in any doubt about that. I need only look this morning at what is reported to have been Theresa May's views on denying education to children living here from certain countries in certain circumstances. On the question of the single market, I am absolutely consistent in this. I think that the UK should stay in the single market. I do not believe that there is any mandate or any justification, economic, social, cultural justification for taking the UK out of the single market. I will make that point to Philip Hammond this afternoon, as I have made that point to the Prime Minister and to others in the UK Government. I hope that everybody in this chamber will get behind that position of the Scottish Government. Willie Rennie. If I can gently say that she did not quite answer my question, momentum is building for this Brexit deal referendum, so I hope in time that she will come to support it. I am interested in what else she might have to say to the Chancellor. Look at what we are facing. NHS boards are contending with unprecedented budget cuts. Councils are facing a £500 million funding crisis. No doubt she will bitterly complain to the Chancellor about that, and so she should. However, I want to know what else she is going to do herself, because this week she gained new income tax powers. I have a plan for a transformational investment of £500 million for education with a modest penny on income tax. Will the First Minister join me, or will she just bitterly point the finger at the Conservatives? I do not know whether Willie Rennie intended to turn First Minister's questions into a stand-up comedy routine, but he has perhaps succeeded on that front more than he succeeds normally. However, there are serious issues underlying Willie Rennie's question, and I should not glide over the fact that I agree with much of the thrust of his questions to me today, which is not something that I can say every week. This Government will set out our own budget plans in a couple of weeks' time, and the finance secretary will set out the budget to this Parliament. That is right and proper. We set out our income tax proposals in our manifesto, and I would remind Willie Rennie that we won the election on the strength of that manifesto. Willie Rennie is right. I will say very clearly to Philip Hammond this afternoon. Again, I hope that Willie Rennie and the Labour MSPs—and I am pretty sure that the Greens will back me on this—that it is not acceptable that the Scottish Government's budget will be reduced by £2.9 billion, 9 per cent in real terms by the end of this decade, compared to when the Conservatives took office. I hope that, with the exception of the Conservatives, everybody in this chamber would get behind me on that message. We were promised, were we not, in the EU referendum that our leave vote would deliver £350 million a week extra for the national health service. We heard from Philip Hammond last week not one single extra penny for the NHS or for social care. It was absolutely disgraceful. All we heard were more cuts and extra borrowing and a bleak outlook for living standards on the economy. That is the price of Tory Government at Westminster. The number of supplementaries is first from Rona Mackay. Thank you, Presiding Officer. Laked Cabinet letters suggest that the Home Office under Theresa May wanted children of illegal immigrants to go to the bottom of the list for school places. Is that a chilling insight into where an increasingly right-wing Tory Government wants to drag the UK? Unfortunately, I take a very simple view of this. I know that there are debates around immigration and some of those debates are legitimate issues that we have to engage with. The simple view that all of us should take on this is that children are children. When children are in this country, we should support them and ensure that they get access to education. I would hope that that is something everybody would agree with on basic grounds of morality and human rights. Graham Simpson Over the past six years, Scottish Government funding for councils has fallen by 8.4 per cent in real terms. That is a choice that this Government has made. Can the First Minister assure us that that trend will be reversed when the draft budget is published later this month? The First Minister We will set out our budget when the Finance Secretary stands up in the chamber on 15 December and outlines our plans for local government and other areas of our responsibility. On the issue of local government funding, we live in tough times. I recognise how tough it is and has been for local government. The Government, though, has treated local government fairly. The Accounts Commission report published this week showed that the decline in local government funding was broadly in line with the decline in the Scottish Government funding overall. There were also some interesting figures published this week that the member, given that he is a Tory member, might want to have a look at IFS figures publishing council-level figures across the UK, which found that cuts to local government funding—reductions in local government funding in Scotland and in Wales, for that matter—were smaller over the period it looked at than it had been in England. Perhaps the member should have a word with his own colleagues before he stands up in the chamber and talks to this Government about it when it is the cuts from his party to this Government that is causing so many of the problems. George Adam Ruth Davidson said before the EU referendum that the leave campaign was based on lies. After the EU referendum, she still said that she wanted to remain in the single market. She since sold out completely, demanding that the Scottish Government signs up for whatever hard right Tory Brexit Theresa May decides upon. How will the First Minister ensure Scotland is protected from the dishonest interest of Ruth Davidson's Tory party? The