So I have a few Unify switches here to review. This is the Unify 24 on top and 48 at the bottom, named the Unify 24 and 48, but technically the 24 is a 26 port model because we have a couple SFPs and the 48 has 52 ports because we have two SFP module ports and two SFP plus module ports on it. So, let's talk about first what comes in a box. I unboxed them in the unboxing. It's not as cool as like an iPhone or anything, so I didn't bother like the whole removal process. If you're into that, I'm sure someone's done that. Power cords in here for each of them. This is the same parts in each of these. Heavy power cord, not one of those two flimsy ones. That's good. The rack ears. I like the rack ears on this. They're not chintzy. They are actually pretty thick. I've seen some of them have almost like paper thin rack ears and these also are like double enforced on the rolled edge here. Also, not sharp. Not going to cut yourself on them. So, good day. Do a nice job on that. Bolts to hold the rack ears. Or, I'm sorry, screws to hold the rack ears and rack nuts to mount in the rack. Your standard rack nuts with the screws. Nice that they include those in the box. And then the unit itself. Now, these are actually fairly substantial. There are metal, complete metal construction top and bottom. So, it's nice when you see how well made these are. Now, the 48 port one. A little bit more in depth. So, it's a little bit longer. So, take that into consideration if you're mounting this in a rack. Make sure the rack has enough depth to handle a 48 port model of this. All they have the measurements and specs on the site. So, let's take a little bit closer look at these before we get into the software. Move things out of the way here. So, I have removed those two screws from the back and two screws from the bottom. And then it just slides apart. So, let's go ahead and open this thing up. Make sure I got to take out the SFP. They keep a little rubber dust covers on them, which is nice. Get those out and let's pop this thing open. Let's avoid a warranty. The good news is, if I'm avoiding a warranty, it's not showing that I'm avoiding a warranty. Because they don't have any stickers that I could find at all to stop me from doing this. Or, I shouldn't say stop me. Discourage me from doing this because I'm gonna do it anyways. Because I want to know what's inside these unifies. So, let's... a little pry, a little pry there. It slides this way out. So, get a little bit of... there we go. And she's open. I open it upside down, I guess. So, flip it over.  You're learning as I'm learning. No editing here. There we go. This is really heavy. Kind of cool. So, you have the unify here in the front and we got some glue around there holding that in. We're gonna look at that. But this is... tap this real quick. Solid piece of metal. Not sharp. I can hold it like this. I'm not worried about cutting myself. And very heavy. Now, let's take a deeper look inside. Power supply, ports, but a lot of empty space. Tiny, tiny fan. Interesting. There's no feedback on the fan. It's not a three-way fan. So, I'll move the camera down closer so we can kind of dig into this a little bit. But this is nice and clean inside. There's not a mess in here at all. All right. So, here's a little bit closer look of what's inside. We see the power supply board over here. Pretty small, compact, clean. And I like that.  Some of these you'll see a lot of different wires. Here's our wires for the LED for the front. Pretty tiny LEDs on there. When we have the different chips for each one of them. So, we have one, two, three, four, five, six, times two. So, 12 of them. So, each two of these control that port. Pretty good size heat sink here and a good size heat sink here for the processor on these. And this is some of the genius of the way they design unify equipment is it all runs with a Linux kernel inside of it. There are cameras, there are Wi-Fi devices, and there are switches. So, you can terminal into these. When we get into the software part, I'll be talking about that. So, let's take a little closer look at the chips on here. Now, it's upside down, but these are some G48209SNG. And I actually googled them and I found a place to selling them, but not a lot of information on the chip itself. But everything's well put together. The board itself, and if you can read this down here. This is a, you know, got the ubiquity stamp on there. I like the way they do this, you know, so I can identify this board. It's got their mark on it. And it's really, it's a nice design. And like I said, the bottom's metal. I think the fan here is a little bit tiny, but they know what they're doing.  They get pretty warm, but not like you're gonna get burned. So, they definitely do push some heat. And these fans are thermally activated. So, they will rev up when it first starts to do a test. And then they turn off completely. And I guess come on as needed when you're doing data transfers and it heats up. Like I said, it's not that high. I don't have a thermal imaging for that. Now, this back over here is because it actually has council access on the backs. Here's the two SFP ports over here. Pretty straightforward. Nothing, nothing too exciting. I want to at least take a look inside so I have a good idea of how this whole system works and looks inside. So here's the 48 port model. Pretty much the same. The two processors on here. Send two of these here. Like I said, I don't know what chips exactly are under there. So, the design is pretty much the same as it was for there. It has the same LED in the front. Same basic clean power supply. They did put two fans. They have one fan on this side and one fan on that side. So, a little bit different there. And you have the four SFP ports versus the two. And this is another difference of the 48 port model. Two of these SFP ports are SFP plus, which means 10 gigabit ports. So, you have two 10 gigabit ports, two gigabit SFP ports, then 48 gigabit ports on this. So, the design and everything is pretty much the same. The software and handling is all the same through the same unified software. They just have a couple more ports, but you get that 10 gigabit. Now, this also has a total switching capacity per the box. 70 gigabit. So, that means everything can be transferring in the total amount of bandwidth they can handle going across. The 70, which means lots of different things talking to lots of different things. And we still have the same thing, the same chips. Same chips exactly and configured the same way on here. Once again, clean design, nice inside everything's metal construction, just like on the 24. A couple side notes, though. I noticed when I opened it up, I see things catched us on camera. Not my fingerprints. These are some fingerprints that are pre in there that it came with. They're kind of hard to see a little thing. I'm trying to turn the brightness up to get them seen better. But yeah, there's a series of fingerprints that are kind of oily ones that are, you can actually feel whatever it is. So, someone had glue on their hands maybe when they touched it. That is an interesting side note. I looked at it, I'm like, huh, there's fingerprints on that.  Some ubiquity engineers. All right, so let's now get into the software. I'm going to go a little bit over the front of the case on these and then we'll get into the software and actually how these work. All right, so it's time to jump into the software. My last little comment is a hardware is, thank you Unify for designing it where the light for the network cable is where where you plug in the cable. I don't like these places that put a separate light on the side of the switch and a lot of manufacturers just do that and it's like, oh, look, I plugged it in, but I have to look for the light and the port number. I like seeing it right next to each one of the network jacks. It's just a lot easier when you're plugging it in. The real magic in any managed switch is going to be in the software that runs it. And I really like the Unify software. We're using it to run everything in terms of the switching fabric for the systems. Now, I have a couple of Wi-Fi in here and I left them plugged in for this demo actually plugged into our network because I wanted to show you some of the connectivity and topology. So the switches are plugged in, they're adopted, they're upgraded. It works just like any other Unify device. So if you're mirror with the other Unify line of products and the Unify controller software, which is free by the way, in case that comes up a lot, they give this to you by their hardware, they get the software for free, but it does only work with their devices. This won't manage other switches or other Wi-Fi units. The switches are DHCP by default. So you don't have to try and figure out some default IP on them. It makes it really easy. And I leave things at DHCP. This allows me to easily build a DHCP table, put all the MAC addresses in there and assign everything where I want it. So I'm happy to leave it that way. But you can go into these switches and I have an eight port, a 48 port and 24 port. I didn't demo the eight port. It really nothing significant on it. This is just for the 24 and 48. They're very similar devices, just more ports. But when you go into config, you have the option if you want under the network to change it to static IP. So you can't statically assign these if that's something you want. So you don't have to rely on DHCP servers being up when you reboot a switch. Anyways, the neat thing is when you have all these plugged in, and I really like this. So a comment about the lights next to the network port, but when you have them plugged in, you also get to see the ports here. It tells you like this one, for example, is not plugged in gigabit. This one is was green versus orange. They got a little color coding here. And a really neat. So let's look at the topology of these. This is a neat thing I want to start with in here. So this is not a map of my building. This is the default map. I've never bothered. Maybe I will load the map of my building in here. And what it lets you do is drag the devices around the show more in the building. That's pretty cool. This is really cool. This is your mapping to show you the different devices and how they're connected. And this is really clever. So what this does is there's the eight port and it goes into where most things are and there's a dumb switch behind it. So the eight port sees everything plugged in directly to it when it's obviously more devices here than the eight port. So it groups them all together because there's a unmanaged switch behind after the eight port. Then we have our 24 port switch and it draws the line. Then that's connecting to our 48 port switch. Then we have a Wi-Fi connected to that and we have our other Wi-Fi plugged into the 24. Then here's the Wi-Fi devices that show up plugged in and are attached to this particular Wi-Fi. And also you can do the link labels. So if you have multiple Wi-FIs it will show you which Wi-Fi it's connected through and give you the flow through. So this is really novel. This builds it on the fly. There's nothing I did to make this and it just shows up. So I can also just say don't show me the clients and only show me this. So if you're building out networks and they expand the contract as you click them. So really helpful for finding things. And also when you go and show clients. Let me zoom out again here. I'm just using the mouse to scroll around. It'll bring up the client over here and I can pull the information and details from that client and find out where how it's connected and how it's connected there. So it's connected