It seems like every Thursday throughout this year Major League Baseball Eastern, but the early only slate is actually bigger It is a five game slate. So, you know what that means It is time for a split slate podcast for today here on the solo shot We'll go through the main slate first. We'll jump ahead after that to the early only slate So that if you're listening after 12 35 p.m. Eastern, you can still Listen to the first part of the podcast there But if you are looking right now for the early only slate discussion before 12 35 p.m. Eastern Check out the episode description wherever you get your podcast and jump there right now And then dive on in the rest of the slate welcome on into the solo shot That's right here on the fan dual podcast network and number fire dot com My name is jim sonnis. I am a senior writer and analyst for number fire dot com here to break down both the early only And the main slate over at fan dual dot com the early only again at 12 35 p.m. Eastern the main at 7 10 p.m. Eastern so again if you want to jump ahead check out the description There will be a timestamp there letting you know where to go If you want to get that main or that early only slate discussion We'll dive in the main slate here in just one second But first a quick reminder to make sure you are subscribed to the number fire daily fantasy podcast feed wherever you get Your podcast because we have nascar and usc coming up tomorrow and they'll be every weekday Pga of course with the pga championship is now locked But every week we do the pga podcast still you're on the number fire daily fantasy podcast feed So go search for The number fire daily fantasy podcast feed wherever you get your podcast hit subscribe If you like what you hear leave us a rating and review as well The nba playoffs are heating up and you can make every game feel like game seven on vandal sports book an Official partner of the nba throughout the playoffs all customers can place a no sweat same game parlay each week You'll get up to 20 dollars and free bets if you don't win Fandal has so many ways to play and best of all when you do win You'll get paid faster than a fast break either way You'll get up to 20 dollars and free bets if your same game parlay during the playoffs does not win Fandal sports book an official partner of the nba Must be 21 plus in select states refund issued as non-withdrawable free bets that expire in seven days after receipt max free bet 20 dollars per week restrictions apply C terms at sportsbook.fandual.com gambling problem call 1 800 gambler who's a fandual.com slash rg In arizona call 100 next step or text next step defy 33 42 in connecticut 1888 789 7777 written cc pg.org slash chat in indiana 109 with it in louisiana 1877 770 stop in new york 18778 hope and why in tennessee call the red line at 1889 and 789 In west virginia 1 800 gambler.net or in wyoming 1805 222 4700 let's take in now to this three game main slate once again lock is at 710 p.m. Eastern the only weather notes for this main slate is that it is colder in boston for the maritas and red socks I would downgrade batters there for that one the pitching preview for this main is slightly as zack gallant checking in At $10,600 from revoltez is $9,700 and george curvy the only other guy above 8,000 He is $8,500 It is pretty obvious to say. I love zack gallant in this spot And it's not just a product of tonight's slate being a shorter one I just think that he is genuinely a fantastic play for dfs gallant is facing the cubs, which is a good matchup for a Righty their active roster has a 27 strikeout rate against righties in 2022 Which is the highest mark on this main slate gallant is also just on an absolute heater to start the year He has made six starts. He has a 2.89 skill interactive era with a 27 strikeout rate And a 31 percent hard hit rate allowed. That's kept his era down at 1.05, which is Basically sigh young level stuff and it's not just the results His his expected era at baseball savant is under two So gallant when you dig in is not getting a ton of whiffs, but that's never really been his game He's a guy who gets a lot of called strikes I think that he will keep up the great stuff He has shown to open the year might not stick at quite this level But he also doesn't need to because I mean even to regress that gallant is going to be very good I've got a projected for 6.9 strikeouts for tonight Nobody else on this main slate is even at higher at five or higher So I think that for this slate you plug in zack gallant and you figure out the rest from there You plug him in you log out figure out the rest in terms of stacking He is definitively the top guy for tonight Now number two in the strikeout projections Is actually frommer valdez and I find that thrilling because I love valdez as a pitcher a real world Major league baseball pitcher But I don't often get to use him in dfs because of the low strikeout rate But I get to using tonight and I'm very on board with doing that in my non gallant line I'm just you as they may be Valdez has some just like sicko level numbers this year his skill interactive era is 3.27 But a 34 hard hit rate and my favorite one he has let up a fly ball 7 percent of the time seven as in seven Seven one single digit seven percent fly ball rate, which is wild He hasn't gotten a lot of strikeouts and those are huge for dfs because they get your points We want points, you know, it's pretty easy helps boost both your floor and your ceiling But I've got valdez projected for hundred pitches which gets him a decent strikeout number just via length and I know the rest of what he does will be good valdez is facing the rangers 22 strikeout rate against leptis not great, but not bad either So i'm very okay with how this slate wound up breaking. I know it's a three game slate But I think this is actually pretty good. I'm still gonna favor gallant by a wide margin But I will take advantage and dabble in valdez when I don't go there I think these two are just rock star level plays and i'm very on board with using both in here But gallant to me is a runaway favorite. I think the top stack here has to be the astros They're facing glenn auto and auto I think is a better picture than his 6.38 e r a and I would expect that to come down But there are legitimate reasons that number is so high Specifically auto is walking a lot of guys right now He's also letting too much hard contact and that's different than the issues He had in the small sample last year six starts last year four in the majors so far this year Because last year's walker is seven percent with a 37 percent heart rate, which means He could get better But we've seen glimpses of these issues from him in the past specifically back in the minors So it's not a huge surprise to see some of those those flaws Crop back up here once again. It's led to a 7.73 expected e r a which is actually higher than his real mark right now Now auto has faced some tough teams But houston is one of the tough teams he faced two runs allowed in four and a third innings Which is not terrible, but they got a 130 w rc plus against righties a 200 iso And both those numbers are far and away the top marks on this main slate It's just a bad situation for auto So I will rank the astros first by a significant margin here And I think that it's it's just pretty obvious why we should want to do so In the small sample auto has really struggled against lefties So we're i'm always high on your don alvarez and cow thucker that I'll be higher on them here That's no change, but we talked to michael brantley earlier on the week how i'm changing my view of him and he's kept up um I guess what I would say is Slowly turning up the knob on his upside I think that it's less appealing with offense getting higher throughout the throughout the league But do still think that brantley is an option to 3000 and the guy I will use within my astro stack Our second stack feels gross, but I do think it's correct That is the arizona diamond backs and it's in part by default because the mariners too many lefties for me to stack Against rich hill. I do like george kirby's talent a lot against the red sox The red sox will be next in this list. So they're third for me, but arizona I like a bit more they're facing marcus strome, which is why this feels gross because I adore marcus strome But he's coming off the covet i help. He's been on it for 11 days Did not make a rehab start so I have no idea what kind of condition he will be in For the start today or how long ago and there were some struggles for strome before his stint on the i l He was letting up a lot of hard contact The ground ball right was down to 46% And his swinging strike rate was 7.3 I would still expect strome to rebound eventually because it's a very good picture But right now he's not the typical mark of strome Arizona is not like a great team, but they're also pretty fun for stacking honestly I dig him a little bit. They got a 182 iso against righties with a 44 fly ball rates I kind of like them It's weird as that may be so the red sox and the right-handed mariners are options But I'd rate arizona a hair higher in this spot And they do have guys individuals who are fun for stacking alex thomas still batting low in the order But he's been awesome since he got called up dalton var show has been Phenomenal all year season long dynasty leagues where he's a catcher eligible sick love it christian walker david peralta They both have fly ball rates of about 47 percent against righties So those four var show thomas walker peralta all really good plays in my mind We'll see if katelle marté can play he's a bit banged up right now, but If he does play I'd be there. He hasn't been great so far this year potentially due to the injuries But if he does play I could be okay with it The problem is it's a hand injury and hand injuries always scare me about it even when they play so I could consider him, but I like those guys all a bit more That wraps up our main slate discussions Let's dive in now to the early only slate if you are listening to this after 12 35 p.m. Eastern. See you tomorrow Check back in there. It is a four or a five game slate for this early only slate Lock is a 12 35 p.m. Eastern for that one and the weather is all good Let's dive in to the pitching preview for the early only slate Chris bassa checks in at $10,400 with you darvish 91 Bruce Zimmerman up to $8,900 deservedly so in jordan montgomery rounds at the top group. He is $8,100 and to me On this early only slate. It is very clear that chris bassett is the top guy in the slate I'd expect montgomery to get a lot of buzz due to the matchup. I like basset a lot more to me personally Bassett checks every box Specifically he checks a strikeout box. He has a 27% strikeout rates so far this year That is the highest on the slate by five and a half percentage points in each guy's most relevant sample And bassett is stretched