First Minister Ruth Davidson's shifting position on those matters shows that she is more interested in standing up for the Brexit years in the Tory party than she is in standing up for Scotland's interests. It is only two years ago that Ruth Davidson said that voting no would protect her place in Europe. She said a few months ago that she wanted Scotland in the UK to stay in the European Union. After the referendum, she said that she wanted Scotland to stay in the single market. Now she has sold out on that as well. I think that what we are learning over this period is that Ruth Davidson's position on those matters, as it is no doubt the case on many other things, is exactly what our bosses in London tell her that her position should be. Pauline McNeill Thank you, Presiding Officer. Franz Ferdinand, Stone Roses, Calvin Harris, Blur, Beyoncé are just some of the acts that have headlined tea in the park, Scotland's award-winning music festival. Sadly, they will not be a feature of this summer's live music programme. Will the First Minister join with me and recognise the huge contribution that DF concerts headed by Geoff Ellis has made to Scotland's vibrant live music scene? Not to mention the Scottish economy, but will she consider what the Scottish Government can do to overcome the problems faced by the organisers who say that there were many barriers leading to the cancellation of the event, and for that matter, any other organiser who wants to organise a live music festival? Scotland should maintain its track record and be a world-leading location for live music festivals. I hope that she agrees. First Minister I welcome Pauline McNeill's question. I know that she was not in the last Parliament, but she should maybe have a word with some of her colleagues about the attitude that she took when this Government did try to assist tea in the park to continue to be the success that it was. Can I pay tribute to the organisers of tea in the park? If it makes Pauline McNeill feel any better, I got some grief on Sunday from my 16-year-old nephew who went to tea in the park for the first time last year and was looking forward to going this year and is bitterly disappointed that he is not going to be going. Tea in the park, the organisers have set out why they have taken this decision. It is a break, not the termination of tea in the park, and I am sure that we all wish the festival every success in the future. It has been incredibly good for Scottish culture and for the Scottish economy, and I hope that we see it back before too much longer. Does the First Minister share my concerns on comments this week from Defence Secretary Michael Fallon that UK shipbuilding needs rebalancing, suggesting a risk to jobs in Scotland? What representations will the Scottish Government be making to the MOD to ensure that it keeps promises made to workers on the Clyde? We will continue to argue the case for Scottish shipbuilding. The Clyde yards, and I know this from my past constituency experience, are the best place in the whole of the UK to build ships. They have an expert and dedicated workforce as well as world-class facilities. We have seen the promises that were made to our shipyards in the independence referendum, which has watered down since then. The member is absolutely right to say that we cannot take for granted that the UK Government will look after the interests of our shipyards. We will have to continue to make the case, and this Government will certainly do that. I think that most people, most fair-minded people, will agree with the First Minister and condemn the failed austerity of the Tory Government. Given the devastating impact that that failed austerity is having on public services and communities up and down Scotland, will she not think again and look to use the powers of this Parliament to protect the most vulnerable in our communities? We will use the powers of this Parliament to protect public services and the most vulnerable in our communities. That is why, for example, we will take a different position to the Tory Government at Westminster over a tax cut for the 10 per cent highest earners in the country. We do not think that that is the right use of resources at this time. We also have to be mindful of the squeeze on people's living standards. We saw a report last week that we are about to see the longest period of wage stagnation in this country since the Second World War. That is what the Tory Government is inflicting on people the length and breadth of this country. We have to take a balanced view of protecting the vulnerable, as we have always done in our mitigation of welfare cuts, making sure that we protect our public services, which we are doing, for example, through our record investments in the national health service, but also making sure that we are taking action to protect the living standards of people across our country who are struggling to make ends meet. John Mason To ask the First Minister in light of comments by the Secretary of State for Scotland what commitments the Scottish Government has received from the UK Government regarding the devolution of further powers. First Minister We have received no commitments at all from the UK Government regarding the devolution of further powers. We saw the comments made by the Secretary of State for Scotland at the weekend as a result of that. The finance secretary has written to the Secretary of State, asking him to explain exactly what powers he is referring to. We look forward to having a discussion on that. We await that answer, but I note that when asked about new powers for Scotland over agriculture and fishing, the DEFRA Minister told the House of Commons that these would be part of a UK-wide framework. That does not sound to me like new powers. Let me say that that would be simply unacceptable. We cannot allow Brexit to become a Westminster power grab and this Government