Γεια σας, είμαι Vicky here, με το νέο αργένα λαϊόδη. Τώρα θα χρησιμοποιήσω αυτό το ελλεφάντος από Stampendous. Τώρα αυτό έρχεται με αυτό το φόνος που μπορείς να σκοτήσεις τη δουλειά. Το ένα στήρα της ελλεφάντης είναι σωλή και το άλλο δεύτερο δεύτερο σχέση. Και also there is a rubber stamp that matches perfectly the solid side. Η κέντω also comes with a stencil. Θα χρησιμοποιήσω τη λαγιά για εσύ, και για εσύ θα δούμε το εξαιρετικό δεύτερο δεύτερο. Και also today I will be working on my bigger art journal, this is by Dilusions, the bigger size, just because the elephant is too big to use on my smaller Dilusions that I usually work with. So you can see the difference here. To start with I am going to apply some acrylic paint and today I am using my Dilusions paints. I am applying everything with my baby wipe and as I am using the colors you can see which colors I am using on the screen. I am using two different baby wipes for each color but I am using both of them to blend everything on my page. I haven't prepared my pages with Jesus so I am working directly on the paper and also what I love about Dilusions is that they have beautiful bright colors. They are really easy to blend and to apply and just to deepen a little bit my background I decided to bring in a third color which again I am applying with my baby wipe. Now these Dilusions paints really dry super fast on your page so you have to move quite quickly if you want to blend them nicely but at the same time using a baby wipe which is already wet it's a great idea because it extends the time that the paint dries and makes your job a little bit more easy. Now since I was a little girl when everyone asked me what my favorite animal was I used to say always elephant so when I saw this set I just had to use it on one of my Arjuna layouts. So now I am using the stencil again I am applying the same colors that I have used for my background and I am applying it by using my blending tool the round blending tool by Tim Holtz. Using the colors that I have used on the background over the stencil is a great tip to keep your background quite subtle. So I am going to keep it as it is I am happy with how my background looks and I am going to work with my elephant. When you are working with foam stamps it's always nice if you spray a little bit of water before you start applying your acrylic paints. So you can see now I have sprayed just a little bit hope you can see how wet it is and this is going to help the paint stay only at the surface and also it's going to make your life easier when you try to clean the stamp. I am applying again Dilutions paints and I am going to mix up two different colors on my elephant I find it easy to apply the paint with foam brush and you can see that with the same foam brush I am going to mix up my colors directly on my foam stamp. Now if you want to contaminate your colors stay away from this technique you can always use two different brushes to apply it. Of course you can use the foam stamp and stamp directly on your project but you know how I live paper piecing so I just had to try it on a different piece of paper first and you will see that I am going to get a great impression and I really have so many ideas of using this elephant set that I probably use it again and again on my projects. So you see the impression here I really love it and since I have all that paint I am going to try and see if I can do second generation stamping and you can see I really get a beautiful texture out of that and I am also going to spritz a little bit of water and see if I can get a third impression and these second and third generation stampings give you beautiful texture perfect for our journal backgrounds. So now I am going to wipe it off with my baby wipe I went to the sink to wash it it was super easy to remove and you can see it's totally clean just like new. So now I am going to use the rubber stamp and I am going to stamp directly on top of my elephant by using my black archival ink. This stamp is going to give a great texture on my elephant and it's not a big deal if you don't stamp directly on top of it we just need the texture for now you see that I don't pay any attention on the fabric at the top of the elephant since I am going to stamp it again and paper piece it later on So for now I am going to use my scissors and cut out my cute little elephant and for the fabric that the elephant is wearing I am going to use my tear quiz and color just a scrap piece of paper and then I am going to use my black archival ink and stamp again this part of the elephant on this piece of paper now instead of placing the elephant on top of the paper I am doing it the other way around so I can get a better impression now I can heat set it with my heat gun just a little bit make sure that the archival ink is dry and then I am going to use my scissors to cut it out So although this is pretty much the same color as the elephant you will see that when I place it on top now I am using again another piece of scrap paper and I am going to blend in those two colors these are the same colors that I have used for my elephant again and I am going to blend them with my baby wipes and to add a little bit of texture I am using this stamp set which is again by Stampentus it has great textures for your original projects for your backgrounds but I am going to use this stamp that looks like a lace and instead of using any type of ink pad I am going to use the same paints on my stamp so that again I get a nice subtle result and I am planning to cut out an umbrella out of this pattern paper that I