out. He's gone a hundred plus pitches each of his past two starts That's helped him flash a good amount of upside We've seen bassett get six plus strikeouts and all but one start He has hit eight in three out of seven and the cardinals have been getting better against righties They're wrc pluses up to 107 and they still have just a 19 strikeout rate So it's not a perfect spot by any means. That's why he checks almost every box match up not quite there But to me bassett clearly the top guy I've gotten projected for 6.2 strikeouts. Nobody else here is higher than 5.4 So to me bassett will be the top guy on the early only slate Number two, I'm going to go you darvish. I think that you could push back and say jordan montgomery But montgomery hasn't gone more than 90 pitches yet this year Kind of a lower strikeout guy. The matchup is very good, but I have my concerns. I have concerns about darvish too But I don't put them second anyway The first concern is the matchup because affiliates are a very good team. They have a 110 wrc plus against righties The second concern for darvish is strikeouts. His strikeout rate is 20 for the full season It does go up a hair to 21 percent in his past five starts with this lot of usage being up, but That's a lot high Not getting a lot of whiffs either with an 11 swing and strike rate That's why I still prefer bassett by a wide margin But darvish has still been solid. He's got a low walk rate. He's got solid batted ball data He's had good results and plus unlike montgomery his pitch count is very high So darvish and bassett are the only two guys on the slate I projected to throw more than 90 pitches darvish is at eight at 97 So i'm not high on him I'm just higher on him than others on the slate again I would expect montgomery to be more popular But I mean like you look at his k-prop and it's like absurd for today Relative to what he's done so far this year. So I think he'll be popular I just prefer darvish. So I will put him second here It's big rudging and I think that it's pretty he's pretty far behind bassett, but I will go basset one darvish two As far as stacking goes. I am waiting for the white socks to Snap out of their slump. They're wrc plus against right. He's still just 82 But they got high temperatures for today. It's 85 degrees That's 15 degrees higher than any other game And I think that we can stack the white socks here and should stack the white socks here They're facing carlos rnandez who's had a brutal start to the year with really rough results He also has a 5.9. Oh skill interactive. ERA. So tough peripherals more walks and strikeouts The batted ball data is not terrible But it's also not good enough to overcome the bad in the plate discipline data We've seen her nandez let up multiple runs in every start He let up four plus runs in half of those six starts So I think the white socks are clearly the top option here And I will treat them as such on this slate the one guy who hasn't really been slumping is gavin sheets He has a 46 fly ball right against righties with a 21 strikeout rate. Its iso is there too You do have a glut of guys who kind of are all eligible at the same spot for the white socks, which can Sometimes be a bit annoying, but the good thing is that sheets Um, you know, I think that he separates above yasmani grandal among the catcher slash first baseman type guys I wish they give him outfield eligibility, but I do think that sheets to me is worth it for sure Get Jose a brain in there the fly ball right bit low, but hitting the ball hard. So I think that sheets Probably above grandal for me in that like glut of catcher slash first baseman That's the one issue I have a stack in the white socks. They kind of get a bit annoying there But do you think that they are the top stack on this slate? I think the other side of that game is also very stackable. That's the royals against vince philasquez And I'm going to rank them second right ahead of the mets and the yankees and it's because of vilesquez's continued struggles That he has had He's lagging behind even last year in some key categories where the hard hit rate is up to 46 percent The strikeout rate is down to 20 percent He is walking fewer guys, but that also means he's letting him more balls and play and Those have not gone well for him so far We have seen vilesquez have some good starts, but there have also been some blow-ups in there too He let up seven runs and three home runs last time out He let up five runs and two home runs the twins in late april The royals are not great But I can't get behind them on a short slate So I think they're my number two stack though again the yankees and the mets are very close You can definitely go with the guardians against um, tyler malley He does let up some uh, some fly balls for sure, but prefer these other teams over them on this slate We just have to use the guys at the upside when we are using the royals Make sure you are doing so and that's tougher with no salvador pares right now Bobby witt is legit. So no questions there hunter doger is solid whip marifield. I think we'll trend up in the near future He's also swiping some bags and your bed and tendy is fine I'm also in on mj melendez who should catch with pares being out. So we got guys It's just okay to be selective in which ones you use So dig into the numbers on these royals guys decide which people actually do have upside and Operate once you decide who you want to roll with there I realize I forgot dinger picks for the main slate. Just realizing this live. Okay, so dinger picks For the main slate will go your don alvarez for the boring one And i'm gonna go with alec thomas for the fun one over there dinger picks for the early only slate I'll have to go to the white sock. I definitely have to go there. I'm gonna go with Man, this is tougher than I thought it was going to be I'm gonna go with two fun ones. Let's just go with two fun ones here glade for torrez against bruce zerman I think we'll go dps plus 490 for a dinger over a fan dual sportsbook So torrez is fun one. I'll go with gavin sheets, too. Maybe he's not fun. I think he is personally So we'll go with two fun ones for this one gavin sheets glade for torrez home run calls So that you're only early only slate and for the main slate I'm gonna go with I forgot who I went already your don alvarez and alec thomas your home run calls for today professional podcaster everybody Doing things on the fly here for today. That is all that we have here for this thursday split slate podcast Hopefully a bit more coordinated organized tomorrow For a regular slate that'll be on friday So if you want to get a Better organized podcast or actually remember to the dinger picks hit subscribe on the number fire daily fantasy podcast feed Wherever you get your podcast We have mlb every weekday usc nascar pga weekly hit subscribe get those podcasts right as they are posted Wherever you get your podcasts if you've got questions for me I am on twitter at jim sonnis j i m s a m n e s you can also follow the fan dual podcast network At fan dual podcast big. Thank you to everyone for tuning in for today. Good luck to you on both slays for today We'll talk to you once again on friday for another night of mlb dfs This has been the solo shot right here on the fan dual podcast network


Dear students, in this module, we are going to see the reaction of capitalism on socialism. Capitalism is a system that is based on private ownership of means of production and the production of goods and services for profit making. Capitalists argue that socialism is insufficient and inefficient because it eliminates the incentive to hard work and innovation and that it ultimately leads to economic stagnation and decline. Capitalistic system, because we see that competition-based and profit-making is the biggest motive for any capitalist so that he can invest his resources and produce new commodities for the people, but the biggest objection of the capitalist on the socialist system is that there is no incentive or motive to eliminate such a system from which competition is eliminated and that is why this system ultimately declines and this system fails. So the capitalist critique of socialism is based on the idea that the free market is the most efficient way to allocate resources and ensure the economic growth and innovation. This system is based on innovation, people have incentives and motives and that is why they invest and go into the profit-making system. But the socialist system produces a lot of stagnation and makes a huge profit. People have no motive to work in any economy and they know that distribution of resources has to be done on an equitable basis, so we don't have to work too much. We will also get as much as the rest of the people are getting. So on the whole, the key motive for a person in this system is to force them to work more and more towards profit-making and when that motive disappears, the capitalist thinks that the socialist system will ultimately collapse. In Pakistan, the capitalist ideas have influenced the economic policy with a focus on attracting foreign investment and promoting the entrepreneurship. So there is a capitalist motive in Pakistan, but the socialist policies have not worked in Pakistan in that way, but the majorly the capitalist system that we see in the world as a prevalence is probably because the strongest motive in this is profit-making and competition. On this basis, capitalism is successfully seeing us in the world today. Understanding the capitalist view of socialism is essential for analyzing the social and economic challenges facing the contemporary societies. Today's world has major challenges, we see them, whether they are political or economic challenges, so we see that the capitalist system is providing solutions to them. However, what we see in the socialist system is that it reflects a kind of utopia, a thought that cannot be acted on, ideally it feels good to hear, but it is not possible to act on it. Because the major reason for this is that whenever the socialist system is trying to enter the world, then that effort or effort cannot be successful. On this note, we see that the capitalist system is prevalent in the world and the major reason for this is that because it believes in the free market economy and it has equal motive for the individual so that they can work hard, innovate and produce more commodities for the sake of profit-making. So the study of capitalism would require a multidisciplinary approach. We do not see it as just an approach. We do not see it as a result of which socialism could not be successful. We have to judge it and analyze it so that we can see what are the possibilities in the future and what kind of economic system can be on the strong position. What we see in the world is capitalism. So will socialism be able to make its place in the coming time or not? It's a food for thought for you.