will not stand back and let that happen. John Mason Her answer confirms my concerns, I have to say. We have had warm words about further devolution from David Mundell before. Does she share my concerns? She mentions agriculture and fisheries. Does she share my concerns that the UK Government has used fishing in the past as a bargaining chip and might well use it again? I think that that is a reasonable concern, because we know from official papers that previously UK Governments considered fishing to be, and I quote, expendable. They sacrificed the fishing industry in exchange for wider interests. I do not think that that betrayal will be forgotten by those in the fishing industry or in the north-east of Scotland more generally. I would take no comfort from the prospect of a UK-wide framework on fishing. The Parliament should have no doubts that this Government will do everything to protect and secure Scotland's interests and the discussions that lie ahead. That will include making sure that any powers coming back to Westminster from Europe do not stay in Westminster that, as far as possible, they come to Scotland. That is what people would want to see us argue for. Adam Tomkins The First Minister mentioned agriculture a few moments ago. Given the ffiasco of the SNP's mismanagement of cap payments in Scotland, there are many of us who worry about agriculture falling under the SNP's responsibility. Why would the First Minister prefer Scottish farming to be run by Brussels and not by this Parliament? Agriculture, of course, is within the Government's responsibilities. I think that what I heard from Adam Tomkins was exactly what John Mason was expressing concern over. I think that we are hearing the ground being prepared for that Westminster power grab that I spoke about. If there are powers coming back from Brussels to the UK, in areas of devolved competence that they should not stop at Westminster, they should come direct to this Government. I would hope that nobody in this Parliament would argue for anything different. Mike Rumbles As we know, agriculture has already fully devolved to the Scottish Government, although common agricultural policy farm payments worth hundreds of millions of pounds will be paid to Scottish farmers through to 2020. Once that ends, we should be free to design our own system of farm payments. Will the Scottish Government, as I have been asking the members of us a long time now, set up a specialist group now to design options that we want to see how our funding should be spent in Scotland post 2020? We will consider all options and we will talk to stakeholders in the agriculture industry and indeed in other industries that are affected by the Brexit vote. We have given commitments to our farming community in terms of cap payments over the next few years. There is a fundamental question that we have to settle first. I really hope that we have the support of Mike Rumbles and the Liberal Democrats, because we do not even have a commitment that Scotland's share of that funding will come to Scotland. Let us do those things in good order. As we fight those battles, because I fear that some of them will be quite tough battles, I hope that we will have the support of everybody across the chamber, including the Conservatives. I will repeat this. It will not be acceptable for powers to be taken away from this Parliament or funding that should lie with this Parliament to not be given to this Parliament and everybody in this chamber should resist those possibilities. To ask the First Minister what the Scottish Government's position is on the ability of the education agencies to deliver the curriculum for excellence. As I said earlier on, our education agencies bring strengths and benefits to education and to the curriculum for excellence. As I said in response to Ruth Davidson, we are asking some hard fundamental questions about school education and the best way to empower schools to improve. That is why we launched the governance review, which will look at the roles and responsibilities of those agencies and of local government and of the Scottish Government. That is the right way forward, and it is a key part of our efforts to raise attainment for all and to close the attainment gap. First Minister, at the education committee both last week and this week, there was an admission from SQA and from Education Scotland that significant issues have arisen about subject choice in S4, S5 and S6, with many parents and teachers expressing their concern that there has been a narrowing of the subject choice because of the structure of the curriculum for excellence. John Swinney acknowledged in a parliamentary answer that he gave on 9 June. What is the First Minister doing to address that concern, given the very serious implications for college, university and job applications? The issues of subject choice are largely determined at school level, but we want to make sure that all young people get access to the qualifications that they want to and are able to take to best equip them for the higher education and job opportunities that lie ahead. Of course, we will talk to and discuss any concerns around that with the SQA, with Education Scotland, with parents or any other part of the education system. As John Swinney has been doing around bureaucracy in schools, around the governance of our schools, around getting extra money into areas of greatest need to help us to raise attainment, we will respond positively to all those issues. While the governance review sets out to empower local communities and schools, as it has outlined by creating a clear national framework, it also sets out proposals to strengthen the middle. What role is envisaged for local authorities in doing so? The OECD review that was published this time last year recommended the strengthening of the middle, the tear of education governance that lies between national