am creating at the moment so I am going to use my pencil and dry a nice curve at the top and then follow the line to cut my umbrella now I am going to use the bottom of that stamp impression as the bottom of my umbrella but as I cut it out I decided that it was too big for my elephant so I went ahead and cut it out even more actually I am following the lines of the stamp that gives me a nice curve down there but I have a nice umbrella for my elephant and now it's time to stick everything directly on top of my art journal to do so I am using a gel medium this is matte gel medium I am going to stick my elephant about in the middle of my page and I know it looks like it's flying up there but you will see that I am going to place him on top of a string there so I am trying to decide where my umbrella is going to go and once I am happy with the placement I am going to commit and stick it down with my gel medium I am also covering everything all my elements with my gel medium and this is going to give me the ability to use my big brass markers to do the shading later on so I am going to stick the fabric on top and you can see that although it's the same colour just because it's not blended in it stands out against the background of the elephant so now I am using my big brass markers for my favourite technique and I am going to add shadows all over the umbrella and the elephant and as I am doing that just to let you know that you can find a full list of all the supplies that I am using today just below the video in the description area as well as on my blog the elephant and the umbrella look more dimensional and now I am going to draw the handle of my umbrella as if the elephant is holding it to do so I used my thin black marker and I am also going to use this marker to go all around the elephant and this is going to help the elephant pop even more against the background I am not going for the perfect lines I am just going a little bit sketchy here and I am also going to do the same thing around the umbrella and you will see that after doodling all around the umbrella I made the lines to the centre of the umbrella just to make it look more realistic and I am also going to use my big brass markers there to do the shadows another one of my go-to techniques is using my white gel pen and adding details on my elements so I am going to do some white doodling now on the different parts of the elephant as well as on the umbrella and I find that just a little bit of highlighting here and there with the white gel pen really helps all the elements pop even more against the background and I love the look and since I was using my white gel pen I decided to do some details on the umbrella so I am drawing those tear drops just underneath to embellish my umbrella even more now had this idea to put this elephant on a string balancing holding his umbrella so instead of drawing the string I am going to actually use a piece of white string I have placed where I want the string to go and now I am going to stick everything down by using my gel medium you can use any type of glue for that but just because my matte gel medium dries totally transparent without leaving any gloss and you won't be able to tell where the glue was I always prefer gluing things on my page with that and since my white thread is going all the way from one page to the other and over the fold I decided to cut it out at the fold you don't really see where the cut is but at the same time it's going to help my book to open and close easier so once everything was glued down I used my scissors to cut out the excess thread and now it's time to work on my quote for my quote I am going with those chipboard letters and these have been on my stash for many many years actually I think those are the same chipboard letters that I have used on my kappa art journal layout for writing down the word cup so anyway I am just coloring them black and to do so I used my black marker I could have used my acrylic paint also and I am going to place them around the thread I am not going to place them straight I am going to make them follow the line so once I am happy with the placement I am going to use my glue and stick them down just to make sure that these are nicely stuck down instead of using my gel medium I decided to go with my taggy glue I am going to use my white gel pen to add some highlighting on the letters just like I always do on the big bold letters I think that it helps them stand out even more to stamp my quote I am going to use this clear stamp set and this is by kaiser craft and I am going to use my black archival ink when I am stamping on an art journal I always like to stamp 2 or 3 letters at a time and not the whole world just because I am working on a bulky surface I won't get another good impression if I do otherwise so now my layout is pretty much finished I am going to do the finishing touches now so again I am using my white gel pen adding all the highlighting on the letters just like I did with the big balance word I am also going to stick one tiny black enamel dot as the eye for my elephant and I am really really happy with the outcome and also I found in my stash those white tear drops these are enamel dots actually which I am going to stick underneath the umbrella just to give it a little bit of dimension there and that was the project for today I hope you had fun and got inspired and if you did don't forget to leave my comment as well as give me thumbs up on my youtube channel here are some close up photos of today's project and if you need more inspiration here are two more art journal layouts that I shared a while back thank you all for watching