Hi everyone, Joe for jaskiescasebrakes.com coming at you with 2021 Panini Mosaic Football Choice Edition quick little two box break. Pick your team number two. Yeah, that's right Peacock and Nebula hunting is really what we're doing. Big thanks to this group right here for making it happen. Thanks to the people who bought their spot straight up and thanks to the people who took part in that filler. Won some teams. Matt Bristow at triple last spot mojo, maybe quadruple last spot mojo, he bought the last group of teams before the remaining teams were pulled for that filler. All right, thanks everybody. This is also a World Cup rig, so I'm going to randomize everybody's names at the end of the video. A name on top gets into our latest promo. All right, there it is choice, the autograph spot, redemption interesting. Got Drew Brees for the Saints, it's gonna be from Matt. Got Jamie Collins to 80 for the Lions, that'll be for Oliver. Got Dan the Man Marino, Dolphins for Allen, that should be out of 80 as well, 65 out of 80. We got Ray Lewis, Peacock parallel, love the Peacock parallels, they look great. What time is it? It's Ray Lewis time for Matt and the Ravens. There's Rondale Moore, Patrick and the Cardinals and Tutu Atwell for the Rams, that's going to be for Patrick, 22 out of 80. And behind Mike right here is the redemption, good luck. It is a rookie autograph mosaic choice fusion, red and yellow, the red and yellow parallels look like, like that. And it's, good luck everybody, N-A-J Najee, Najee Harris, still got until next summer to redeem that, Steelers, Chad Cromwell, there you go, another box. Got Michael Thomas, that's a catch, nice. Saints that's gonna be for Matt. We got Stefan Diggs and your autograph is Cornell Powell, rookie auto for the Chiefs, Patrick with Kansas City. See another Peacock there, let's see what we got, it's Javon Curse for the Titans, Patrick, 78 out of 80, Hunter Long for the Dolphins, it's gonna go to Allen, we got Deo Ode-Yingbo for the Colts, Patrick, 44 out of 80, you like that, you like that, one out of 80 Kirk Cousins, Patrick with the Vikings, what a game for him. And the Peacock is Christian McCaffrey, Panthers edition heading out to Daniel, Carolina, I think Caroline's going back to Baker Mayfield. Alright, there you go gang, nice quick little two box break of choice, now who's gonna win that World Cup spot, let's gather everybody's names again, 1-32, New Dice, New List, name on top after three and a two, five times, fingers crossed, good luck, get the lucky rabbit's foot, the lucky horseshoe, all that one, two, three, four and five, only the name on top can get it, good luck, a lot of sad faces here, 31 sad spots but one really happy person. Remember you're already guaranteed a box if you get a spot in the World Cup promo and if you get randomized to the right team, it's gonna be pretty nice too, alright, so from very close Patrick, but appreciate you and everyone else forgetting in, but happy to only one person can be happy, happy times for, it's Patrick, no there was no doubt about it, Patrick Cox, congrats to you, after five times your name's on top and you are in that World Cup promo, if you click the break schedule, click over to the World Cup promo tab, we'll have a whole running list of all the winners, there you go gang, I'm Joe, I'll see you next time for the next one, bye bye.


This is our session on WHMCS. I'm Taylor. This is Pilot. I'm pointing in the wrong direction. That's correct. And we're going to walk you through, well, really, Pilot is going to do the bulk of the driving here, and I'm here for, I think the technical term is color commentary in the sports industry. Moral support? Walk you through WHMCS kind of where it fits in the domain of one's own management, you know. Ecosystem? Ecosystem. That's a good word. I don't say puzzle, but I don't want to make it sound confusing. But there is like layers to all this stuff, right? Like we talked earlier in the day about kind of how the three big systems fit and sort of what roles they play with WordPress being the front end. And we're going to get to WHMCS in a second, and that's really about managing users in the system and what they have access to and if they have accounts and things like that. And then later on, we'll talk about WHM, which is kind of more the servery stuff, basically. But so I kind of think of WHMCS as kind of, I liked in my head, I think of these as layers and like the outer layer being WordPress. A one layer down is WHMCS and WHM is even one further. So we're going to talk about WHMCS. That stands for Web Host Management Complete Solution. Terrible name. I don't like that. I don't like that at all. Yeah, it's a bad name. And we're going to kind of walk through it and if you have any questions a while ago, feel free to put them in Discord. And yeah. So I'm going to get Pilots screen up here and we'll showcase WHMCS. Yeah. All right. So basically we've talked a little bit about this before. As Taylor said, we talked about how the three systems work together. Amanda and I mentioned WHMCS a little bit in our WordPress session. But the main thing to think about WHMCS as I like to think of the domain of one's own system is layers where WordPress is the outer layer. It's what you'll be using the most often. It's what the users will see and have access to. WHM, the server is the innermost part that'll have the nitty gritty settings. It's where data is stored, things like that. And Taylor and I will talk about that a little bit later. But WHMCS is the middle. It's the bridge. It connects everything. It's responsible for making single sign-on work with WHMC. WHM. And just having everything hook up cleanly. So the idea of single sign-on is used in WordPress so that users can sign in with the credentials that they know. They don't need to learn any new credentials for their C-panels. And WHMCS is responsible for taking that information and going, ah, single sign-on to this account means deliver this C-panel from the server, make it available in WordPress. WHMCS is also responsible for the original provisioning of accounts. So earlier, Amanda and I showed off what it looks like for a user to sign up, that sort of 10-second countdown that we were talking about. That is the time when WHMCS is saying to the server, hey, this user signed in, asked for this. Can you get it set up? And I'll send it right back. I like WHMCS. I think it's fun. You aren't going to need it too much. It's useful in long-term user management, particularly deprovisioning, which is something Taylor and I are going to talk about tomorrow. But that's just a good overview of how to think about WHMCS and what its role in the, as we said, ecosystem is. So we're going to start with just the basics. And we're going to use me as a test case because if you can see recently, I set up a new account. That is the account that we set up in the WordPress. It's right down here in the corner. That's the account that we set up in the WordPress session with Amanda. And that's the example of when we were creating it then. WHMCS was getting everything set up over here. So let's just hop in. If you want to see the full client list, client here means everyone who has ever signed into WordPress. If you sign into WordPress, even if you don't create a C panel account, you are registered in WHMCS as someone who has touched the system. This is also useful because WordPress is great. It's super useful for on-the-ground troubleshooting, for managing all the day-to-day. It's not awesome in the keeping records and logs department, which is also what WHMCS is really good at. So if you want to see all of the users who have ever signed into WordPress, all of the things that they've done, you can go to view, search clients here, and it'll show you a big old list of everybody. I'm not going to go in there right now because StateU.org is our sandbox site that people use to test out Domain of One's Own, which means that there's just a whole bunch of people in there. And I already have the little account that I set up, so we can just go straight to that and show you what a user profile looks like. So just type me in. I am extremely searchable. Nobody else ever has my name in the system. You can see I have a terminated account because I was testing this. You don't have two first names like I do. I do not. Although I imagine Jaden's pretty searchable. Kind of. But like I said, sometimes it's someone's first name, usually spelled in E though. That's true. Yeah. I have two accounts listed here. One is terminated because I was testing some things earlier and then I got rid of it so that we could use me as a demo in the WordPress session. So here is just the overall summary page. You can see first name, last name, my email address, my address, which is not in the system because it's not really relevant. You don't need that. In your institution setup, the address here will be listed as the institution's address for every single user. WHNCS is by default a billing software. We actually use it to manage our own clients that reclaim. But you don't need billing for anything that we're doing for anything that we use WHNCS for. So you can ignore that. Don't worry about it. One thing I wanted to point out here too before we go further in the profile is that the email address is importantly what single sign-on is looking for in most almost every domain of one's own setup, right? So if that email address is not correct or if it changes, the user won't be able to log in their account and this is where you'd probably have to fix it. Yes. If you ask us at Reclaim, we can help you diagnose or fix it, right? But that comes up every once in a while. Yeah. I believe we had an admin actually at one point who reached out to us because they had changed their name for, you know, personal reasons, lots of reasons to change your name and changed their email accordingly and then tried to sign into their account and went, oh no. WHMCS was like, here's your new account if you want it. And they were like, no. So we just had to make sure that email matched up and once that was the case, they were set. Yep. Sometimes we've had rare occasions too where a school has changed in bulk all like the format of all email addresses and that also can affect it too. And in case you'd reach out, we can help you with that change. Sure. Yeah. So moving on from the email, you'll see, again, on the idea of this as a summary, this lineup here shared hosting is just all of the C panel accounts that I have ever signed up for. There's two total, one active because as I said earlier, I terminated an account. I got rid of it so that Amanda and I could use my account as a demonstration for the sign up. The other thing is I talked earlier about WHMCS being a record of everyone who's ever signed into WordPress. That is an important distinction because our domain of one's own licenses come in blocks of 500. That is not 500 people in WHMCS. That is 500 C panel accounts on the server, which is a different thing. People can sign into WordPress and get registered in WHMCS without ever actually creating their C panel account, and so they will not count towards that license. This is a summary, again, so you can scroll down and you can see people's accounts. This is the accounts. They also have options for domains. If your school offers top-level domains, which is a pretty niche case, but it does happen, those domains might be found here. Hopping over now, there's two tabs that I use, really that I would use as a domain of one's own admin when I did that, which was products and services and log, and we'll get to that in a minute. So products and services is where you can look at the details for a specific account.  