government and schools. That means, among other things, considering the role of local authorities and agencies in leading and supporting improvement, exactly what we have been talking about today. I agree with the OECD that increased collaboration and greater leadership in that middle tier is essential to support our ambition of raising standards and closing the attainment gap. That is exactly why the governance review has included the question of how, for example, school clusters should operate and how councils can collaborate regionally to improve school performance and education. Those are all live issues being looked at under the governance review, and I will repeat what I said earlier on. I would hope that all members with an interest in this area of policy contribute to that review, because the Government looks forward to taking its findings forward early in the new year. The First Minister has repeatedly prayed in aid today the Scottish Government schools governance review, but that governance review is about centralising control of schools and their budgets away from local authorities. Can she explain then how that will address the problem of the dysfunctionality of the SQA and of Education Scotland lead-bearing committee this week? That is one of the really depressing things about those debates. We have a consensus, albeit that we might have disagreements about how to do things. We have a consensus that we need to reform our education system to tackle some of those problems and drive up standards. We have published a governance review to have an open, honest, fundamental look at our school governance. At the heart of that review is a presumption—I think that it is on the first page—that that whole review has been taken forward on the basis of a presumption that roles and responsibilities lie at individual school level. It is about the opposite of centralisation. It is about decentralising power down to individual schools. I recognise that this is a priority area, not just for the Government but for parties across the chamber. Let us have a grown-up debate. Let us not just immediately indulge in default opposition and sloganeering around this. Let us have a grown-up debate about how to take our schools and our education system forward. To ask the First Minister what steps the Scottish Government is taking to address workforce issues in the NHS. We appreciate the achievements of all of our NHS Scotland staff in delivering safe, high-quality health and care services day in and day out to the people of Scotland. Staffing has increased to historically high levels with more than 11,000 additional staff since the Government took office, including more than 2,000 qualified nurses and midwives, and more than 1,500 more consultants. We are also producing a national health and social care workforce plan to discuss with staff how we ensure the right numbers and the right mix of skills across acute and community health services. That builds on the creation of our nursing and midwifery workforce planning tools, which have helped to drive increases in the nursing establishment. Despite the warm words that the First Minister has answered, after 10 years of this Government, the reality is in fact very different. Under this Government and this Health Secretary, 9 out of 10 nurses say that their workload is getting worse. 1 in 3 nurses say that there is not enough of them to do their jobs properly. There has been a failure to properly workforce plan with nursing vacancies up, midwifery vacancies up, GP vacancies up, consultant vacancies up, waiting times up, number of failed standards up and private spend up to when will the First Minister wake up, take responsibility and act for our NHS. Annas Sarwar might like to ignore or pretend that the fact does not exist, but since this Government took office, there are 11,000 more people working in our NHS now than there were then. That includes more than 2,000 extra nurses. There are record numbers of staff working in our health service. Yes, they are working hard and they work under pressure because of the rising demand for health services, largely due to the ageing population. That is why we are not saying job done. We are continuing to invest more and more in our health service so that we can employ more staff, but also reform services so that we build up social care, primary care and mental health services in the community to take the pressure off our acute services. There is a lot of work still to be done around that. I would not say otherwise, but our health service is performing better in many key indicators than the health services in any other part of the UK. Let's get behind those working in our health service, get behind the investment plans of this Government, get behind the reform plans of this Government, because every time we bring forward a proposal for reform and our staff and colleagues oppose that proposal for reform. Labour has no idea the lowest level of funding promise of all parties, completely bereft of any positive contribution to make to this debate. As long as that remains the case, we will get on with doing the hard work for Scotland's patients. Emma Harper To ask the First Minister whether she will provide an update following her visit to Dublin. The purpose of the visit to Dublin was to build on the already strong economic, cultural and political links that exist between Scotland and Ireland. Following a meeting with the T-Shark in Dakenny at the British Irish Council last week, I met in Dublin with the president of Ireland, the Deputy Prime Minister and the Minister for Foreign Affairs to discuss continued co-operation on a range of issues. I also engaged with more than 120 Irish-based business chief executives at an event hosted by Ireland's National Business Confederation to stress that Scotland remains open for business and will continue to be an attractive place to