This is one way that I teach the strategy counting on using dot cards with my students.  See, there's two cards, okay? And I would have the class and I would count together the dots on the two cards. One, two, three, four, five, six, seven, eight. Then I would ask them, boys and girls, how many dots are on the two cards? And they would hopefully tell me eight. If they tell me something different than I would count the cards again until they agreed as a group, there are eight dots on these two cards. And I would say, gosh, I wonder if there's a faster way to count the dots on these cards? And they might give me some ideas and different things that they think would be there. And then I would tell them we're going to learn the strategy of counting on. All right, boys and girls, how many dots are on this card? And then we would count them. One, two, three, four, five. How many dots? Five. Excellent. Boys and girls, how many dots are on this card? One, two, three. How many dots on this card? Three. Okay. Now, which card has the most dots? Hopefully they would see that the five has more dots than the three. So we would take five and put it in our head. We're going to hold the five in our head. Boys and girls, don't forget it. What number's in your head? Five. And then we're going to start with five and count on. Five, six, seven, eight. Boys and girls, how many dots are on the two cards? Eight. That is right. Let's try that strategy again. Boys and girls, here are two more cards. Okay, let's count the dots. One, two, three, four, five, six. Can we count that faster? Can we do that job any quicker? Hopefully they're going to say we could count on. If they do not, then I would say, remember we can count on. Which card has the most dots? One, two, three, four. I'm going to put these dots in my head. Four. Remember, don't lose it. What's in your head? Four. And I'm going to start with four and count on five, six. How many dots are on both cards? Boys and girls, six. Then we're going to move on to two more cards. We're going to do the same process, but this time I might have them do more of the work. Boys and girls, which card do we start with? Hmm, which card has the most dots? Hopefully they notice this one and then we would count it. One, two, three, four, five, six. And put that number in our head. What number is in our head? Six. Start there. Six, seven, eight, nine, ten. How many dots are on the cards, boys and girls? Ten. The strategy is counting on and it's quicker than counting dot by dot. I would continue this until every student was confident. If they just weren't, I would take cards like this and put them in a bag and do small group activities and to build their confidence. If you have no cards, you can also use dice. They work the same way and count the dots. This is one way that I would teach the strategy counting on to my early childhood students.


Hello everybody, welcome to my channel. It's Eva from Bohemia and crafting and I'm here with another envelope craft and today I'm gonna share with you What I what I Decide to do with my own own mistake I did T died those envelopes and I forgot that it has this foldable strip with sticky sticky backside And I left it this way so on a most of my envelopes this Strip it's glued here, so I was thinking what I'm gonna do with it I can somehow extend it that's true But if I will be a little bit more creative, I can do more pockets from one that I decided so I did measured Where is my scoring board? Oh Blind Okay, I took my scoring board and I did measure how far from the edge Starts the window to make exactly or Needle sorry for my hands. I'm in a very grungy projects right now. So I'm very sorry for my hands. I did measure this space and It's five eighth five eighth of inch this this space so in exactly same Distance I did made score line here Five eight eighths of inch from this edge of that window here to make it Nicely beautiful this way to make it similar on both sides what I'm gonna do next I'm gonna take my And I'm gonna put my envelope About half inch behind that score line About half inch. So where is my score line? I'm gonna place that score line here. It's about half inch Like this. So I do have score line here And I will have something to glue it inside to create my envelope to make it possible to make it easy for me I'm gonna put this corner here.  I will have beautiful envelope so first I would like to Create exactly same Angle on this opposite side. I'm gonna fold it together those two sides and With my scissors. I'm gonna follow this shape like this and here this piece It's in angle so I'm gonna put this in that angle as well kind of similar not exactly same probably but kind of similar So I've got this one I'm gonna take that smaller piece here I'm gonna take back my scoring board and I'm gonna make score line on that open open side I think about three eighths of inch that doesn't have to be big big edge for making envelope. So I guess about three eighths of inch and I'm gonna do same I'm gonna put this small corner here Here so I will have this fold Which will help me to create my pocket this fold and that fold here Like this and again, I would like to have this side same like this side same like it's this side So I'm gonna fold it together Not gonna press it too much. I just need to fold those edges and here with my scissors. I'm gonna follow the shape So I've got this one and here that cut like this So I've got similar pieces. I'm gonna start to decorate this small piece First what I would like to do it's reinforce that backside to make it for myself more easy. I'm gonna Unfold this this long piece and fold it over it and I'm just gonna slide inside book page Just gonna slide inside the book page and glue it there It doesn't have to be all way down there. Oh my glue is leaking. Look at that. What is going on?  