to back area Wi-Fi. Goes over here and lets you kind of drill down. Really slick. This is just part of the software and it works for the ports for things. So let's go over here to the clients. And here's my computer. Tom Spuder. And when I click on this it goes right to the port that my computer's plugged into. So it's really easy to find things. So it's on the 48 port switch and we named it 48 port switch and it's port number nine. And it'll let me go right to that port. So this is really slick the way the software helps you find things. So if you don't have a label network when you plug all these in you can easily go in here and start labeling out your network and your ports and understand what's connected where and start making the changes. Now back to the devices. Now when I first plugged them in before they're adopted part of the Unify they'll be unmanaged. I just want to note they work fine unmanaged. I mean you don't get to take advantage of all the features and why would you buy one if you're not going to manage it but just so you know out of the box they work as a switch. So here's all the devices and let's jump over to the network settings and show you how you build your network settings in here. So go over here go to networks and here's the network that we're on in 192.168.3 slash 24. So you can just edit this and you know set your network settings. You want to build some VLANs. No problem. So we have test three VLAN test VLAN and the VLAN ID form. If you want to create a new one pretty easy we're gonna say VLAN only. VLAN 40 because we have the idea of 40 and it's up to you how you want to name it. They have the you know nice text naming here and then we're going to go ahead and hit save. Now what this does when I jump to the device is real quick to show you all these switches went to provisioning mode and what that means is that setting gets pushed out and provisions to the switch. Now whenever there's provisioning there's a slight pause in the network not long but if you're paying you'll see a few seconds pause for the provisioning to happen and it kind of disrupts the switch for a second and if you notice the order at which they did it went through the eight port. The 48 port took a little bit longer than 24. I'm guessing just because there's more ports to program takes a slightly longer time but it's really it's a matter of second so it's not a big deal but what I think is a little bit annoying is when I do things like this you can name any port whatever you want. So this is port six and we're going to go ahead and name it because I know port six what does it have in here. The back area we fee plugged into it as we said so we're going to call this the wi-fi port port for what was called wi-fi for back area so apply great I applied it it's provisioning it so if everyone's running full tilt on the switch there's going to be a slight delay before it works and it's like I said it's maybe only one or two seconds but if you've worked in you know high-demand environments even a second blip people go oh my gosh everything pause now it doesn't show disconnected on the network it doesn't cause that level of problem but it does pause network traffic slightly just wanted to make a side note of that but I thought it was odd that it doesn't even when I name something so I didn't know functionality to switch I just gave it a name now let's go back into the ports and just show you a couple other things so you have these options in here for the profile overrides and the different profiles that we set up here now this is kind of cool because this is a two-part thing so here's the v-lands we set up here's v-land 10 v-land 40 test v-land 3 and it's got the name and brackets there so you know which v-land tag it is really simple and it shows up on all the switches so we're gonna go over here to ports on this 24 port one and grab any random port even if it's not plugged in doesn't matter profile and we can choose those networks and v-lands this is kind of slick because it actually has a couple different options in here so if we go back over here to our settings profiles switch ports you can build actual profile so all or disabled which is disabled at port all together so you can actually disable ports on there so if you're worried about security you go I want the ports disabled unless I implicitly turn them on definitely an option there and here's where you create a v-lands we can actually create a profile and some test profile so let's give it a real simple name here now if the switches are poe and you can mix poe and non poe switches this profile maybe you want it to modify the poe settings what's the native network for it what are the tag networks and go through there so we can say native land I'll say select all but maybe we'll drop out this one so we want it to be able to route just these networks and then we hit save and it's going to go up here to the switches you're going to see them switched to provisioning it's going to takes a second it doesn't it's pretty fast then that profile will show up in there so here's the one we created some test profile land link negotiation auto so you can edit it because it's an editable one so self-created one let me go over here to devices oh we have a port open already so let me close that so I can get to one and here's a custom profile we set and that allows us to set specific parameters on the port so if you have some specific parameters this makes it really easy to apply a bunch of them at once also if you want to apply a bunch of them at once you can do it this way you can select a few ports and group these into a vlan or our custom profile however you want to do it but that's really easy to grab segments of the switch and push all the settings to that segment of the switch makes it really easy for management because you can say okay this block is grouped to this and this block is grouped to that and as you notice I'm selecting them they're physically laying out over here how those ports are based on the ones I selected so it kind of gives you a visual reference of how the switch is laid out what the switch looks like this is also kind of cool to me cancel what I was doing here so close this close and I'm going to show you an eight port switch I'll pop this out real quick I love the way it does the things now this is the eight port one let's go to the 48 port pop this one out so you can create kind of these floating windows when you're doing it as well so you can kind of look and compare side by side just intuitive software like this makes the switches a lot easier to manage a lot easier to use and also you may have noticed that there are uplinks and downlinks on these so when you're looking at the network the ports the users that are attached to this network uplink to this is the 24 port switch and by clicking it it lets me pop this out again so now here's the eight the 48 and the 24 and we're going to look at the downlinks on here and it looks at what the downlink network devices are so we know the uplink port gives us a little symbol then we can see the downlink devices so we know this is uplink to the eight port switch and downlinked to the 48 port switch and downlinked to the LTS office Wi-Fi and when we jump back over here to the map so topology a couple of these out of the way and just close them and we don't care about the clients we just want to show the devices we'll take out the link labels make it clean we can see that so it goes here to here to here to here it lays it out for you so you can see as you build your network and as they plug in it builds this in real time so you can make sure that when you're doing some documentation that your documentation shows what this does so you know someone plugs something in wrong there's a really nice feature and it's just really cool the way it does this it's doing it on the fly we also did some testing it does this and things to take about five minutes to refresh you can though and i'll show you this real quick in the preferences you can enable the refresh button and the preferences and i went up here to the user and enabled that it puts this little button here so if you're doing something you don't want to take a glance at it because i want to know now what's going on you can do this and kind of force a refresh of the devices on on there and it will re-queue all the information so it builds the latest information it only seems to delay a few seconds from then for things that are on different devices so that's definitely really cool the way it does that now sorry what a couple of features the switch has you can look at the performance of the switch it shows you a cpu an information on there like the utilization information memory usage load averages i don't know how super relevant these are you can also go into the config on all the switches click on the debug terminal open terminal and you're presented with the standard linux command terminal in here i like it because you don't have to you can ssh into these but you don't have to use any external software that way you can just jump in this way it's already dropped in at the like root slash management level and we can go cat slash proc cpu info and see that these are all running little arm processors so they're pretty lightweight but get the job done and i don't think the load's overly wrong because it's not telling you the load of the network when it tells you load it's telling you the load of the processor you can actually run top on here and i've noticed when we're passing traffic back and forth on here it's not dumping a bunch of load onto this because the chips themselves handle all the offload of the actual switching itself so it pretty straightforward now in the services by default it has our tsp enabled but you can go back to stp or disable that feature all together you also get 802.11x control if you want to set that up so you can able you know locking in through a radius server the ip 802.11x mac authentication so that is a feature on there so you can really lock these down so your standard features you get with the managed switch now something kind of novel here and we'll go over here to the 48 port one and pop it out close that when you're editing the ports the other options that come up let's say we want to group some ports together for link aggregation you can link aggregate all the different ports together you just have to do them sequentially so we're going to go here and here's the mirroring option for a port so if we wanted to mirror it and put the other port that you wanted to have a mirror on you can aggregate the port so we'll go ahead and aggregate a couple of ports together and then hit apply and when we come down here now i only have to edit and it says aggregating port 45 pretty straightforward and simple so it makes it easy to do and makes it easy to edit and if you want to turn that off just turn it back into switching apply they're back to being switching ports i believe you can aggregate the SFPs as well yes so it will let you aggregate the SFPs as well so that's cool so i can do that and i can aggregate the SFP ports so this does have two 10 gigabit SFP plus ports and then two SFPs this is only under 48 that i'm aware they don't have any 24 port miles i've seen or i'm aware of any coming out that have 10 gigabit on them that would be kind of nice if they did but i don't think too many companies make those now other options on the ports if you can assign it specific vlands like i was showing so you can easily assign that there to say this port is for that vlan enable port isolation or manually also override the duplex modes on here so pretty common stuff that you can find in a managed