invest. Finally, I had the privilege of addressing the Shanard, the upper house of the Irish Parliament to stress again the close links between Scotland and Ireland that I hope we will see flourish in the years to come. Emma Harper I thank the First Minister for that answer. Despite the howls of horror from Murdo Fraser and other Tories that Scotland would dare to engage directly with another country on matters of mutual interest, isn't it the case that closer Scottish Irish co-operation could create significant opportunities for both nations? Isn't it clear that other EU countries increasingly want to engage with an internationalist Scottish Government as the UK's Government's focus becomes more narrow and isolationist? The First Minister Most of the people that I spoke to in Ireland at the start of the week are horrified at the direction that the UK Government is taking. We have to remember that the Brexit vote did not just disregard the interests and views of people in Scotland, it also completely disregarded the implications of Brexit for the Irish peace process and the Good Friday agreement. There are very real issues of real concern to the people of Ireland that they are now faced with having to work through in order to deal with the negligence and the recklessness of a Tory Government that wasn't interested in those issues during the referendum campaign. It is important that, whether it is in Ireland or any other part of the European Union, we give a message on Scotland's behalf that Scotland is open and internationalist and outward looking that we want to work with other independent countries for the common good. Right now, the Westminster Government is giving the complete opposite message to that, which is why it is more important than it has ever been that we take Scotland's message to Europe and the world. Lewis MacDonald Thank you very much. For the avoidance of doubt, can the First Minister tell us if she had any formal discussions on Brexit with the Irish Government in Dublin this week? The First Minister I can say that Brexit featured in pretty much every single discussion that I had—government-wise, politician-wise, economy-wise in every other sense. The Irish Government, like other European Governments, is not formally negotiating with the UK or any part of the UK before the triggering of article 50. That is a position that is well-known, or certainly should be well-known, but it is important. It was recognised in Ireland, as it has been recognised in other countries that we have been speaking to. It is important that Scotland's position is understood that there is an awareness of the fact that in the UK we are not all right-wing Brexiteers, like the Conservative Government, that there are people who want to continue to build relationships and to work co-operatively with other countries across Europe. I will be proud to continue to send that message across Europe. I hope that, even if we do not get support from the Tories on that, we would get support from the Labour Benches as we do so. That concludes First Minister's questions. We will now move on to members' business. I would ask members—it is in the name of Ash Denham—to lead quietly, as possible. We will take a few moments to change seats.


In this lecture we will see the relations between transfer matrices and the fixed parameter we have obtained. And also we will analyze one of the basic optical cells known as FODO cells. Also we will introduce a new parameter namely dispersion which takes care of the dynamics of the particles which have momentum deviated than the design. So we will start this. Now solving the Hilse equation we have seen two methods. One is the piece by solution in which we have breakdown the optics in the smaller pieces and then in each piece keeping the key constant we have opportunity solution. This is similar to what we solve differential equation in simple numerical method. This means we probe the equation in different smaller segments and each segment we solve the equation. And second and more elegant way was to introduce the solution using some optical parameters, these parameters. And when we were obtaining the solution by this method we have got invariant of motion namely as atoms. In this case if k is periodic then we can obtain solution in which twist parameters are also periodic. Means in the case of periodic k there may be possible range of solutions among which we obtain those choose those parameters which are periodic nature. We say this is the best solution. If we know values of twist parameter two locations can we connect the particles trajectories or particles coordinate between these two parameters or between these two locations. If yes we can have a relationship between the twist parameters and matrices because matrix connect the coordinates between these two points. And if we can connect these two coordinates at these two locations in the twist parameters we can have one-to-one relation between the matrices and twist parameters. So, we are going to do that. Now as Hill's equation we have a general solution in this fashion x is equal to a root beta cos phi plus b root beta sin phi. Here beta and phi are the function of the s and because this is a second order differential equation. So, we have two constants of integration a and b with these constants are determined using the usual conditions. And if we differentiate this x with respect to s we get x prime and which is a alpha root beta cos phi because we have when we differentiate this beta root beta we will get one upon two root beta d beta by ds and one upon two beta prime is minus alpha which is written here minus alpha upon root beta cos phi. Then we will differentiate this phi. So, we will get minus 3 upon root beta sin phi d phi by ds and d phi by ds is one by beta. So, this root beta and one by beta will give you the one upon root beta which is zero one by root beta. Similarly, we