So here is a list of all of the accounts that I have. The one that's been terminated is in red. That one no longer exists, but you can see that when it existed it had this domain. It was on the server. It doesn't exist anymore so you can't sign into it with C panel, but it was registered on for managing it, we are going to actually we'll stay here if we hopped to this it would look exactly the same be a hundred no different at all but we are gonna hop we're gonna stay here because the this account is terminated so this username and password is useless and this is being live recorded so I don't want to show off more cPanel credentials yeah that's why it's terminated right we terminate these after shortly after workshops so that yeah they're not just out there but yeah yeah is it so you know information security but also this account's gonna go away in a day max but so the next thing or the big thing to look at here is the module commands there's three main ones that would be relevant and then a couple of others that I can talk about so WHM CS is where we would do deprovisioning work and the idea being that if there comes a time when a user no longer needs their cPanel account either because they've graduated or they were using it for a course and they don't want it anymore you would be able to use these commands to manage that suspension just suspends an account in that it makes it no longer publicly available the account data still exists the account is still on the server but it's not something that users can access it's not something that people can go to that domain and see the site it's just offline and they'll get an error when they try to log in that says this account is suspended now yeah exactly and so you might use suspension actually in the case of sometimes very very infrequently I think I mean I haven't worked here for five years but the number I've heard is maybe once in the past five years there comes a case where a user is posting things that the institution doesn't want associated with them or that violates the terms of use or something like that maybe something risque and that is a great time to suspend the account you're not getting rid of the data yet but then you can sit down with the user and say hey we maybe need to have a talk about this about cleaning up your account about not doing this and maybe figuring out what next steps are you can use that time to clean up the account to figure out how the user is going to proceed how the institution is going to proceed and to bring that account back online you just don't suspend and it's as simple as that terminating does remove the account fully gets rid of it takes it off the server the account data is gone we keep backups for 30 days after an account is terminated so within that time we can restore an account that was mistakenly terminated if needed but that after that you know it's gone although we are happy to push those backups to a third-party location that the institution has so you know it doesn't have to be gone in general I do want to say that you don't have to do this manually it's fine it particularly in bulk so if you are bulk deprovisioning in case of graduation you can come to us and say can you suspend these 150 accounts I don't want to go through and press all the buttons myself because that sounds like a terrible use of my time and we'll say yeah we have a script for that we'll just run it it'll just go like that and we'll talk about a lot more about deprovisioning and stuff like like mentioned earlier we have a session tomorrow on that but it is I think good to kind of see this where it is in here because there are times where you want to do one-off suspension unsuspension or termination and this is where it lives yeah exactly so the module command there so those are the big three there are also the module can't commands create change package and change password I'm going to cover them really quickly change password probably the most important of the three in that sometimes the connection that WHMCS creates between the single sign-on in WordPress and the server will get unstuck we'll get unglued rather is sort of the way to put it so a user will sign in and they're not getting an error message they're basically just getting a blank screen because that cPanel and bed has not come over from the server that information hasn't delivered and the first step in that situation is basically to come in here and hit change password and that just rebuilds that bridge and recreates that connection it can never hurt to do this so this is a great first step for troubleshooting that's still a more niche use case so not part of the main three change package we'll talk about this a bit later in the WHM session but accounts can have different packages which defines what resources are available to them what the account settings are for them and so if you wanted to change the package we don't have an option for it here but there would be an option to switch what that is and then hit the change package button and that would swap them over on the server that would control that and then create I've never heard of anyone using this create creates the account from scratch again so it still exists but it's blank so if a user came to you and said I love this I've had a great time this has been wonderful I definitely want to keep using this but I also want to get rid of everything I've ever done I want to clean slate I want to start from scratch you could hit create and it would do that yeah I I would as a if I was in your shoes as an admin I would be very very explicit with them on mentioning what that means because I think especially folks who are new to this but even if you're not it can be really confusing folks end users right students faculty who are using their account their CPn account to distinguish between are we restarting a WordPress site or restarting the entire account what's going to be changing here right so it is good I think I'd be very careful about pressing that button of course backups could be restored if that needed to be done within 30 days but yeah it's kind it would be a weird request not that it hasn't happened it definitely definitely people will ask for that but just make sure before you click that button that they don't want to just restart a WordPress site and which case they could do that in their CPn with install Tron and that they maybe have other things on their account like a couple other sites or something like that so yeah I like to cover it because I like to make sure that you know what the buttons do so that you can choose whether or not you're pressing them well any reasonable assumption to say I bet that button doesn't work if the accounts already created no it does it does it does something yep only press that button if you are sure yeah I guess you confirm but you know still yeah yeah and then I think the other thing that I really want to touch on is the log so earlier I talked about how WordPress is really great for troubleshooting for going into checking on users accounts things like that it's not great for record keeping but WHMCS is so it's possible to do some of the account management stuff we've talked about in WHM it's all manual there basically and it also doesn't enter into this log so this is just useful in terms of keeping track of information it says when things were created it sends what says when things are terminated so you'll see that account was created I got an email about it that account was deleted that account was created I got an email about it that account has the new account has not yet been terminated but you can see which admin was responsible for this WHMCS does allow for multiple administrative accounts so we recommend that everybody on your team has their own separate one linked to their own email their own username it says when it happened which can be really useful just for tracking things down we really really really recommend that if you were going to do user management in the ways that we've talked about particularly suspension on suspension termination that you do it here just so you can keep track of things it's very very useful yeah changes that you make here will apply to WHM but changes that you make in WHM won't automatically apply back here right yeah this is not a two-way between WHMCS and WHM not a two-way conversation it's a one-way conversation and yeah pretty much every case so yeah exactly I'm just trying to see how much time we have Taylor do we have enough time to go into the emails do you think yeah I think we do okay cool so one of the nice things about WHMCS in the same way that it's managing all of these users all of these profiles is that you have the option to send mass emails and we'll also talk about this for communications purposes tomorrow in the deep provisioning session but I'm just going to navigate it to it right now if you have this version of WHMCS if your version of WHMCS looks like this this is where you would find it and this is the name email campaigns under the utility section if you have a different version of WHMCS it's gonna look a little different yeah in clients mass mail tool yeah so this tab and then you know mass mail tool isn't listed here but if it were that would be where you go so you would going to email campaigns utilities email campaigns allows the sending of an email message to a group of clients ranging from every client on file to those who meet specific criteria what that means is pretty much what it sounds like you can send an email to everyone in the system or a couple of people depending so WHMCS allows for things called client groups so if you wanted to say all right everyone who is graduating in the class of I guess 2023 that's our school year now everyone who's graduating the class of 2023 their account goes into a client group and then I'm gonna send specific emails to them saying oh you're graduating soon what do you want to do this is why Taylor and I are going to talk about it in the deeper reasoning session tomorrow that's one of the really useful things about WHMCS in general Taylor yeah it's it's just a fantastic tool this this email campaign or mass mail tool like it said or like pilot said that we're gonna demo it more tomorrow a little bit but but just know that it is powerful because you get a nice email like you know visual email templates and stuff that can be configured but out of the box it will use a pretty good template that uses your your school's logo it's kind of built in there I believe and so that's that's nice and obviously it can send a bunch of email at once but then crucially because it's like a mail merge tool you know it'll you can do things like include people's name and domain or account name if you wanted all kinds of information in the email to personalize it rather than just being a to who they concern exactly so that's great it's built in I think it's a really powerful tool for admins it's also probably a good idea to make a client group and put yourself in it to do test emails so you can just you know make one that's just you or maybe you and a teammate that can you know try the email out and then roll it out to everyone it does give you nice previews but I don't know I'm always anxious when I'm about to hit the button on a bulk email so I like to do double and triple checks but it's a great tool and we'll dig a little bit more into it tomorrow hopefully so yeah measure twice cut once that's I think most of what I wanted to cover in WHMCS is there anything you think we're missing the only other thing I wanted to mention is that I think is worth mentioning is maybe that this tool you know you'll you be provided with credentials to log in but you can make other accounts for other folks who may need access on your team if that's the case WHMCS lets you make accounts directly into the interface you can share credentials if you want to but I always think it's a good better idea to have multiple people have their own logins that way you can revoke a login if they leave yeah that's possible you can do it yourself you can ask us to do it in a ticket but it's it's very easy to just do the other manage admins page so that's a good that's a good thing to do if you have someone else that needs to be in here and working with these accounts for sure and it also means in addition to what Taylor said of you know you you can just revoke that if they end up leaving the institution it's also great for that log that we were showing earlier because there is that section that says this user this admin is what was responsible for this action in the system who did what here when that can be yeah a life just trying to depending on the situation so yeah awesome well right anything else I don't think so can you stop my screen share please yeah so that's our tour of WHM CS and up next is gonna be WHM see you all soon see you all soon