switch i just really like how easy they made it to do and how i can just label things on any port of what's on that port actually i had my laptop plugged in here and i unplugged it so it still just labeled tom's laptop this is kind of tool i like how it puts a little eye on there when you set it to port mirroring so if i mirror port i edit it real quick you just pick the port you want to mirror pick the port you want to mirror it too and away you go you end up with a little mirror on there so right there port mirroring and if you notice in the background it paused for a second and flipped is that was re provisioning it so kind of neat so if you had some monitoring devices you want you can just go mirror a certain port to push all the data also to that port look so these are pretty straightforward things you get with a managed switch and it comes in here i just really like how intuitive so i'm not trying to log in a web interface for these and instead of logging into a web interface for each individual one is what i meant so instead of trying to go into each one i can do everything from here and it just cascades to the everything else and when you add new devices it gets all those same vlands so it makes setting all this up pretty much a breeze you don't have to try and figure out and match everything when you set up a new switch you just adopt it into the network in all the settings including custom profiles and all that just come right back in with it so pretty much a good overview of these i'm really happy with them the performance and everything you know we did basic testing it didn't really run any problems i didn't have enough devices to really load this up and i didn't have an sfp tank to do that i believe you can find some tests that people have done on these but they work as they say on the box uh from what i've read in the forums and reviews there's they they claim the spec on them they match the spec they are full of gigabit uh non-blocking plenty of bandwidth you can get through here and it just works really well they really haven't had any headaches with them we've deployed these for clients these ones are getting deployed at a larger installation i wish i could show some of the installations we've done uh but unfortunately there's a lot of you know security reasons and privacy reasons we don't show clients we build everything in our lab and show you how it works but hopefully this is a good overview of these switches and the uh i'm probably doing a unify review of the unify controller software again because now that we've got to this version 5622 it's probably been about a year since reviewed the software overall and that's one thing i really like about unify is their software keeps getting better and we were just laughing at just how old this a wi-fi device on our network is when it says lts office wi-fi this is one of their version ones i don't know three or four years ago we installed this still works great still getting updates the software still handles all the updates firmware updates and everything for it and still functions with this one that is only i don't know it arrived a week ago so it's it's not too old i know it's a slightly older models i think they have v3 hardware out now but unify keeps updating the software so you keep getting more features so you see you get everything you see here but if you buy this six months from now there's probably gonna be a new version with more features added to it so the unify software keeps improving keeps adding features and uh you just keep updating it i've been really excited for the company because they're also very responsive if you find any flaws in it you post it in the forums they're very quick to get updates on these and close bugs if you find them anyway it's hopefully helpful and make some decisions on these give them a big thumbs up really happy with the device no complaints with it and it works really well all right thanks for watching if you like to content here if you have some questions leave me in the comments below


Welcome to Introduction to Annotated Bibliographies. In this video tutorial, we will guide you through the process of creating a well-structured and informative Annotated Bibliography for your research and writing needs. Let's get started. An Annotated Bibliography is a list of citations to books, articles, and other sources, along with a brief summary and evaluation of each source as they relate to your research area. It helps researchers organize their research materials, critically evaluate sources, and provide a concise overview of the literature on a particular topic. Think of an Annotated Bibliography as a roadmap through the vast literature that exists on a topic. Annotated Bibliographies are important for several reasons. They allow you to outline the depth and breadth of your research area. They help you evaluate the credibility and relevance of sources. And they serve as a foundation for your research by providing a comprehensive list of sources to explore further. Let's take a look at the components of an Annotated Bibliography. Each Bibliography entry typically consists of three main parts. The citation, the summary, and the annotation or evaluation. The citation includes relevant information about the source, such as the author's name, publication title, date, and so on. The citation style you choose should be based on your research discipline. If you have questions about citation styles, feel free to reach out to a librarian or consult the citation style research guides located on the library's website. The summary provides a brief overview of the sources content, highlighting the main arguments, research methods, and key findings. The evaluation or the annotation portion offers your critical analysis of the source, discussing its strengths, weaknesses, connection to other sources, and its relevance to your research topic. Now that we understand the components, let's discuss some tips for writing effective annotated bibliographies. Tip 1. Begin by carefully reading and understanding each source. Take notes and highlight key points that you want to include in your annotation. Tip 2. Be concise and focused. Annotations are typically around 150 to 200 words, so make sure to provide a concise summary and evaluation without getting too detailed. Avoid summarizing results that are outside the scope of your research or your interest in the topic. And tip number 3. Read good annotated bibliographies to understand their structure. You can find examples on the library's annotated bibliography library guide. Creating an annotated bibliography may seem like a daunting task, but with practice and attention to detail, it becomes an invaluable tool for your research process. Feel free to visit the annotated bibliography library guide at the link posted on the screen. Thanks for your luck with your research. For more information, contact us at library at Tulane.edu or visit our website library.tulane.edu. Thank you.


everyone and welcome once again to another edition of the Red Brown and Williams real estate show. I'm Shannon Deskins and you're used to seeing me with Jennifer Brown Day, but today I have Paul David Brown, presidency of the company. Nice to have you here. Thank you, Shannon. Glad to be here. I think Jennifer's got some time off. She does. Some well-deserved days off and she'll be back next week, but excited to be off this week. Well, having you here, we're going to be able to talk about some services that you guys offer that Jennifer and I sometimes don't get the time to talk to, so talk about. So we'll talk about that as the show goes on. Sure. But the first one we want to talk about is a commercial listing. Now, we'll have a commercial lease later in the show, but this one's for sale. That is correct. This is a property that we've talked about before, Jennifer's talked about before on the show. It's a prior bank branch on Northlake Drive in Prestonsburg. It's a corner lot, about a half-acre, a little over 1,900 square feet, a couple of unique things here. You do have three drive-throughs. Of course, you've got the bank vault. Very nice building. The building is very well-kept, has up to about 20 parking spots. It's on the busiest street in Prestonsburg. There's a lot of through traffic in that particular part of Prestonsburg. You're close to the high school, close to Wendy's, and not far from the courthouse. So it's a very good location with the drive-through as a unique feature. Also the vault. A lot of parking. It's an excellent property and the price was just reduced. So that makes it even more attractive. Right. And when we'll tell you the price in just a minute, I'm sure if you're in the market for this, you're going to be surprised in a good way. But like you said, this is the road that goes through Prestonsburg by the high school, by Wendy's. You know, be creative with this. I mean, we say it was a former bank, but there are a lot of different businesses that could utilize the drive-through. Like you mentioned before, a utilities company. Yeah, that's true. We've sold several buildings similar to this in the past. There are pharmacies, for example, because of the drive-throughs there. Could be a utility company, a TV cable company, anything that the drive-through would be an advantage to. And then, of course, again, the building is set up very nice, has a lot of parking on a very busy street, easy in and out, straight off Northlake Drive. And then we've got some pictures on the screen also of the interior. So it's very, it's ready. I guess you could say, we say move in ready a lot of times with residential, but this is a commercial building that's also move in ready. Absolutely. You could buy this property, move into it very quick time, be ready to operate. There is a place, a pole there already for signage. The lot is ready. The building's ready. It is truly move in ready.  And then we're going to tell you the price now, $319,000. This was just reduced, I think, today. That's correct. So if you're looking to start a business and you need a location, or maybe your business is growing and you want to look at a second location for this price, you could do that. Absolutely. It's a very unique location, a good location for anybody that has any kind of commercial use. I'm assuming the Prestonsburg office will be the main one handling this? That's correct. You can call the Prestonsburg office at 886-3939 or call any of the other offices and any staff member from RB&W can help you. Okay. Now moving on to the second listing that we're going to talk about today. Now this one's residential, but we're going to move into Johnson County. That is correct. Very nice colonial home. It's got an in-ground swimming pool, a little over 3,700 square feet, four bedrooms, three and a half baths. As I said, it's got an in-ground pool. It's very nice, a concrete in-ground pool. It has a gated entrance. It does have a detached garage as well as an attached garage. So you've got places to put your toys, concrete drive. It's kind of up on a little knoll, a little ridge that overlooks the valley. Very good location, private location. People have already relocated. So this property is on the market available to be shown at any time and it can be occupied basically on closing date. They could move into the property and be ready to go enjoy the swimming pool before summer's over. And you were going exactly where I was thinking about going because a lot of people right now, school is out. I'm sure swimming pools are bonuses at this time of year when you guys do showings. And we're still early enough in the summer, so I guess it's possible somebody could get through this one, get through closing and still be able to use the pool this year. Absolutely. It is a heated pool, so you could get into this house, enjoy the swimming pool four or two or three months this year before the swimming season's over. And then let's talk about the location of this. I mean, you are just outside of Painesville, but you are right off US 23. So you're looking at, you know, Louisa is not that far to the north. You're looking at Pikeville to the far south, but you've got Preston'sburg right there that's accessible too. So commuting wouldn't be a problem. Not a problem. 