will differentiate this term. So, we will get alpha upon root beta sin phi and b upon root beta cos phi. So, this gives you the x prime and as I have put earlier that this a and b can be determined using the initial conditions. So, let the initial condition like this. Let the initial phase phi is equal to zero and the amplitude function of this parameter beta has the value beta zero at that location. And the initial coordinates of the particle be x0 and x0 prime. So, if here we put x is equal to x0 and a then root beta is root beta zero because it is the initial. Then cos phi phi because we are taking initial as zero. So, cos phi will be one and here it is the sin phi. So, initial phi means zero. So, this term will be zero. So, we will have x0 is equal to a root beta which is written. Similarly, we will obtain the initial x prime. x prime initial is x prime initial zero because sin phi itself is zero but phi is equal to zero. So, these are the two equations which relates initial coordinates to initial parameters. And using these two equations we can obtain the a and b. So, now here constant values of a and b are as a function of initial parameters initial coordinate at zero and initial this parameters beta zero and alpha zero. Now, we can put the values of this a and b in the solution in this solution. So, we do that after a little bit of algebra means when we will put the value of this a and b in this equation and arranging the terms together of the x0 and x0 prime. You will get x is equal to root beta upon beta zero cos phi plus alpha zero sin phi and coefficient of x is a prime zero will be beta root beta sin phi square with square root. Here beta you can say suppose this is the orbit of the sin proton and this is our initial point where we are defining beta zero alpha zero and phi is equal to zero. This is our initial point initial and second point is say here where we are talking about beta alpha is that this parameter and between these the phase advance is phi. So, this beta and this beta are at this location and these are at this location and this beta zero and this beta zero are the parameters at initial point. So, now here you can see that x has been written down in terms of x0 and x prime zero means in terms of the initial coordinate. So, now the coordinates of here x and x prime here the coordinates were x0 and x0 prime. So, now x has been written down in terms of x0 and x prime zero. We did this using the transform matrices. Similarly x prime can also be written down using these values of a and b and when we do a little bit of algebra we got this equation. So, now these two relations give us the coordinates at another point here in terms of the coordinate of the initial point. So, this is similar to the transform matrices. So, if we compare these terms using the transform matrices from here to here means suppose we have m1 to transform matrix from point 1 to 2 which we can obtain using the multiplying transform matrices of each element which occurs between these two points then that matrix and this matrix should be the same. So, now this you can see is exactly in the shape of transform matrices but this transform matrix contains the twist parameters as the elements means we have now transform matrices in terms of twist parameters. We can also obtain the transform matrices in terms of the magnetic strength the magnetic effective length L etcetera which we did earlier using the piecewise solution then these two matrices must be equal because these both are the solution of the same equations. So, if we do that we equate these elements we get the connection between transform matrices and twist parameters. Now, here you can see that if suppose this is a orbit of the synchrotron and this is our initial point as I said initial point and this is our final point or point 2. If we move the point 2 and reach here after one term in this case beta should be equal to beta naught and alpha should be equal to alpha naught. When you will do this you will get beta upon beta naught here beta upon beta and this will be cancelled out. So, you will have cos phi plus alpha sin phi. Here beta beta naught will become beta because beta naught equal to beta and here 1 plus alpha alpha naught upon beta beta naught this term will become minus 1 plus alpha square because alpha naught is equal to alpha and beta naught is equal to beta. So, root beta beta naught will be beta. So, this is gamma which is written here and similarly these beta naught and beta will be cancelled out. So, we will have cos phi plus alpha sin phi. So, this matrix is for the one term where we have periodic solution of twist parameters. Since if we want to know the transfer matrix of one complete term in terms of this parameter where we are choosing the periodic solution then transfer matrix is this. Now, this matrix can be written down in a very interesting form. Our matrix was cos phi plus alpha sin phi beta sin phi minus gamma sin phi and cos phi minus alpha sin phi. This was our one term matrix which we obtained earlier. Now, this can be written down in this fashion in the form of summation of two matrices. The first matrix is cos phi 0 0 cos phi and second matrix is alpha sin phi beta sin phi minus gamma sin phi minus alpha sin phi. So, you can take common cos phi here and here sin phi. So, we will do that. So, 1 0 0 1 and alpha beta minus gamma minus alpha sin phi. Now, you can see that this is the unit matrix 1 0 and 0. And if we multiply this matrix with itself then what will we get? We will see this alpha. We will get alpha square minus gamma beta here and alpha square, you know that alpha square plus 1 is equal to gamma beta. So, alpha square minus gamma beta will be minus 1. So, this will be minus 1. This element will be 0, this element will be 0 and this element again will be alpha square minus gamma beta which is equal to minus 1. So, here you get the identity matrix and here this matrix is that kind of matrix whose square gives you the identity matrix with minus sign. Means we can write down this in this version. The square of this matrix is minus unit matrix. Means one term matrix can be written down as unit matrix cos phi plus j sin phi. This is similar which we write down as unit is to eta phi is equal to cos phi plus eta sin phi. Means one term matrix can be written down in the Euler form. In the Euler form what is the use of this? Suppose you want to know m one term power m means after n terms what will happen? Using this relation you can obtain m power of m one term very easy. And another important property of this matrix is the trace. This matrix again I am writing for it as cos phi plus alpha sin phi here beta sin phi here minus gamma sin phi and here cos phi minus alpha sin phi.   