What's going on everyone? Sam here with late in sports cards ripping 22 tops dynasty baseball hobby five box case break number 53 random left side serial numbers there's a look again at your random results as always you can find those on the website under the results tab as well as a link in chat it's good luck guys let's do it some dynasty sorry again for having this break to lead about 20 or so about 20 or so minutes behind right now putting Sean to sleep over there plus one box one here we go 10 spot on the bookend William K Ryan Mountcastle three colored game use patch auto nice one there 10 of 10 part of the letter there I'm assuming that's m from Mountcastle would be my guess but if I do say so myself might check out there uh it's going to be six of 10 six spot is Viviana Fernando Tatis jr three colored patch auto that is game used as well very nice congrats on that one there Viviana at the six spot last night Donnie probably Donnie one of 10 one spot ammo Jose Ramirez nice Jram three colored game use patch auto stud oh yeah best third baseman I think well maybe our natto one of the best third baseman one of you say if you make a definitive statement like that someone's gonna be in the comments oh yeah that's gonna be numbered something of something one of five Bryce Harper three colored patch auto that's nasty that is game dated 916 21 as well uh one spot ammo again congrats ammo two big time cards coming away not bad there we go ammo very nice our natto machado Jram Devers I would agree with that maybe you can maybe make a case to flip flop machado and Jram but I think that's probably uh true oh god please have this guy come into the breaking studio and take all of his tape off here yeah what's going on here another one of 10 George Springer ammo with another card congrats man two colored patch auto for the blue jays all right that is going to do it for the break guys thanks again for the fill thanks again for your patience up next 10 bucks Tuesday


Hi, this is Dr. Don. I have a problem out of Chapter 8 where we're dealing with the difference in two population proportions. In this problem, we're told that we have a study about the effectiveness of using magnetic insoles to treat a form of heel pain, and it tells us that 53 subjects wore the insoles. 48 did not wear the magnetic insoles. We're given an alpha, and we want to answer the question, can you support the claim that there is a difference in the proportion of subjects who felt better? We assume the random samples are independent. When we look at this information, one thing that should jump out to you given these pie charts, that we're dealing with two categorical variables, which we have counts. And when we're given counts and a categorical variables, those are proportions, all proportion hypothesis tests that we run use the z-test. First thing we have to do is identify the null and alternative. Here it says, can you support the claim there is a difference? If there's a difference, that means that the two proportions are not equal. So the proportions of the two groups are different. And if we look at the options there, we will find over here that proportion one equal portion two, and the claim is that the two proportions are not equal. The first thing we need to do is find the critical value, and we're going to use stat crunch to do that. Remember we can go up here to question help, click on the drop down box, and open up stat crunch. Okay, I have stat crunch open, and as usual we start with the stat button. We drop down to calculators because we're using the z-test, and that is the normal calculator. We have a not equal, which is a two-tail test, so I like to use the between calculator to do that. Our alpha is 0.07, which means that our confidence level is one minus alpha would be 0.93. And when we use the between calculator, we put that confidence level in here, 0.93, and click compute, and that gives us our chart showing the rejection regions. Now here the 0.93 is the confidence level area, so our rejection regions are these white areas on either end of the two-tail test, minus 1.81 and plus 1.81. And those are the answers they wanted in the problem. We scroll down here, and we've given the rejection region and the critical values. Now we need to get the standardized test statistic, z, and then make a decision and draw a conclusion. So we'll go back to stat crunch, and we go back to stat. This time we go not to z-stats. We've got a tool for proportion stats. We've got two samples, and we have a summary since we have the count. And we bring this up. Number successes in the feel better magnetic side was 17, and the total was 53. The feel better in the non-magnetic was 22, and the total was 48. We want to run the hypothesis test for the proportion difference. Here we're saying that it was 0. There is no difference as the null, the claim was the alternative, that the two proportions are different. We just click on compute, and we get our answer. You've got a rehash there of the counts, successes in totals, the test statistic, and then the standardized test statistic over here, 1.42 rounded, and a p-value of 0.15, which is bigger than the alpha 0.07, which means we fail to reject the null hypothesis. If we bring back up our chart here, we can see that this minus 1.42 falls over here somewhere, and that is not in the rejection area. So again, if we use the critical value approach to the hypothesis test, we get the same answer, fail to reject. So we go back over here to the final thing, and we've decided to fail to reject. The claim was the alternative, so our answer must be at the 7% significance level. We always need to give the significance level since if the significance level were different, we could get a different decision and different conclusion. But here there was insufficient evidence to support the claim because we did not reject the null. I hope this helps. And if it does help, please consider subscribing to my YouTube channel, Stats Files. Just click the big red subscribe button.


Hello, everybody. Andrea here. So let's talk about working interviews. So if you are a dental hygienist or a dental assistant, and you are called upon to participate in a working interview, so this can work one of two ways. I find they can call you in for an interview first to see if they even like you to see if they're a good, if you are a good candidate for the job and then if they like you they will say well why don't you come back tomorrow next week whenever to do a working interview so we can really see how you are in the office and as a person as a dental professional, or they could simply call you because they liked your resume or they heard about you from somebody that does happen a lot in our profession, where we don't even have to send in a resume so many times we just get told by so and so that they know a friend, a dental assistant, a dental hygienist who's looking for a job and then they'll call you and even instead of just talking to you first they'll say well why don't you just come in we'll talk to you that day and let's do a working interview so I've had to do them as well. I find I had to do it more often when I was a dental assistant. I shouldn't say more often when I was a dental assistant. I got the job right away like after a working interview but as a hygienist I found they hired me, but would say you know if we don't like you or if you're not a good fit for the office then we'll just let you go before the three month probation. So we're in interviews so what are they and what to expect.  I know it's nerve wracking you're going to be nervous because you probably feel like you're being watched, but honestly nobody has time in a dental office to really watch you. I just want to see if you're good with patience, and if you basically know what you're doing but at the same time they realize you're new to the office they will not expect you to be perfect and I can promise you that. I have seen many working interviews in my time where I'd be working at the office and the dental hygienist was having a working interview or the dental assistant. What you're looking for like I said is are they good with patience meaning, are you going to sit there and look at the wall, or are you going to talk to your patient. Are you going to take initiative, are you going to clean up the room, disinfect the room right away or are you going to sit in the lunch room, twiddling your thumbs well the room is dirty waiting to be cleaned so we look for initiative. These things I think are common sense but apparently they're not because I've actually seen these things not be done so I've seen it where I'll be working on my patient and I'll kind of walk by the room and think okay. That room's dirty no big deal but where's the dental assistant or the dental hygienist she must be doing something else helping another patient doing something else yet she's in the lunch room or she's in the back having a snack or something. That's a core initiative I can't say that enough. We look for your personality to you don't have to have energy you don't have to be bubbly. You don't have to be shy you don't have to be whatever. It doesn't matter what personality you have but do you mesh well.  Are you going to come in and pick fights with every member of the dental staff I know that sounds silly but we look for things like that we don't want you to do that. Are you going to help out even when you're not asked so what I tell people all the time is, let's say your patient cancels. Well, again, don't just sit there twiddling your thumbs go to the dental receptionist ask if they need help. Say my patient canceled. Can I help you with something because again they realize you're new to the office they don't expect you to be perfect but anybody can file charts. Anybody can. I don't know, take this to the back room or anybody can open up boxes in the supply closet and help unpack things. Things like that. Anybody can do that. If the dental receptionist doesn't need help then go to the dental hygienist and say can I help you can I help you record your probing numbers can I help you disinfect your room. Can I help you take your tray for you to sterilize it. I mean you might not know how to work their sterilization lab so okay I wouldn't suggest doing that, but you could at least take the tray and put it into the sterilization area. If anybody is in there you can say, Oh, I'm just going to watch you because my patients not here I'd like to see how you guys do this, the sterilization process it might seem simple, but every office is different on how they do it so ask for help. These are the things we look for. If anybody don't just simply leave and say okay bye see you later. Ask anybody if they need help and then go to whoever kind of brought you in in the first place was it the office manager who you had more conversation with were they the ones who had hired you for the working interview or was it the dentist themselves if they're not busy you know go into their office go into their op and say thank you so much. It's been a good day I hope I did well for you. Any feedback I'd love to hear what you thought or just say thank you it was so nice to see you I would love to work for this office if you'll have me. Something like that so I hope that helped you guys let me know if you have any questions and I'll see you guys in the next video, click like if you liked the video and make sure to click subscribe because I do upload videos often. Thank you guys bye for now.