Careful. I want to say careful So I've got Bucked and a little bit reinforced that back of my pocket I'm gonna fold it back again, and I need some strip of paper I've got here some left over so maybe I can do that I'm gonna slide it in and make for myself a note. I Think here Can be it's exactly look at me I'm gonna take my guillo team And put this where I made my small mark So this card should fit inside Yeah, it should be Fitting inside I'm gonna use the corner punch and put those two corners make it a little bit more decorative and I'm gonna use Walnut stain distressed ink from ranger And this dress little bit that piece of cardstock To make it possible to glue it inside and make another pocket. I Need to take my scissors and cut right here. So this pocket will have holder and Here I do have holder for this pocket. I'm gonna just slide it there this way I Like this I'm gonna put glue here on that small piece and Here on that longer So I just created one more pocket for this pocket. I like to say that And before I will glue this to together I'm gonna a little bit A little bit decorated. I think I'm gonna use embossing folders. I've got some I just bought from From eBay look at those folders. These are a scissor embossing folders. I love those And these and here postcard and this one and here That meters and this one really beautiful beautiful folders I'm gonna use Where is my pocket? Oh, here is my pocket. This is too big. This is empty. I know it's upside down But I actually don't mind too much like to I Don't mind too much that it's you know upside down that it will be To the relief or what is it? Relief will be kind of inside and here will be like negative emboss I'm gonna emboss it this way and we will see It does look good, I like it So what I used is place Place setting and key sets and here is number 657 669. I hope oh my camera doesn't zoom. Sorry. Sorry here and here is the name place setting and key set here If you are So I've got my embossed piece here, I'm gonna take this is drawing pen it's 808 size of that pin and because I can't kind of show it. I'm gonna just do do the link You know those sewn effects here all around because I like that sewn effect And if I would like to show this one, I will have to unglue it totally or Make that pocket smaller, which I don't want to do so I'm gonna use my pen I'm gonna distress it a little bit and I'm gonna use that walnut stain. I should distress it first. I guess Yeah, this is from my grungy project But it will be inside it will be hidden so I can take it I'm gonna distress it all around and here like this and a little bit I'm gonna give it a try And if you are interested in my tool in my distressing tool, I made a video about my favorite tools I Made that video before I bought my brushes for stenciling, which I really love So this is buffer For your nails it has those four different, you know It's long like this I guess and I just put it with my scissors on three pieces and I'm using it where it's that cut I'm using it for a distressing but before to be able to use it It's good to take sanding block and sand it to make it like a rough rough or what is that right word? Like I'm distressing distressing tool with that sanding block here But I do have video about my favorite tools I will put link down below to that description box So if you will be interested to have a look Guess I'm gonna leave it. I'm not gonna make it too grungy and maybe It's all good. I've got here a piece of cheesecloth and someone asked me of the like More informative info how to say that about that cheesecloth unfortunately, I I don't have the packaging from that anymore. So I don't remember the I'm not sure if it's Grammash or How it's called, you know with paper. It's GSM with cheesecloth. I have no idea. What is it plaits or pleats? Or what is it with cheesecloth? How many threads in you know in the row probably not sure how to explain it But I made a video where I showed The packaging I just can't remember which video it was to have a look actually It's a long time ago. Come on go there I'm just gonna glue it this way. Will I? Yeah, I like this But here a few labels Maybe I can take some Accurate size this one, it's cool Who this one will be good. Okay, so I'm gonna make just very simple decoration Just that labels specimen labels makes a really beautiful decoration. They always make it Interesting like you are waiting. What next? It will be So I'm gonna I just add the glue here on that fold on this fold and I'm gonna glue it down so right now I Do have pocket here If I didn't glue it together all together I think yeah, good. I do have that pocket Good pocket here, and I do have pocket here, and I'm gonna add This specimen label just simple decoration like this Maybe I should stamp something on it, but you know I kind of like it this way and Maybe I've got so many so many strips of cuts like really again a huge amount of of cuts Stips like this like literally So I'm gonna take I'm gonna take one of these I'm gonna use my walnut stain Distress ink and Distress it heavily Heavily heavily and I'm gonna cut Small piece fold it over Yes And here I'm gonna cut These edges. I think it can go this way. I'm gonna take a needle Sorry, I couldn't couldn't talk because I had a needle