So modulus of trace of our matrix must be less than 2 for stable motion. What does that mean? Suppose we are connecting various magnets for making the objects like this and now by putting matrices of each element so first element is drift then focusing lens then drift then de-focusing lens then drift then dipole magnet then drift then focusing lens then drift then de-focusing lens then drift and we multiply these matrices to get an overall transfer matrix and if you found that the trace is greater than 2 means no bounded oscillatory beta term motion is possible in that kind of objects. So we have to change the strength of our magnets so that trace becomes less than 2 and in case of synchroton no motion will be possible or synchroton cannot be run if trace is greater than 2 for that matrix. So one term matrix in the synchroton should have trace less than 2 for stable motion. So we have to check whether our matrices overall matrix produces a trace less than 1 if not then we have to change our optics accordingly. Now in one complete term means we started from the initial point and in synchroton we again reached to this point this is one complete term if the phase advance of this one complete term is phi this is the phi so phi by 2 pi this will give you the number of betatron oscillations in one complete term the number of betatron oscillations in one complete term is known as betatron tune and this betatron tune is very very important parameter for analyzing the beam dynamics and synchrotons we will see a little bit about of betatron tune when we will study about the chromaticity in later chapters there will be two betatron tune one for the horizontal plane and one for the vertical plane now we will analyze the tools which we have learned so far using those tools we will analyze some optics so let the very simple optics here some focusing quadrupole, then drift space then defocusing quadrupole, then drift space then focusing quadrupole, then drift space then defocusing quadrupole then drift space like that this is repeated means this is a periodic optics in which this basic cell you can say this basic cell been repeated many times. Here it is the focusing quadruple so f this is drift space means open space you can say o this is again a defocusing quadruple so you can say this is d and again open space o. So this kind of optics is f, o, d, o photo optics so this cell is photo cell and now you can see that in this figure there is a repetition of four such cells and it may continue like that. Here we are assuming a very simple optics means focusing quadruple and defocusing quadruple have the same strength in magnitude. Sine wise will be different focusing quadruple has minus k strength and defocusing quadruple has the k strength. So the strength in magnitude are same for both the quadruple magnets and length of each drift space is same. This drift space has the same length as of this disk space and all other drift space also have the same length as of this. So now if we draw once cell only which is repeated then this will be look like so from point a to point b we have one photo cell and here you can see that when we obtain the cell in this fashion in this cell this quadruple magnet is half only and this quadruple magnet is also half and this is the full quadruple magnet in this cell. The remaining half will be in the next cell and this remaining half will be in the previous cell. So now designate this drift space by L. This is the length of the disk space. Consider these quadruple magnets as the thin lines means we are ignoring the length of these quadruple and taking it as a point focusing lens. So from a star to symmetry point I am talking about this point symmetry point you can see that this is the symmetry point means here you have focusing quadruple length and de-focusing then you put a mirror at this location P you will get the complete optics. So P is the symmetry point. So up to symmetry point if we calculate it the remaining will be the same. So M of half de-focusing quadruple M of drift space length L and M of half focusing quadruple M means matrices. So these will be the transfer matrices and in this order if we will multiply we will get the matrices to the symmetry point. So let us do that. The first half cell will be first of all the particle will see the focusing lens. So 1 0 minus 1 by F1 then a drift space of length L and then de-focusing quadruple of length L. Up to the half cell de-focusing quadruple is also half. The remaining half will be after symmetry point. So here what we are writing down F this is the focal length of the half quadruple. For full quadruple the focal length will be half of this. So after multiplying these three matrices we get this matrix. And you can see that this element is with minus sign means this shows overall focusing in this particular plane. In later half after the mirror symmetry the order of the focusing and de-focusing magnet versus and then and when we multiply it we get matrix similar to the above here plus sign and here minus sign. Now if we multiply these