everybody forced to your ripping case number one twenty twenty two national treasures baseball hobby Is release day? Yeah, this a random team style break The check not the checklist. I mean you find the checklist online. You can find the results of latent sports cards calm at any time There's a link in chat for you Let's get started. Let's see what we got Where did Sam put the knife What are these guys doing at night? They are up to no good. I was in chat last night. They're going crazy Dude, I wasn't like I was in chat It was like told there's like, oh wait, I have to break tomorrow I am I'm about the color. I'm about that Like it's like a red like in like a beige gentle almost and like a beige. Yeah. All right y'all What's going on Jonathan happy release day everybody to releases today They all are in baseball, I don't know if this one seems a little Yes, it's pop popping up, but we'll see we'll see. I don't know to expect Well, we're gonna have a fun first box here. It looks like Yeah, I think there's more books in in baseball from I remember it's been a while, but Patch card Joe Musgrove Padres 1925 that's an astros patch player worn Oranges from his time with the Stroze Padres first hit colossal Jersey Spencer Howard Rangers 33 of 99 Red Sox Jersey card Rafael Devers 17 to 49 player worn on the Devers Got mariners Jersey Otto drew Ellis 31 of 99 Mariners player worn Jersey Otto diamond Is it diamond Jersey Otto diamond auto just a diamond auto there? Well, that's a cool design Dodgers with a Gavin Lux auto three out of 20 It's not like a like a shadow box. It's about GGS Gavin Lux of 20 Dodgers Otto. He turned out to be pretty good. Is that a Jersey there too? I think that's a oh, that's kind of neat. There's a Jersey like behind him.  I yeah jumbo gear signatures. That's pretty neat actually very innovative for an NT All right, raise now on card Jersey Otto Randy Arosa rena 31 of 49. He's a nice card player worn use Randy Arosa rena Love his signature. It's crazy every time Got rookie material signatures three-color jumbo patch twins Jose Miranda 3240, how about the Korea thing dude the Korean thing is wild Still getting big big time money though, I think I see Recognize the auto because I just got a couple of my cards. Oh, yep a one-of-one printing plate relic auto Riley green Tigers big hit That's so sick as Blake's buddy Tigers Who's got Detroit, let me see that's awesome. That's probably a 180 mag. I would think Detroit Matthew F That is freaking awesome Printing plate patch Otto of Riley green This will still be a prospect his rookie year is gonna be this coming year. They prospect patch printing plate auto I've recognized the auto and I was like, I can't recognize anything else about the car But I can see the auto from here. Yeah, I didn't know Bigger than a way here. Yeah, it's just a filler on it Oh, what is this now?  I love that sick x 16 of 17 legendary material signatures duals Supra Mars. Yeah, Blake's with me today. Yeah. Wow. This is what this is the first box. It's awesome sweet ec It's a great design man. This product was really nice I think And raise rookie material signatures Shane boss 13 of 25 awesome rays patch as well on the boss Yeah, for sure one of the goat relievers One of the nastiest sliders Plus back in the day he threw high 90s gas One of the best relievers one of the best one of the best mops in all of baseball history Eckersley. Oh, yeah, got one of the best mops ever for sure a lot of salad on top of that head Alright next up. Oh field gear like that. I designed to Jersey Conor Seabold Red Sox 47 and 99 Play your warn. Yeah with some filler as well Jersey card Boba Shet six out of 99 Boba Shet And then on the back of this I would tag Tiger since you can't see nothing on the Boba Shet Oh a satchel page Jersey Relic St. Louis Browns should go to the Orioles game-worn satchel page This stuff is fun, man. This stuff is awesome Let's see Yes satchel page goes to the Orioles St. Louis Browns became the Orioles He has other teams in here, too Yeah, that's a really awesome legendary Jersey Pretty much all of it, right Yeah, since everything is a hit in NT baseball Printing plate auto TJ Friedel Reds rookie on the plate. We've seen both printing plate autos be on the plate, which is awesome Reds TJ Friedel sup Elon sup Ryan Congrats on the boom again Matthew that that Riley Green was nasty. There you go Reds TJ Friedel Really nice materials patch out of Dalton Jefferies A's to 25 three-color patch Reds legend TJ Friedel is that what you're saying next up is a Juan Gonzalez Treasure material auto it's a 10 one gone as a guardian Juan Gonzalez Guardians Sup Shane Good first box so far or a good first box. Are you missed a lot of different sizes top or stuff, right? Yeah, I'm like Booklets and every day Rookie materials signatures national Josiah Gray 68 of 99 the nice jumbo patch there printing plate patch auto of Riley Green On the plate, too. I don't remember. I didn't watch Juan Gonzalez very much as a kid That was a little before me in my watching days, but I don't know as a guardian All I think of is Rangers with one gone although. I'm sure he played for more than just the Rangers and Guardians Jose a bray you legacy signatures three of 15 white socks The designs look awesome this year in my opinion bray you there Yeah Obviously some new And Philly's Luke Williams rookie jumbo material signatures here booklet Luke William 17 and 99 Philly's three pinstripes on the jumbo Player one When is it supposed to release I was gonna say we're still way on like I'm It's such a it's to me is weird how like baseball and basketball are so different with releases like NT football comes at the end And he basketball comes like right During almost Okay box three No, it's fine unless we get like a huge one, okay, I mean, yeah, I'll let you know that Jersey Juan Yepes for the Cardinals a field gear the design is awesome Jumbo Jersey Jose Ciri for the rays now finally a raise Jose Ciri to 99 Speed demon right there dude so fast Is it okay with NT baseball Patch card air your don two out of ten Astros three color patch He had a one career at bat for Cleveland what He's I'm almost as much of a guardian as as he was Just get me at the plate one time. We have the same amount Jersey Auto on card Joe Ryan rookie silhouettes Nice card twins 34 of 99. Oh 140 abes Okay, so he was with them before then he went back to them. Okay. Okay. Yeah, I was like he had a one at bat a Jairan Durand this is one of my favorite designs right here little polarizing, but the the The acetate over the patch with the auto is really nice Jairan Durand red socks three color patch auto So all of the like the young guys have been player worn so far any the legends have been game worn Haven't seen anything other than that. That's a cool Durand though Got a Prentice ink our Elvis Martinez blue J 17 of 99 The new diamond back right Rob is Martinez. He was part of it. I was lost. It's cool, right? Rob is Martinez on car the new diamond back part of the Seth beer trade Rookie material signatures white socks Romeo Gonzalez 14 of 99 There we go white socks crazy patch on that one He had more MVP's than Griffey was that has that's kind of wild That's pretty that's pretty insane. He did go ham for like four years. Oh a Ronald Cunha, Jr. Auto 32 out of 99 Atlanta on car to Cunha auto and see looking great so far today everybody Thanks for filling up the first few cases here Jersey auto for the Dodgers Nick Nastrini What they'd be doing who's messing with the mic? He breaks when he breaks Alright, here we go. We've got Hall of Fame Materials Barry Larkin 31 of 49 Jersey book card Game war and Larkin Jersey book card Does I have a team on it? It's gonna go red Okay, it says Cincinnati right here. So we're kind of teamwork. Yeah, let's say anywhere else though Yeah, it goes Reds though. So Cincinnati. Alrighty last one Matt pulled a Bud Selig auto. Oh, did he fool it? Bud Selig autos get random to the trash can. I'm just kidding What you got?  You have to have to hate it, right? I guess so. Everybody has to all the time Blake Blake can't he's not allowed to Blake does not condone my actions Bud Selig, right? Yeah, I was I was joking. I did he did he do it on camera. This is a commissioner a Jersey auto Elias Diaz 40 of 99 Rockies Oh That's cool Stars and Stripes Jersey Dylan Carlson 54 to 99 Cardinals crazy design Well, I got they got the Carlson breaks the Carlson cards that I got from breaks Jersey cartatis Padres to 99 Your burger beer question needs to know. Oh, it was Marino not a Elvis. Yeah, it was Marino. I'm sorry It was definitely not a Elvis Martinez.  I am not sure mojo Give me one second We must have gotten more if we do have it Jersey auto Reese Nair to 49 Padres jumbo Jersey Auto Andrew Vaughn White Sox to 99. He's gonna have a big year. I He's gonna have a big year. He's pretty much going right the first base, right? To replace Vaughn and they're gonna get him out of to place a brave and they're gonna get him out of the outfield Which is good him and Eloy have no business playing outfield Keep him at the plate.  