15 minutes to Preston'sburg, 10 or 15 minutes to Painesville, 30, 35 minutes to Pikeville. I and as Louisa as you said are very close and you're literally are a couple minutes off of US 23. Houses like this that are very convenient are great for those who have to commute. Absolutely. Again, the private location, if you do have kids, they've got a space outside. They're not stuck inside, but they have a space outside, a lot of room to play. In addition to the swimming pool, you've got a big yard, a nice yard. So it's a really nice property. And it's gated, which a lot of people for security reasons love that to hear that. That is correct. So definitely the Painesville office, I'm assuming, will be your lead office for this one. Painesville would be the lead office on this one, the phone number in Painesville 789-8119, but as with all of our properties, any location can assist them with any property. Right. And now when you do call, mention 105-648, that is the MLS number that will pull this listing right up. And the price on this one, if you're in the market, 449-9. And as Paul David said, it is move in ready. Now moving on to something that Jennifer and I haven't had the opportunity to talk about before is we've got an absolute auction coming up. You being the auctioneer, you're a perfect one to talk to about it, but this one's in Pike County. That is correct. It's on 319 at Hardy. It's about four and a half miles away from the main road from 119. So it's very convenient to Williamson, South Williamson, Pikeville. It's not very far from the Tug Valley Appalachian Regional Medical Center. So it would be within 15 minutes there. You're within 20, 25 minutes of Pikeville. But it's a good location even though it's off the main highway, it's still a very good location. As Shannon said, this is an absolute auction, which is a little bit unique with a property like this. That means that the property will be sold on this day regardless of the bid. So if you are looking for a startup home, if you're looking for a retirement home, if you're looking for a place for a child, perhaps it's going to get married in the near future. On July the 16th at 11 o'clock, this property will be sold by absolute auction. So regardless of what the bid is, this property will sell that day. So if you have anybody that has an interest in a property looking for that first home, this would be the perfect opportunity. Just like any other listing that you have, if they call on this one the Pikeville office, you can schedule a showing. So treat this one as if it's a home that you're looking at buying. You can go ahead and do your showing. And I think you and I have talked about before, you could even go on as far as having an appraisal done or a home inspection. That's correct. You can go ahead and contact your bank. We can even send you the information on the property, photographs, schedule the property so that you could pre-qualify yourself with the bank. You could have the appraisal done. You could have any other inspections done prior to the day of the auction. So literally the day of the auction, you would already be approved. You'd buy the house. We could close it very, very quickly. It is move-in ready. It's an older home, but it's been renovated. It's got a new roof. It's got a lot of new floor coverings in it. The kitchen is nice. It's got a really nice yard. Somebody that might have an interest in putting in an in-ground pool. Then you have a yard out back that you can do that. And again, it's conveniently located. It has all the amenities that you would want. It is ready to move in, and again, it will be sold on July the 16th, and whatever the best bid is, they're on the property. I mean, you don't find this opportunity very often is to say, well, I've got X amount of dollars set aside, and I'm approved X amount of dollars to buy this house, and then you only end up paying half of that. And a lot of absolute auctions that auction companies will do are on foreclosure properties or properties that are dilapidated or in very bad shape, and that's not true with this. It's an unusual opportunity for somebody looking for a house. If you need directions, you want to schedule a showing for this one. I'm assuming the Pikeville office will handle that one, Jennifer and her staff. That is correct. 437-2333. You can call and make an appointment. We can meet you there, let you go through the house and look at the house prior to the auction day, see if it's something that you have an interest in, and then you'd be ready to bid on the day of the auction. This one's one. I'm going to follow up with this one just to see how much it goes for, because that one's unique, as you said. That's it. It truly is. Now, moving on, let's go back into the Paintsville-Prestonsburg area. Now, this one is a lease, but it's a commercial lease, and it's a building many people familiar with that area will recognize. That's true. It's the old Rainbow Mobile Homes office building, which is on 321 between Paintsville and Prestonsburg. What's unique here, again, is that it is a commercial property for lease. It's in very good condition. Not only do you have the property itself, the building itself, which is a little over 6,600 square feet, but you've also got up to two acres that go with it where you could do some additional things. You wanted to build an additional building. If you wanted to have a mobile home sales, then you would have a display lot. If you wanted to have a car sales, if for some reason you need a lot of parking, you have parking there available. It's in very good shape. It is a property that can be shown at your convenience, anybody that wants to look at it, we can show it with an appointment made at any time, and it is conveniently located between Paintsville and Prestonsburg. You are basically halfway in between the two, so it could easily be somebody that has a business interest and Prestonsburg could locate here or Paintsville or somebody that's looking for something regional. Right. And then it's interesting that this one is a commercial lease because there are reasons that a lease may be more attractive for some businesses than purchasing, than really taking that leap in purchasing. You may want to test the waters first. This is a perfect opportunity for a new business. Absolutely. A lot of people who get into a new business or maybe they're taking over an existing business and they're a little shy about, am I going to be here five years or ten years from now?  Then the opportunity to lease for a year or a couple years would give them a chance to kind of get their foot in the water, determine whether or not they want to stay in that business. And then they could get a long-term lease at some point if they wanted to and remain in this location. But they would not be working with a mortgage, trying to make a mortgage payment and be concerned that if their business doesn't work, then what am I going to do with this property? Correct. Now, this is one, Paintsville or Prestonsburg offices, either one. Let's give both of those phone numbers. Sure. Paintsville is 789-8119, Prestonsburg is 886-3939, either one of those offices will have the information and they have keys to the property so they can show the property at their convenience. Right. Just tell them it's the commercial listing, the Old Remo Homes office on Route 321. They'll know exactly what that is. Absolutely. Now that brings us to the point we're going to close the show on today is that services that you guys provide, a lot of people may not be familiar with. So if, like I say for this one example, the one we just talked about, if someone owns a commercial piece of property but they just don't want to go through the hassle of dealing with the renters and collecting the rent, you guys provide that service? Absolutely. The commercial property that we've already talked about, part of the inventory that we have in our property management portfolio, we do property management for strip centers, for townhouses, for apartments, for individuals on rental houses, for all kinds of different property where the property owner perhaps lives out of the area doesn't want to have to come back, use the property to take care of either renting it or doing some kind of maintenance. We take care of all those things for them. And again, we do from very large shopping centers where we are leasing to regional and national tenants, to smaller apartment complexes, townhouse complexes, even individual houses. We'll make sure that the maintenance is done, that the tenants are paying the rent, that you have tenants in those occupancies. And it is a service that we offer that not a lot of real estate companies offer this particular property management type services. And Red Brown and Williams does do that. So if someone is thinking about buying a piece of commercial property, but their only reservation is I don't either want to have the time to deal with it all, but there's such an opportunity there and they're on the fence, you can pretty much take all that hassle away from them. Absolutely. If they're thinking about buying a property, they don't want to manage the property themselves, we can do that. If they already own a property and perhaps they've owned it for a while and they just say, I'm tired, I'm tired of it, I just don't want to do it anymore, then they can turn that property over to us and we can manage that property for them. And at the end of each month, they get a check and do not have any of the other problems that you'd have with rental properties. Which is the perfect case scenario. Right. Okay. Well, I hope that we've given everybody today a lot to think about, from commercial to residential to leases to services that you guys offer. I think, hopefully, your phones are going to start ringing after this show. Absolutely. I hope so. All right. Well, thanks for coming in. I'm going to step out now and let you end with your real estate minute. Thank you. With the sluggish economy and the gloomy outlook from many experts, it's easy to become pessimistic about our future. I would argue just the opposite. The people of East Kentucky have always been an innovative, hardworking and God-fearing people. With our struggles come new opportunities, new direction, new determination, and if we stick together an improving economy and better place for our families. Groups such as One East Kentucky have been formed to promote the people and communities of East Kentucky. Local chambers of commerce, rotary and other clubs, churches and county and city governments are working to make a difference in East Kentucky. Today there is more quality real estate available than ever before. Interest rates are low. Banks are competing for loans. New construction is increasing once again. Do we have a way to go? Absolutely. But the people of East Kentucky are up to the challenge and Red Brownham Williams Real Estate Services is in the fight with you. Please call Red Brownham Williams Real Estate Services for all your real estate, appraisal and auction needs and allow our family to be a part of yours.