in my mouth it's not Safety to talk And I'm gonna Decorate it a little bit. I'm just gonna make small decoration using piece of my Scrubs and wrap it together as close to that. Yeah, it's not too close Okay, and now where I did fold it before I think here I fold it Okay, I'm gonna a little bit move it this way Fold it Over the edge here Like this I'm gonna pull it a little bit just Small amount not too much just a little bit so it's Picking over the edge here and I'm gonna let it dry So I've got first envelope done. It's easy. It's nothing too hard. Maybe I can Try to distress these a little bit more a Little bit more visible just simple and Kind of delicate Delicate the creation and I'm gonna move to this other envelope and I would like to have book envelopes book envelopes book pages Inside as well to make it stronger and a little bit more decorative So I'm gonna just slide piece of book page inside That's just like this. I'm gonna put there a glue to glue it down here Just like this and I'm gonna cut that extra with my scissors I'm gonna cut from this side like this and of course I would like to have Book page here as well Did I enforce this side that top one as well? Here I will need a little bit more. I've got I've got quite a lot of book pages around so I'm gonna use Also my leftovers here gonna put glue just on that bottom because I'm not sure how far it will go Here on the top and I slide it in Then the next one So I'm gonna put glue on that the rest of that envelope here inside And I'm gonna put glue here To make sure it holds everything nicely like this so now I can Take my scissors and put it around. I am waiting for my glue sticks. They are much better to use on bigger pieces Then glue like this because glue like this makes those rows you can see Where you put it where you are using when you are using glue sticks, you know, it makes a consistent coat I'm not sure how to say that right So I do have reinforced the inside this one and that top one as well I'm not gonna glue it together yet I think I'm gonna fold it a little bit different way to make that envelope kind of Nice for eye the shape of that envelope So I'm gonna fold it about one quarter inch Yeah, about one quarter inch How is the right word?  I hope you are all well You do have rainy days now here in England But I guess it's only good Because was quite hot hot so now The nature it's taking holiday. I guess from those hot days. I hope you are all safe and Healthy and I'm gonna try to make kind of Kind of you know Collection so I'm gonna use You can place it this time If I will place it I think It will be not so easy this way I can place it. Oh, yeah, I can Maybe no I have to place it this way How far you gonna be I guess I'm gonna use that Embossing folder the upside down again, but before I will do that. I've got here those strips I'm gonna Little bit this this one just a little bit not too much. There's all these edges Before I will Do embossing effect. I'm gonna take stumps And I'm gonna make some small stamping first Yeah, it will be exactly this this bigger key I'm not sure if you can see that will be on the fault. So maybe that will be really decorative So first I'm gonna do Small something I've got here those beautiful stumps from Prima marketing I love them so much, and I totally forgot that I do have them here. You can see in number of those stumps It's from Prima marketing. This is the number of that collection I'm not sure if that have somewhere the name Here is just four pieces Let me take it off. No, I don't see any name. Maybe I'm blind But it's it has those four pieces really gorgeous stumps, so I'm gonna use I'm wondering how it was on that piece This way somehow I'm gonna use this it's kind of grungy. It has script and I really love this stump It's beautiful.  Where is my bone folder? Here is my bone folder I'm gonna hold that stump in the air And with my bone folder I will try to do just Yeah, it's better other way It's better this way Just part of stamping. Good Yes, this way. Good So just part of stamping very light stamping And it's better to do it when you've got stumps On the bottom and you put your paper over it and then very lightly you go not press too much if you will press too much you will Move that paper a little bit more and it will be what is that right word blurry? I think it's blurry your stump will be blurry. So I do have that stamping. I'm gonna put their Decoration Where is my embossing folder? Oh, it starts to be too long video again So here will be key Make possible that I will see that It's just like decoration here To add there a little bit more. I think it was somewhere here I'm gonna put small piece here where was that original fault of my envelope to reinforce that Area to make it stronger to keep that shape, which I gave it now Okay, so I'm gonna use that embossing folder and I'm gonna emboss this small piece Small Where is it? Oh, I like it Go watch Oh, it's so windy and now I'm gonna try to a Little bit a little bit make visible that embossing I'm using just corner of my crazy tool if I will use brushes those brushes will give Embossing powder Inside as well. So I don't want to use Brushes and I don't want to use Any other tool because I'm not too skilled with another tools Here we've got another embossed effect and I totally forgot my stitching So I'm gonna take my pen And do that stitching now So I'm gonna take my pen and I'm gonna do stitching all around of this window It will make decorative effect here. I've got embossed effect. So I'm gonna just skip it Maybe it was good idea that I didn't do That drawing before here and here All around except those embossed pieces These I'm gonna skip That was actually good idea Wait with that stitching or forget that stitching before I mean this don't Do the link I like that word do the link You know doodle not doodle, but doodlik It's what is it for babies? They are in oh What is it?  