Why just every time he pulls a Camila Duval He goes do all I do all I Started that and then I stopped cuz You know that's that's the same thing what can I say? Oh, that's nice Paul Molliter Brewers patch auto five out of five that is clean Game-worn patch auto Paul Molliter Give me a second mojo. I'm gonna find out He needs a DH so he can play the field every now and then but he needs to be like, you know He can have like 30 games or less in the field. That's about it Whenever they whenever they play and like the National League. Oh wait National League has DH. I don't mind. Never mind He's the day off outfielder We've got a John Heasley rookie signature jumbo material 99 of 99 for the Royals John Heasley Royals and Oh treasured stats insert is honest Wagner 24 out of 99 Nice inserts that is not technically hit But that's a cool card Honest Wagner One of the goats one of the OG goes Thank You Cortice So, yeah mojo we have it if you can see in chat there Cortice is our one of our managers We'll get that done for you tonight. Yeah, I probably just couldn't find it cuz We must have just gotten it back in stock Okay, let's do a recap here. Everything's basic recap in this. So we got Relics here Tatis Carlson Elias Diaz yard on Alvarez pose a Siri Hey Juan, yep as Connor Siebold satchel page. That's a really cool one that goes to the Orioles I would probably tag that Fusion yeah, cuz it says st. Louis on a boba shit Joe Musgrove Spencer Howard Raphael Devers that Musgrove was a Padres just had as an ash doors jersey on it Got autos now. We had that nice Paul Molliter for the Brewers Camilo de Val Andrew Vaughan Yep, Nick Nastrini, Romy Gonzalez our Elvis Martinez still a blue J not traded like I said earlier Jaren Duran the really cool. I forgot these are called SSS something swatch signatures Really cool though with the acetate over the the patch there Joe Ryan for the twins There's Jose Abreu Josiah Gray Dalton Jeffries Nice patch out of there Juan Gonzalez guardians Jersey out of the 10 We had a recent there for the Padres Colt Tucker D backs Drew Alice Mariners Randy Rosarano rays Gavin Lux Dodgers Shane Bosz rays Jose Miranda twins The Riley green printing plate patch out of one of one ego tigers in a Kunya auto one card to 99 for the Braves Printing plate auto rookie Reds TJ Friedel one of one And then books we had a Jersey book card of Barry Larkin for the Reds a Jumbo signature material was Luke Williams for the Phillies And the legendary material signatures duals was Dennis Eckersley Doesn't say it on this one, but This is Dennis Eckersley for the Cardinals Dennis Eckersley Cardinals Yeah, and that's gonna do it. Thanks again everybody case do come up in a bit


So this lecture is part of an online algebraic geometry course about schemes and will be on differential operators on a ring.  So this is Bessel's differential operator.  And we can think of this as being a map from if we want, we can think of this as being a map from polynomials over the reals to polynomials over the reals. You notice that this operator is are linear, but it's not linear over r of x. So if we let this operator d be that, then d of fg is not equal to f of dg in general, though it is if f is real. So what we want to do is, suppose we're given a ring A and an A algebra B. So we think of A as being a sort of base ring. And we want to define the concept of a differential operator from B to B. More generally, we could take M and N to be B modules and ask what is a differential operator from M to N. So that's what we want to define. So let's start by just having a look at a very simple differential operator. D is differentiation with respect to x and here we'll take A to be a field. Let's take A to be the reals and B to be just polynomials over A. And then what properties does this differential operator have? Well, we have Leibniz's rule which says that d by dx of x times f equals x times d by dx of f plus f. So we see that it doesn't commute with x. The difference between putting d by dx and x in a different order is this operator here. So what we can do is we can say d by dx of x equals 1. Here we mean by x we mean the operator multiplication by x. And if we've got two linear maps x and y then by the Leib bracket of x and y we usually mean x, y minus y, x. So this formula here is just the same as this formula here. It says that if we apply both sides of this to f then they're the same which is that formula there. And similarly we see that d by dx of f where f is the operator of multiplication by x is just d by dx. So this is an order, so this is just a linear map multiplication by this function. So we can say the order 0 linear operators, sorry, the order 0 differential operators are just linear operators. And in order 1 differential operators such as d by dx has the property that d by dx of f is order 0. It's just the operator df over dx. And this gives a strong hint about how we should define order n differential operators in general. So we have a definition, d is order n differential operator if, well first of all, we want it to be linear over the basering a, but it's not necessarily linear over b. And secondly, the commutator of d with f for f in b, that should be order n is of order, less than or equal to n minus 1. And we also say that order less than or equal to minus 1 differential operators are just 0 operator. So this sort of defines differential operators inductively. So order 0 are just those that commute with multiplication by elements of b. So they're just linear maps. And order 1 differential operators are 1 whose commutator with an element of b is a linear map and so on. So for example, let's find all linear operators, all differential operators of the ring b equals r of x. Here we're working over the ring a, which is just the reals. So we don't want to worry about differential operators, which might not commute with elements of r. They're all going to commute with elements of r by definition. Well, there are some obvious examples. If we just take x to the m times d by dx to the n, then you can see that this is an order n differential operator. And of course, we can take linear combinations of them. So we can take sum over aij x to the i d by dx to the j for aij in the reals. And the question is, are there any others? Well, this is quite easy to prove that there aren't any others because if we take d by dx to the n and commute it with x, we get n d by dx to the n minus 1. So from this, it easily follows that any differential operator of order n is of the form some order n plus 1 operator commuted with x because you can get any order n minus 1 operator by commuting some order n operator with x. So suppose e is a differential operator of order n, then ex is order n minus 1. So this is of the form dx where d is one of these operators here because by induction on n, we know that any operator of order differential operator of order n minus 1 is of this form. And therefore, by this observation, we can write it like that. So e is equal to d plus an order 0 operator. And the order 0 operators are just linear. They're just multiplication by elements of b. So we've shown that any differential operator e must be written as one of these operators here. In other words, the differential operators using this funny definition by commutators is just the same as the obvious definition of differential operator you get from analysis. Well, now let's try looking for differential operators of z of x. And there are some obvious ones. We can just take sum of aij dx to the i d by dx to the j with aij in the integers. And are these all of them? Well, no, there are some extra ones. So this is not quite like over the reals because there's extra differential operators. We can take a half of d squared over dx squared, for example. So this takes x to the n to n n minus 1 over 2 x to the n minus 2, which is a perfectly good differential operator of order 2, even though it's got this factor of a half in it. In general, you see that all that's more generally, we can take things in the form sum of aij x to the i d by dx to the j over j factorial. And this will be a differential operator with aij and now still integers. And does this give all of them? Well, yes, it does. It's fairly easy to check because just as before, we can now show that d by dx, the n over n factorial bracketed with x is just d by dx, the n minus 1 over n minus 1 factorial. So we see that every differential operator of order n of this form is the commutator of some operator of order n plus 1 with x. And now we can just copy the proof that we gave for differential operators over the reels and see that every differential operator over the integers is of this form. So we see that differential operators over polynomial rings are more or less what you would expect, except if you're not working over a field of characteristic zero, you have to watch out for the fact that you sometimes get these slightly unexpected denominators allowed in differential operators. Moreover, there's one other thing we can do with differential operators, we can normalize differential operators. So if d is a differential operator, it's called normalized if d of 1 is equal to zero. And now we can write d, any differential operator d is d naught where this is normalized plus some constant k with some constant c with c and a, where c is just equal to d of 1. So this is normalized order n, and this is just order zero where this is order n. So any differential operator can be written as the sum of normalized operator and a constant. Differential operators, by the way, form a filtered ring. So if we get this sort of ring of operators and so on here, fi is the order less than equal to i differential operators from b to b. And it's fairly easy to check that fi times fj is a differential operator of order at most i plus j. So we get a sort of filtered ring. By the way, normalizing shows that we can write f1 as normalized operator plus something in f naught.  