Good afternoon, everyone. I'm Gunfrey Berra. You can call me Jet. I'm actually a senior Java developer for legal match Philippines. Our office is actually in Sibu, which is actually a U.S. company. Then I'm also a co-founder of Devkon Iluilo, both of us, Jingoy Dai, and the president of Flamenco Productions Incorporated. The focus of my talk is more on the fresh grad side, even though yes, some of the freelancers as well. Anyone who is a student pa, sino ma students dito? Very few, okay, there. Graduating or what year? Fourth year, so very good, okay. So from fresh grad to professional guide to choosing between freelance and employment in IT. This is a common mistake of some of the students jumping after graduating from IT course. They jump into a freelance career path. So why is it that I mentioned that is wrong for fresh grad to jump into a freelance career rather than employment? Okay, first let's define first freelance versus employed. So when you say freelance, you're doing multiple jobs with different clients at different time, which means, ikaw may hawak ng oras mo, usually sa freelance. So while in being employed, you work eight hours a day, okay. Then you have a boss sa freelance. You have a client, but you don't have a boss. So why is it that I mentioned that is wrong for fresh grad to jump their career into a freelancing rather than being employed. Number one mistake, how do you cost a project? Because common for in schools, because I've been in the academy for 12 years, nagturo ako sa academy for 12 years. Hindi nagturo or there are some courses or some maybe universities that teaches costing for a product or project, especially in the software engineering subject. Okay, common mistake. How are you going to cost your project as being a fresh grad? So anyone who you think you can tell you have any idea of how to cost your project. Then number two, standards. Are you very confident enough that what you learned in the four corners of the classroom are already standards that you could accept a project? So most common clients that I have met, especially local, so they think that they could get a cheaper project by assigning the project to fresh grad. And what happened is mostly it is a disaster. Number one, students don't know what standard is. Because that is not actually being taught in most of the schools. So that's number two. So that's the problem sa, sabi kong, I don't want students or, as I mentioned, that it is wrong for students to jump automatically from fresh grad going to a freelancing. So then why you should employ in the first place? Actually, I'm not talking about the salary here. Because the speaker before me is actually a freelancer. And the speaker before him also doing freelancing. So I'm not talking about the salary of being a freelancer and being employed. What I'm talking about here is gaining knowledge in a standard form of software development or engineering. So you cannot get that by just doing freelancing. Or maybe you could after several years, pero it will took you long to gain that knowledge. Unlike being employed, you have a supervisor, you have a team lead, you have a product manager, you have the architect, who will guide you in your experience in working for several projects. So that's actually my point. I'm not talking about salary because I am also doing freelancing since 2011, since until now. Even though I'm employed, when I actually, what do you call this? Nung nag-sign up ako as a speaker for WordCamp, I was actually a freelance. Right now, I'm employed. So just to make a clarification, I'm not actually referring to the salary here. I'm just actually referring to the knowledge that you will gain of being employed in a certain company. For example, if you work in a big company, IT or a tech company, you will have to learn a lot. Number one, those technology that was mentioned before, like the Jingo and the Mark. Those technology, you cannot learn them in schools. You cannot learn them in the forecourt. Mostly what being taught in classrooms are the basics only programming, basic programming 101, then web development, and everything are basics. So you cannot learn, like CICD, let's say technology, or learning tech like liquid base, something like that, into my database migration using liquid base. So mostly you cannot learn that in inside the classroom. That's why I would suggest, I prefer or I suggest that most fresh grad should employ first rather than being a freelance. Let's talk about the advantage of being a freelance and being employed. Of course being a freelance, you could work anywhere. But right now, because of the pandemic, being employed, you can work also anywhere. Diba? There are jobs, full-time employment that overwork from home. Or one example, if you're familiar with company Orange and Bronze, they don't call it as a work from home, but rather work from anywhere. So they provide you the laptop. They don't care if you're going to work in a internet cafe, in a co-working space, in hotel or your home, as long you get the job done. So therefore, the concept of being a freelance that you can work anywhere is not na, hindi na siya ganun ka different sa, what you call sa, being employed. Because for example ako, kami nila Mark, Jingo, we are all employed or certain companies, but we work from home or we can work anywhere. As long we have the internet, we have the laptop, we can work anywhere. So it doesn't necessarily that yung iba gusto mag freelance because they want to work anywhere or they want to work anytime they want. Okay, let's go to advantages of being a freelance work. Flexibility. Of course, this is one advantage of a freelance. You get to choose your own project. For example, may kausap ako ka kanina siya na, siya na yun. Rather than investing her time in mobile development, siya rather choose being a freelance of a certain technology. So you get to choose. When being employed, you don't have that, you don't have that luxury of choosing of a certain project. For example, you only want to focus on web development, but your company accepted a project that will cater mobile application development as well. So you will be forced to undergo training, all those stuff, to be able to work on that certain project. So in freelance, you could choose actually. So that's one advantage. High earning potentials. So being a freelance, you could work multiple clients at the same time. For example, if you have a client paying you 100,000 a month, then another client paying you 100,000 a month. So working with two clients, you are earning 200,000 a month. While being employed, you only have one source of income. That is your salary, 1530. Diverse experience, opportunity to work at various clients' projects, gaining exposure to different technologies and industries. Dito, you could actually, for example, you are working with, you are doing projects for WordPress. Then you want to learn, let's say, reactive. So you get to choose again another client that one of the requirements is reactive. Let's say, if you want to do Java programming, you could do so. That's one advantage of being a freelance as well. You could pick or you could have diverse experience with multiple technologies. Disadvantage. Income inconsistency.  Let's say, before pandemic, you have all these clients, then when pandemic struck, all of your clients were gone. So what will happen to you? So you don't have any income. So, possible that you're earning six figures right now, the next month, you will be earning a little less. So, there is no inconsistency. Unlike being employed, you have a fixed salary 15 and 30. Lack of job security. Of course, your client can cut your service anytime they want. In being employed, you are protected by company rules and regulations. Or if you are employed in a local company in the Philippines, you are protected by Dole. One example. Soal responsibility. Freelancers are solely responsible for finding clients, managers and administrators. So, when doing freelancing, it's actually very the competition is very, very stiff. So you have to have a very, very good portfolio. In order for you to find a client. So, being a student, what kind of portfolio are you going to show a certain client if you are a fresh grad? So, the possibility for you of getting a client is slim rather than those freelancers who already have experience for several years. Now, let's go to employment. Advantages. Of course, as I mentioned, stable income. You have a fixed salary. Let's say you are earning 100,000 a month. So, 1530. So, minus all the taxes. So, you get at least 40,000 every 15,000 or every 30,000. So, paycheck to paycheck. Job security. At least the company cannot fire you sa big laan. Of course, unless if you are working with a U.S. company, you don't have a local company. You don't have a local office in the Philippines. So, tendency, there are certain U.S. companies who can fire you on the day mismo. Let's say may violations ka. So, pero when you say job security, at least there are certain companies naman that will give you notice period. For example, two weeks or one month or let's say there are certain rules and regulations within the company that let's say you can only get fired for a certain number of violations. So, in freelancing you cannot do that. So, professional development. Of course, there are certain companies who send their employees for trainings, especially when handling new projects. Or mostly, if you are under in a tech company who are actually outsourcing projects if you will be assigned to a new role usually the company will send you for trainings before you will be able to handle that kind of projects. Now, disadvantage of employment. Okay. Limited flexibility. What you earn as a being employed, that's it. Let's say if you are working in a government you are earning around, let's say, 20,000 a month. So, wala na. That's your salary. You only get 20,000 a month. Unlike being a freelance you could get multiple clients. So, limited earning potentials then last is the lack of autonomy lack of control over project choices and decision making process. As I mentioned sa being employed you cannot choose your project. Actually the boss chooses the project for you. So, you cannot decline if the boss tells you to work on a certain project na hindi mo sya what you call, di mo specialty. But as I mentioned disadvantages the company will send you to training before handling, before you will be able to handle that kind of project. Okay. But what is the best part of being a freelance or employed? Of course. Here. Your job pays the bill. Your business pays the lifestyle. What do you mean by this? Which means you can do this. You can do both. You can be employed and at the same time you can do freelance. So, your employment pays the bills and your freelancing actually pays for your lifestyle. What kind of lifestyle if you love to travel then let your freelancing do that for you. So, for example ako I'm employed with the legal as a senior Java developer but at the same time I'm also doing freelancing as an IT consultant. So, previous speakers, I'm not going to mention na lang but they are also doing freelancing. So, the focus actually of what I'm talking here this afternoon is actually this is just for the fresh grad guiding them that don't jump when you graduate in the in universities, in IT courses don't automatically look for a freelance job. As much as possible look for a tech company that will develop your skills. Then later on you can decide whether you like to be being employed or being a freelance but why choose when you can do both. Thank you.