two matrices together we get a complete matrix of the photocell. And so complete matrix of the photocell will look like this. These two elements are equal and this is 2 L1 plus L5 and this again shows the focusing characteristic of this photocell. Now if solution is periodic if you want to see that solution which is periodic in nature then this matrix must be equal to one term matrix. Means what we can do this element will be equivalent to beta sign for and this beta will be the beta at the location of the starting point of the cell where beta in the focusing plane will be the maximum. Why maximum we will see that. So we have made this kind of matrix this is our cell this is focusing quadrupole this is de-focusing quadrupole this is again a focusing quadrupole. So after focusing quadrupole before focusing quadrupole we will have like this and this magnet will focus the wing so size will again reduce so this will give a location of maximum beta means at this location d beta by ds will be 0 means at this location alpha will be 0. Similarly alpha will be 0 here and after this lens after de-focusing quadrupole again wing will become divergent so this will have a beta minimum point this point is beta minimum point and here again alpha will be 0. So now if we will compare element by element so beta sign phi will be 2l1 plus f and because here alpha is 0 and we know that gamma is equal to 1 plus alpha square by beta alpha is 0 so gamma will be 1 by beta. So at this location we can write down that this quantity which is equal to minus gamma sign phi because alpha is 0 at this location so this will be minus 1 by beta sign. So this element should be equal to beta sign phi and this element should be equal to minus 1 by beta sign phi and we did this these are the two relations. Now if we divide this equation by this equation then sign phi will be cancelled out and only beta max will be eliminated with square sign and here you will get 1 plus alpha f upon 1 minus alpha. So this gives you the value of maximum beta at this point this value of maximum beta in terms of magnetic or optics geometry means what is the length of the digital base what you what is the focal length here chosen for the quadrupole using these parameters you can obtain what is the value of beta max here this beta max is for a particular solution which is periodic in nature. So this beta max will give you the periodic solution of this prototype so using these two transfer matrices comparing these two matrices one obtained by piecewise solution and other one obtained using the quiz parameter we can get this solution or values of these quiz parameters at the different locations of the optics. If we multiply instead of dividing these two equation beta will cancel out and we get the value of the phase sign phi. So sign phi will be this so now we get beta as well as phase advance in this cell. Similarly m11 element with one turn matrix in one turn matrix we write down cos phi plus alpha sign phi and beta sign phi then minus gamma sign phi and then cos phi minus alpha sign phi because at that location alpha is 0 so this will only cos phi and cos phi is written here it is 1 minus 2 L square and because cos phi must be smaller than 1 and greater than minus 1 when you put these limits you will get the focal length of half quadrupole should be greater than the drift space length means if you want to make a stable photocell this condition has to match means the chosen quadrupole should have the focal length greater than the length of the drift space between the two quadruples. Now as cos phi is 1 minus 2 sin square phi by 2 so sin phi by 2 is L by f why are we why we are doing this kind of calculation here from cos phi to sin phi by 2 because sin phi by 2 will give the phase advance of the half cell and at the mirror symmetry we have seen that there will be beta minimum so by knowing these elements we can obtain what is the value of beta minimum in this photocell we have obtained the values of beta max now we will obtain the values of beta because up to the half point the starting point will have beta max and at the symmetry point we will have beta mean so e square root of beta mean beta max and multiplied with sin phi by 2 because we have either here at this location now one term matrix will not be used here here we will use complete matrix that is root beta 2 by beta 1 cos phi plus alpha 1 sin phi and root beta 1 beta 2 sin phi this matrix will be used here because up to half cell no periodic solution will be there periodic solution will be for full set so this is written here basically so using this now we know what is the value of beta max put that value of beta max here put the sin phi by 2 from here and you will get beta minimum so now you have beta max now you have the values of beta mean and the phase advance means you have obtained values of these parameters completely at different locations of this cell


Next, we're going to go back and add a slider joint to the rack here. So assemble as build joint, I'm going to select my two components, my rack, and then choose the base. Then I'm going to go to motion, change it to slider, give it the edge you want it to slide about. So I'm going to click right on that edge, right on that point, and now I've got that motion. There we have it. We have the rotational and the translational here, the slider. Perfect. The other thing we can see here is we are defying some laws of physics. So let's go ahead and fix it. And to do that, we're going to go back to assemble and we're going to select motion link. The important thing to remember with motion link is you set it between joints and not between components. You have to go to your browser here and tell it which joints do you want to set the relationship with. So here we want a relationship between the revolute and the slider. Usually you see something like this. It's just kind of spinning like crazy.