You might wonder if f2 splits as f1 plus something. And in general, it doesn't in any natural way. So there's no way to extend normalization to splitting off it. We can't write order two operators canonically as the sum of an order one operator and something. Incidentally, although we won't need it this lecture, I'll just remark that we can form the corresponding graded ring where we take the sum of fi over fj. So fi over fi minus one. So this is a graded ring. And this, in fact, commutative, which is fairly easy to check. So although differential operators don't commute with each other, they're not too far from commuting. You can turn them into a graded ring by taking the associated graded ring. So we can also define the universal differential operator. So suppose you've got b is an a algebra. We can define a map d to a module b. That is a universal order n differential operator. If any other order n operator factorizes through it. In other words, suppose we've got a map n and an order n operator here, then we can find a linear operator from m, a unique linear operator from m to n, factorizing it. The existence of a universal linear operator of order m is almost obvious. So m is generated by elements d of b for b and b, modular relations forcing d to b order n. If you look at the relations for d to b order n, which we will actually write down fairly soon, you can see that just a lot of linear relations between these elements here. So it's obvious that a universal linear operator exists. And similarly, there's a universal normalized linear operator of any given order. Now we find the module of differentials omega b over a is the universal, well, actually, we don't really just have a module. We also have a module with a map d to it is the universal order one normalized a linear differential operator. In other words, if we've got any module m and some order one normalized a linear operator from b to m, then there's going to be a unique map from this module of differentials to m. And let's see a few examples. Let's take b to be polynomial rings in two variables over a ring a. You can take a to b. Let's just take it to be the real numbers. Why not? Then what's omega b over a? Well, it's generated by the elements d of f for f in in b. And you can see it's generated as a b module by dx and dy because d of f is just partial derivative of f with respect to x of dx plus delta f over delta y of dy, where this formula follows just using the fact that d is a first order normalized differential operator, which means that d of fg is equal to fdg plus d plus g df. And you can also see that there are no relations between dx and dy because if we take the free module with basis dx and dy, then the map taking df to this thing here is, in fact, a first order normalized differential operator. So omega b over a is just isomorphic to b plus b with a basis dx and dy. As another example, let's see what happens if we've got a field. Suppose we take a to be the rationals and b to b. The rational is extended by the square root of minus one. And let's ask what is omega b over a? Well, it's generated by d of i. So we need to work out what d of i is. Well, i squared equals minus one. So two i di is equal to naught, because d is normalized. So di is equal to naught. So omega of b over a is just zero. And the same thing works for any separable extension. So suppose we've got some a as a field k and b, let's write it as big k is a finite separable extension. So we can write b is equal to big k is equal to k of alpha, where alpha to the n plus a n minus one alpha to the n minus one and so on plus a zero equals naught for some alpha. And we need to figure out what is d of alpha. Well, this says that f of alpha equals zero. So we find that f prime of alpha df is also equal to zero. And now f prime of alpha is not equal to naught because the extension is separable. So df must be sorry, that's f prime of that should be a d alpha. So d alpha is equal to zero and therefore the ring of differentials omega b over a is again just zero. Well, I said that's what happens for a separable field extension. What about an inseparable field extension? So let's take an inseparable extension where k is k of big k is little k where we adjoin a to one over p is some a in big k. Well, this time if we try and work out d of a to one over p, let's put b equals a to one over p, we see that b to the p equals a. So we find p times b to the p minus one dp is equal to zero. And now this doesn't imply that dp is equal to zero because p is equal to zero. So we don't get any conditions on d of p. In fact, we find that omega of big k over k is one dimensional generated by d of p, not d of p, d of b, that should be a b. So this is one difference between separable extensions and inseparable extensions that inseparable extensions have non-trivial modules of differentials. So another example, it's usually fairly easy to calculate omega of c over a. So for example, suppose a is some ring, and let's put b to be a ring of polynomials over a in x1 up to xn. Then omega b over a is pretty easy to work out. It's just a free module with basis dx1 dxn. Now suppose c is equal to b over some ideal i, and we want to work out omega c over a. Then you can fairly easily see that c is still going to be generated by dx1. So omega c over a is generated by dx1 up to dxn. But this time it has some relations where whenever f, if f is an element of i, then we get relations saying df equals nought, where df is just equal to sum of df by dxi times dxi. So for example, if we want to work out omega c over a, where c is say, let's take an elliptic curve. Let's take a to be a field k, and let's c to be k of xy over y squared minus x cubed minus x. So here we've got the coordinate ring on an elliptic curve, and the ring of differentials omega c over a is generated by dx dy, and we're quotient up by the relation 2y minus 3x squared 2y dy minus 3x squared plus 1 dx. So we just get a resolution of omega c over a by b squared with kernel b. So this maps 1, 0 to dx and 0, 1 to dy, and this maps the element 1 to whatever it was, 3x squared plus 1 times 1, 0 plus 2y times 0, 1. So here we've got a resolution of the module of differentials by two free modules. So more generally, if you do this for arbitrary rings, you find that if c is equal to b over a, b over i for some ideal i, then we find we get this sequence i goes to omega b over a, tends with c, goes to omega c over a goes to 0. So in the example we had earlier, omega b over a was generated by dx and dy, and i was generated by 2y, sorry, i was generated by y squared minus x cubed minus x, and this methods d. So the image of this element i would be 2y dy minus 3x squared plus 1 dx. And doing this for more general, the proof for more general rings, c and b and a is pretty similar to the case, the example we did earlier. Well, Hart-Shorn gives a formula for omega b over a as i over i squared, where i is the kernel of the map from b tensor over a b to b. And the map from b to omega b over a takes b to b times 1 minus 1 times b. And the question is, where on earth does this come from? So I want to explain why this is true. And what I'm going to do is I'm actually going to do something a little bit more general. So what I want to do is to look at a map from b to m, where d is going to be any order n operator. So here this map d, we're taking little d to be order 1 and normalize, but I'm going to forget about normalization and look at all orders for the moment. And we can have a map from b tensor over a b to m, which takes b tensor c to b dc. And we're going to make this into a b module by letting b act on the left. So this defines the b module structure. You notice there are two ways of making this into a b module. We could have b acting on the left or b acting on the right, and we're going to take b acting on the left to define the b module structure. So this is now a homomorphism of b modules. And we're going to define a map from b to here by taking b to 1 tenths of b. And we notice that this is not b linear. So this map is b linear and this map isn't. And what we're going to do is try and make this into a universal order n differential operator. So, well, we can't do that quite yet. So first of all, we have to look at what relations does an order n operator have. So suppose d has order zero. Well, this means dA minus AD1 is equal to zero. What about d having order one? Well, this means the commutator of d with multiplication by b is order zero. And if you figure out what this says, it says that d of AB minus ADB minus BDA plus ABD1 equals zero. What about order two? Well, if you work it out, you find this says dABC minus ADBC minus BDA minus CDAB plus ABDC plus BCDA plus CDAB minus ABCD1 equals norton. You can now see what the pattern is. For order n, we're getting two to the n plus one terms where we sort of sum over all subsets of n plus one variables. Anyway, you can write this as follows. If d has order n, then d vanishes on i to the n plus one, where i is the ideal of B times over AB, sorry, is the ideal. i is the B module generated by B times one minus one times B. And you can also check that this is equal to the kernel of the homomorphism from B tensor A to B taking B times C to BC. And so you see from this that if we take B times over BA and we quotient out by i to the n plus one, then the map from B to this taking B to one times B is now is an order n differential operator. And furthermore, we can also see it's a universal differential operator, because if we've got any differential operator d mapping to m, then the fact that d is of order n means that the image of i to the n plus one in m is just zero. So we do indeed get a map from B tensor B to m taking B times B or B times C to B times BC. So B goes to B times over AB over i to the n plus one is the universal order n differential operator. Well, we haven't said anything about the normalization yet. So now let's put in a normalization. Well, B goes to one tensor B and B tensor B over i to the n plus one is not normalized, but we can normalize it by mapping B goes to one tensor B minus B tensor one, because this now takes one to one tensor one minus one tensor one equals zero. So this is normalized. And the image of what one tensor B minus B tensor one is now in the ideal I. So we get a normalized differential operator. If we take i over i to the n plus one and map B to B tensor one minus one tensor B, this is universal normalized order and differential operator. Now the case, Hartshorne is using in his book is just the case n equals one. So the universal order one differential operator whose image is the space of differentials is just i over i squared with this map here. Okay, so that's all we say for the moment about differential operators on rings. Next lecture, we will generalize this and discuss differential operators on schemes.