Okay, all right. Thank you. Go ahead. Okay, so this will be the locks lecture I believe. So in the in the second lecture basically were introduced to the problem, whether we have regularity localize this or so put it differently so to two, one of the focuses was whether we have regularity implies F regularity. So, so now we're going to sort of look at a stronger conclusion. So let me put this open problem. Here. Right. Well, you don't let me write. Sorry. Let me start over. Apologize for that. So let me. Okay. So let me mention this open problem. Okay, so in literature this was having referred to the weak imply strong problem. Okay, so I believe we have seen the notion of strong of regularity. Right. So, or let me probably recall that. We call. Now, I believe when Lincoln define this, there is a qualified so the ring assume to be a finite I'll continue to do so. Okay. So, and a finite, let's say it's reduced. Okay. R is strongly of regular. If for all see not in any minimal primes. There exists the E such that this map. So R goes to because R is reduced. I can take peace route and then repeat. So I take P to the East so one goes to see to the one over P to the E this split. Okay, that's how we define. Okay. All right. So, so I like to mention some approach to this problem to this and I want to maybe characterize both properties. We're using modules. Okay, so the first theorem. I want this, of course, was due to Hawks and uniquely. So the following. So R is weekly of regular. Even only if for every pair. So, and is contending M with M funnily generated. So N is actually tightly closed in M. So any the same as the type of closure of an email. Okay. Now the keyword here is finally generated. So because in a moment we will see a very similar characterization of strong F regularity but we're going to drop this qualifier funded generated so the final statement for strong F regularity will be R is strongly ever even only if for every pair or modules. Find a general not every some of you will be tightly closed. Okay. All right, so let's prove this. Some direction requires a proof because if I assume the statement for modules I can simply replace M by R and M by I. So assume. So R is weekly of regular. So let's assume there exists such a pair. So N is in M, but finally generated. That's crucial here. And so N is not tightly closed. So that means I can pick. So there exists a Z, which is in the target closure but not in M. So we want to reduce to the, to the ideal case. Here's how. So consider all some modules of M that doesn't contain Z. The set is not empty because N is in there, right, our assumption. So you can buy sales one llama you can see there is a maximum element. So there is a maximum such module. We're going to call it L. Okay, so certainly and is contained in L. So Z is not in L and is contained in L because he's containing L. I know that the type closure of and it will be contained in the type of over L. So that means he's doing the type of L but he's not in L. So I can replace M by L now, because the condition is preserved. All right, so we may replace M by L. Okay. So we're looking at those triple. So I have a Z, I have L, I have M, right. I can. So by, by modding out L, we now consider Z, because he's not in L. So Z is still non zero. And, and, okay, so I'm replacing L by zero and M by M model L. Okay, so now we're looking at the condition so Z is not zero and Z is contained in the type of zero in L. Okay. So what's the benefit of doing this benefit is, well, because L is the maximum sub module, which does not contain Z. So once I kill L, I know Z is contained in every single non zero sub module by the construction of L. But put it differently. If I consider a cyclic module generated by Z, so R dot Z. So M is an essential extension of the cyclic module generated by Z, so R dot Z. So now let's consider any associative prime of M. So say P is an associative prime of M. So my claim is P must be a maximite. Okay. So because P is an associative prime, so I know there is a natural embedding from R model P to M. So I may consider R model P as a sub module of M. And Z must be contained in R model P, not only that, Z is contained in every single non zero sub module of P. So if P is not a maximite, so the dimension of R model P is at least one, then R model P cannot contain one element that is in every single ideal. Okay. So now if dimension R model P is at least one, then it does not contain an element that is in every non zero ideal. Okay. Because every ideal of R model P now can be considered as a sub module of M. So that implies P is a maximite ideal. So now from now on I'm going to write P as M. Okay. By the same reasoning you can show there's only one associative prime, a maximite ideal. Okay. All right. So now I, you can, because M has only one associative, so a similar reasoning, by the same reasoning, or you can say, you will want local R to M as totally fine as well. So, you know, let me just do that. Now consider R local at M. Because M is a maximite ideal, so R local at M is still weakly irregular. Still weakly irregular. Okay. All right. So M will still find a generated and has only one associative prime with the maximite. This means M has finite lines. So this implies M has finite lines. So that means a power of the maximum ideal will kill M. Okay. All right. So the next step is probably the only step I won't prove for you. But I do need the property of weakly of regular ring. So R M. This is weakly of regular. So we know that this implies it's normal. Okay. I believe we have seen this before. It must be called a normal ring. Okay, it's normal. And now there's a theorem by Milhochster back in 1977. This tells us so every power of M is an irreducible primary ideal. Okay. And this is where he introduced notion called a prosimistic or instinctive. All right. So normal rings are normal domains are approximate or instinctive. So every power of the maximum ideal must contain an irreducible and primary ideal. Okay. So that means there exist an irreducible and primary ideal. So Q that can tend in M to the N. Okay. So now so M is an R mod Q module. Okay. So because Q is irreducible and R mod Q is a tinier. So R mod Q is a Gorenstein and it's self-injective. So this implies one and two. So R mod Q is self-injective. So E is a Gorenstein. But this is where the name approximate Gorenstein come from. Okay. So let me do a quick proof. So one way to characterize Gorenstein-Renyi is that it has a primary ideal. Well, primary means a general by a full set on parameter that is irreducible. Now, because Q is irreducible. So the zero ideal in R mod Q must be irreducible as well. But zero ideal is a primary ideal of you because we're looking at our team. So the ring must be Gorenstein and our team in Gorenstein are self-injective. So meaning R mod Q is actually injecting module. Okay. So now the assumption is Z is containing every single non-zero cell module and my M is finalized. So Z must be contained in this non-zero cell module. Okay. This is called the soccer. Now the soccer must be one dimension of our assumption because if the circles are sort of K vector spaces and the one dimensional K vector space if it are different, the intersection must be zero. So Z can only be containing one copy of the K vector space. But Z is containing every non-zero cell module that will force the soccer to be one dimensional and only one copy of a K. Okay. So now let's combine these two things together. R modulo, so Z general soccer. So the secret cell module generated by RZ, so sorry, I mean one more step. So this tells us, so the cyclic module generated by Z is actually one copy of the relative field. So M is an essential extension of the relative field. Now R mod Q is actually injective that contains K. That tells us M must be containing R mod Q because the injury, for example, injury of how all relative field is the maximum essential attention of K. So given any other essential attention, you better have injection from that essential extension into the individual. So that tells us. So M can be embedded into R modulo Q. Okay, so now the zero sum module in M now corresponding to zero in R mod Q, therefore corresponding to Q in R. But R is weakly irregular. So Q is tightly closed. That tells us zero must be tightly closed in M. Now since Q is tightly closed. So zero must be tightly closed in M. But that's a contradiction. Because we look the presence of element Z. So Z is in the toddler zero in M, but Z is not zero. So that would be contradiction. Okay, so any question on this page? I do a question. Sure. Can you explain again why M is finite length? I mean it's finally generated. Right. So, so if you have a final general module, there's always a prime filtration. Oh, I see. Right. But the prime module can only be maximized. Because the maximum idea is only associated prime. I see. Okay. That means that prime filtration actually gives you the competition series and it's finite. Okay, thank you. You're welcome. Any other questions? Well, at the end of the day, am is just the objective, how the residue field of arm modern. Yes. Because of course, if this is an essentialization of blah, blah, and then you do the whole argument and at the end you are saying okay, I'm injecting site these and but what I am understanding if I am not wrong, and it's injected. M is the injective hall of arm of M. Capital M, capital M, I mean. Oh, capital M is just an essential extension. So it may not be. Okay, so you don't know whether M, capital M is the injective hall. I'm pretty sure you don't know. We don't know that. Let's just go here. So M is actually a sum module. We find the general sum module of the injective hall. So R module Q, that's the injective hall. Ah, okay, okay. Okay. Like I said, so R module is self-injective. So R module is actually injective in the local. So it doesn't split. So that forces it to be the injective hall of. Thank you. Okay. Any other questions? Okay, so if not, I'm gonna try to add a new page. Okay. Yay, it works. Okay. All right. So now I'm gonna categorize as a strong f-reglarity, but there's a point to make and just an approach to prove whether or to prove that weak implies strong. So here will be the, so theorem three. Again, this will do to Hoxter in a unique way. Okay. Okay. So, let's say R is, all right. So I mentioned the principle. I'm gonna plot the principle here. It's a complete local domain and these are finite. So since I mentioned finite, so must be in character B. Okay. Then the following are equivalent. Okay. So part A is, so R is strongly, probably efficient for a moment, is strongly of regular. Okay. And part B is, so N is tied to the closed in M, right? So this is for every module. Okay. Instead of finite, general, every module M and every sum module N in M. Okay. And C is, well, we don't have to look at every R module. There's one module that captures this property, which is the ingenious power of the rat you feel. So this is just EEs. Sorry, let me just say this is R and K. Okay. Okay. So, okay. I won't prove, I need to prove three implications here. So A implies B, B implies C, then C implies A. B implies C is trivial. So I'm gonna skip the implication A implies B. Now the proof is quite similar to our proof on pre-the-page and plus something about this, the forbenism map. Okay. The idea is quite similar to the pre-the-page plus the idea in the implication C implies A. So I'm gonna just prove C implies A, right? So proof of C implies A. So say, so U is a generator of the circle. E is a generator of the circle of E. Because this is in general, how we know that is the circle of the one-dimensional, okay? Now, since, now E is an, is, so that means, so the secret sum module generated by U is just one copy of K, that's what means. Now, the indiate of how of K is certainly either an essential, it's a maximum essential extension. Right, okay. So that tells us this condition holds if and only if U is not in the total closure of zero because U is contained in every non-zero sum module of E. Okay, so if the total closure of zero is not zero, it must contain U, okay? So that means it's the final part of the check, U is not in the total closure of zero in E. All right, so to do that, we're gonna go back to the definition of total closure for modules. Now, to somehow ease the notation, I'm gonna use R to the one over P to the E notation, okay? So one may view the Frobenius or rather the E for Frobenius as this inclusion, okay? Right, so once you do that, because in the definition of total modules, we need to apply the Paschian Spiro function to the module. So this F E, now this becomes the R to the one over P to the E now turns there over R is E, okay? And so the actions, so here's R, I need to tell you the module structure. So this R acts where this is Frobenius, okay? All right, so okay. So just by the definition of total closure of zero or total closure of the modules in general, what is this sign now? I'm just changing the notation from the Paschian Spiro function F E to this fraction power of R, okay? So U is not, so U, sorry, U. So U is not in the total closure of zero in E amongst to, for all C in R third, well, meaning C now there. For every non-zero element C, there is an E such that to basically I'm just doing the negation of the definition of total closure of C to the one over P to the E turns there with U. This is not in the total closure of E, okay? So P to the E turns there with U, this is not zero in this tensor product, okay? Now, which is equivalent to the following. So we're gonna tensor this R linear map where one goes to, so one go to C over W. So one to the P to the E. So tensoring this with E, the image of U is not zero. Okay, I'm just translating this condition on the bottom on the left, okay? Now, because E is an essential extension, so since E is an essential extension of the circle which is generated by U, this condition here to the non, the image being non-zero, so the image of U being non-zero, now E is equivalent to the injectivity of this map. So tensor over E goes to R over E, okay? So it's identity on E, but on the other hand, the map from R to R to the one over P to the E is sending one to C to the one over P to the E, okay? Now, I want to check this is actually injective. So why is it equivalent? Because if there's, assume there's a kernel, and this is isomorphic to E by the way.  So the image of U being non-zero means this map must be injective. So now, so harm this into E, so we turn injectivity into search activity now. So it's equivalent to the search injectivity of, you know, I mean not skip any stuff. Into E goes to harm P and E, okay? All right, this is isomorphic. Now here I'm using the fact my ring is complete. So harm E into E just R. So for the harm module on the left, I'm using a junction between harm and tensor. So this will be isomorphic to harm. R, P to the E into R, and now this is isomorphic just to R, okay? So that means this is surjective. Well, surjecting means that I can hit one. So that means, so E, there exists, phi in, let me write this way. Back to R, such that, okay. So let me give this map a name, maybe I call it state C comma E, okay? Such that if I can pull this to C, this is identity on R, okay? So that's exactly the condition we're looking for. So that means this map from R to R to one over P to E where send, we send one to C to one over P to E. This map actually, because I find the inverse, the left the inverse for it. So that shows R is strongly of regular, okay? So that will be the proof of C in point, okay? And you're watching on this, okay? So if not, I'm gonna move to a new page, okay? Now, if we combine these two characterization together, they tell that one approach to proving that we can apply strong, okay? So these two characterizations tell us, we may consider the following. We may consider the union of the particular of zero, the m where, so m is a finitely generated sum module of E, okay? Because individually, if we consider the particular of zero in m, m is finite generated. So individually, this should be captured by the weak of regularity, okay? Then we take the union, the whole bit, this union will capture strong of regularity. So let me state that. Certainly, this is open problem and this is actually equivalent to the weak implies strong condition. So I believe this is four now. I'm gonna write this away. So, so type of zero in E, whether this is in the same as the big union because this union certainly is contained in the type of zero. Okay, so I should put the question mark here, okay? Now, this problem is equivalent to the weak implies strong problem. So here the one we do see it, so quick proof. So if R is weakly F regular, then by the characterization, every individual one now will be zero because m is finite generated. So m is finite generated, okay? But that means the union is zero. If the union is zero, then based on the open problem, that says zero is totally closed. And so by the characterization of strong of regularity that shows the ring must be strongly irregular. So this will provide at least one approach to attack the problem whether weak implies strong, okay? Now, but can we actually achieve anything using this approach? The answer is yes. So this brings us to the theorem by Bernoulli-Lubasnik and Nicaraguan Smiths. So, but this has a name. This is called, I should say, this is called the finite test take type color of zero, so finite test take on type color. So meaning you take the type color inside the finite generated sum module and take the union over that. So let me mention the result, five. So the content is un-engraided. So the reason for sort of for us to look at the graded ring is the following. In the previous lecture, we've seen that even for the LC problem, you can actually solve it for the, in the graded setting. So that's at least one indication. The graded setting should be somewhat easier, okay? So F finite is weakly F regular, even only if it is strongly F regular. Now, I won't be able to prove this in like 10 minutes. Initially in my notes that I send to Stashna, I had to completely prove, but I don't think it can fit in 10 minutes. So let me just mention sort of the crucial idea here. So was the actually prove the following? So at the technical heart, here is their serum. So the technical core is the following. Again, this is due to the basnik and Karen Smith. Well, the proof is that the following under the same assumption. So R is still un-engraided and finite, okay? And say any Athenian graded ring. Sorry, Athenian graded R module. Then the following holds. If you take the time to close out with zero in M, this turns out to be the following union, okay? So delta or delta is ranging all delta. So means we truncate M because M is Athenian. So we know that there is upper bound on the degree. So after a certain degree or beyond certain degree, M is entirely zero. So if we truncate at a degree, now we have only finite many degree pieces and that is at a finite generated. So this is finite generated. So that's their idea. So instead of considering all the arbitrary finite generated some module, they consider some special one, okay? The truncation by degree. And they succeeded improving that. The tauticulory is actually the union of tauticulory in such truncations. And that's of the problem in the graded case, okay? All right, so like I said, upshot is once we have the accreditation, you do have this approach. But how do we actually generalize their approach in the graded setting back to say the local setting, which is real, the harder problem for weak implies strong. So here, let me mention sort of an open problem. So the analog of this truncation. So here we take the truncation, right? So what's the analog in the local case? The analog of this in local case is the following. I can take the pieces that's secured by a power or maximum idea, okay? So we may call this M for example, okay? That'll be a local analog. And so sort of the open problem or just if it's equivalent to before, so I'm gonna write this as four prime, maybe. So whether the tauticulory of zero in E is the same as the following union, I take the tauticulory of E sub N, okay? So it's four over N. Again, E sub N means the sum module that is queued by N's power of M. And that's finally generated because our module M to the N has sine N lines. And so you harm into E that you have sine N lines. All right, but this is wide open. So this is wide open, certainly, okay? So that means this weak implies strong problem is wide open in the local case. So now I probably move on to say some partial results. But before that, any questions on this page? If not, let me move on to the partial result. So now that's the partial result. I won't be able to prove any of this in that five minutes. So let me call this theorem. Okay, this five, I believe. Oh, sorry, the five was the theorem by this was six. So I'm just gonna mention a whole bunch of partial results now. So weak implies strong if, so one, if the dimension of R is three, this will do to Williams. So the protein is also somehow to extract a uniform bond on the kernel. Oh, sorry, let me step one, take one step back. So local mileage. So the indivisible E can be viewed as a local homology of the canonical module. Now, local mileage is the drug's limit of kazoo homology. So we need to understand the transition maps in the drug system consisting of the kazoo homologies. So the idea is that to analyze the kernel of those transition maps and to extract some uniform behavior, okay? And then he's to succeed in dimension three. Now, in dimension four, but it's not quite a local case, I need to put in some qualifiers. So R, so this will do to Arbobar and Postro, very, very recent, okay? So he's published in early this year. So assume that this is a finite generated KL in dimension four and K has infinite transcendent degree over the finite field LP. Over the finite field LP, okay? So under the assumptions in dimension four, we imply strong. Now, their approach is a finer analyzed analysis of this transition map of the kazoo, between the kazoo complexes. It's too technical for me to state that, okay? But now maybe lastly, why did I say four? This too, because dimension four, okay? Now, if R is comacoli with unisolated, oh, just sorry, let me take that back. Let's say if R is Gorenstein, okay?  Now, four, this is due to, again, due to Dubasnik and Smith in a different paper, okay? So if, so R is comacoli with unisolated, non-Gorenstein point. So meaning, so R local at the P is Gorenstein. If P is not a maximum ideal, okay? And lastly, let me just mention this result by any rock sink. So if R is Q Gorenstein, but of course, he put something even stronger, he showed that if you are Q Gorenstein, then splinters are strongly of regular. Okay, I think I need to stop here. Thank you for your attention. Thank you, Wenliang. Wonderful talks. Are there any questions? Just a little curiosity, who proved the result for R Gorenstein? R is Gorenstein? The one that you left as an exercise. Oh, sorry, I should, yes, let me write. This was already proven originally by Paul Hawks doing Hewney, okay? Are there other questions? If not, well, thank you very much, Wenliang, for wonderful talks. All right, thank you for the invitation. And we will see everybody on Monday. All right, see you on Monday.


It's not so bad to separately reinvent the wheel too, you know, I think that different teams of people working on similar products come up with different solutions, and slightly different from each other, and there's kind of a natural selection. You know, the more innovation we have, the more rapid progress we make. And so, you know, I don't think that's necessarily too bad, but the way we are interconnected now means that we can collaborate on that, and we can all try to figure out, you know, in the academic world, one of the big races was to discover the Higgs boson, right? And these competitors, at CERN, and these competitors were from all over the world, physicists from all over the world, were collaborating together, sharing all their research together, and coming up with the solution together. Because the result will impact everyone. So that's something that benefits everyone.


keep us in the back of me. It's making me. I told you I'd draw people. I told you I'd draw people. Anniversary. Since 1960, AT&T people have made the Oklahoma City work with the promise of high technology and what it holds for the future. We know how deep the little switches and computers we've had here in Oklahoma State. The lead AT&T has charred AT&T's work, the switching systems and the computers and AT&T bills here also raise the Oklahoma City work a world showcase for what American people can accomplish using American technology. We're proud of the delegations from all around the world from here to see the future in action. We're even more proud that you are here today to share with us this very special anniversary celebration. I'm proud to be in the home of your champions, the Oklahoma City 89ers and I'm people by making our tax code more simple and fair. I'm a business side of present tax. Code has a ton of corporate tax pay with 46%. I'm not delighted to see so many families here today because when it comes to the income tax you pay our plan represents the most important for the value to keep more of the traditional dollar you were. Right now individual tax rates go all the way up to 50%. You know what that means when you work overtime, right?  If you're promoted to a better job if you're able to save some money and invest it then fewer of those dollars or fewer will go to Lionel and Sanya pockets and more will end up in your wallets where they belong. It gets inside when I shoot him but I'll say it now that I'm so grateful that all the people that spent all their weekends bringing this up for an outdoor affair and they spent all last night changing the ground for his side but they're all of you to be out here. I know you've honored me greatly and I'm very thankful to all of you here. I'm assuming Mickey by your presence that we also have our special guest has arrived. I'm excited about that. Speaking about Mickey Edwards, you know we talk about the House of Representatives. My mother once told me don't say anything if you can't say something nice so that's all I'm going to say about the House of Representatives. I might take this moment since we have it to introduce my family because they are responsible for me being here and if they would still looking through the curtain to see if the signs are coming in. We're flying in with him on Air Force One and also we're flying out with him on Air Force One. He spoke to the Oklahoma legislature that went tonight where Bardsville, Oklahoma had experienced the tornado and did quite a lot of damage and I said something to the president that they did a lot of damage. He told the pilot, he said well let's go down and take a look at it so we're flying over Bardsville, Oklahoma at 4,000 feet in Air Force One surveying the tornado damage. The President of the United States. A person with leadership that this country desperately needs and deserves, he's the right leader at the right time, our president, Ronald Reagan. I'll be careful or I might get carried away and start singing Boomer sooner. Should I have said right of Cowboys? But I always get a thrill out of babies grow up to be Cowboys. So I forgot to say that Cowboys can sometimes grow up to be president. America needs Don Nichols too. He's carrying on in a fine tradition of Dewey Bartlett and Henry Bellman and I have to believe that your young senator in this state, still brand new with plenty of heart and plenty of hope for a match made for each other. You elected Don Nichols as one of the members of that Republican pahoma against the federal establishment in Washington D.C. He's been a firm defender and a firm voice for the rights of the family. He's a keen understanding, brave and mortal threat to human liberty and he understands that we can't preserve peace because he's still finding and doing away.