I have to have a look I will I will Google it in the second. I will have a look What is doodlik because I have no idea when baby cry and You won't make him asleep. So he needs to you know You need to get Doodle I'm not sure the right word for that So I've got my stitching And I'm gonna choose some label This time I need some bigger one, but I'm gonna choose again to block one here or Maybe this one This is too big or it's not I Like this one more actually and maybe also some Lace Lace but I'm gonna put just what I've got here so where I need here I need to rip it off I'm gonna Distress the edge a little bit And I'm gonna put a glue How it looks like with this Yeah, I think I can do that Pardon me.   I just hit my camera. I'm very sorry. Sorry for that shaking I said that right. It's do me Do me. It's what you gave to kids to small babies when they are crying and you want them To fell asleep easily and peacefully So they do have do me. It's doodlik. So do the link It's kind of funny for me I'll do the link. I'm gonna give the number nine. I like number nine Oh, it's so windy Okay, I think it needs some upgrade. It's need some color So very quickly my best combination I think Acrylic paint double espresso from ranger I love that combination because it it makes always vintage stuff always vintage look especially on metal Not upside down think tool To dry it a little bit now a little bit of the white color And I think this time I'm not gonna even up there the blue color I'm just gonna Take distress ink that won't stain Good It's safety and I'm gonna add that Ink to the edges Just a little bit And I'm gonna glue it here Like this So we have that front here. It will be folded So we have decorative top on that envelope And we have decorative top here and that backside I'm gonna do just with the doodling It's so good So yet Do me it's doodling in my language in a Czech language if you will ask Check from Czech Republic. Okay, I'm gonna probably keep it this way. So now I can Well, I can choose Here I don't have to have two But although I cannot do two pockets here as well if I will have some card stock I don't have here this one. How big it is But I don't have piece Of envelope here on this side. It's kind of folded inside There you are. Oh, you can So I can do that double pocket here as well I'm gonna have a look It's what I actually need. Okay. I'm gonna enjoy it I'm gonna put it here strip that strip I'm gonna Use for holding this card.  We've got pocket there Okay And like that. Oh hold hold properly. I just go to my tag. Okay. I'm not gonna give it Just yet Not just yet. I'm gonna place it there a little bit late. So this is my sharing for today Two envelopes Very calm envelopes nothing too crazy. I hope you did enjoy it. I hope you will try it to cut your envelopes some way And maybe I should do this strip as well somewhere. I will I will decide it later probably somewhere here I will see so this is my sharing for today. Have a wonderful day. Take care about yourself and see you next time. Bye


This is stock number 9274. We are here at Summit Automotive in Fond du Lac, Wisconsin, your new and used Ram truck headquarters. This truck is a 2011 Ram 2500 Crew Cab Long Box. This truck has the 6.7 liter Cummins diesel. From this HD video you'll be able to tell that this truck is extremely clean all the way around. Has XD Series chromed alloy rims. Has BF Goodrich all terrain tires with about half the tread left. Bright silver metallic is the color. You can see it has some nice HID headlights, LED running lights. Front grille is in really nice condition. Headlights are nice and clear. I didn't see any dents or dings on the front bumper. Passengers side rims in nice condition and as you go down this side of the truck you can see just how clean the body is. How reflective the paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down you can still see the truck here the truck and have confidence in the vehicle that you're looking at before you even get here. Cab looks really good. Down this side of the truck look is in really nice shape. Has factory chrome step bars. Rockers look really good on the bottom of this truck. Back rim is in nice condition as well. And these back tires they have probably a little bit over half the tread left. I'd say 60 to 70 percent of the tread on there. Framing under bodies in really nice condition. Has all the remaining factory exhaust so it hasn't been modified in any way. And once again those low rockers look really good. Frame is nice and clean. Underbody very little to no corrosion. Has the LED taillights as well. Back up sensors. This one has a backup camera. No major dents or dings on the tailgate. Has backup sensors like I said. Has a spray in bed liner. Has fifth wheel bed rails. And that tailgate is also a locking tailgate. As you go down this side of the truck just as clean as the passenger side. This back rim is in nice condition as well. Like I said down this side very very clean. We want to give the most accurate representation of the vehicle as possible so when you get here there's absolutely no surprises. And that you can have the confidence to come take a look at the vehicle because you've watched the full video. Those mirrors do fold out for towing purposes. You'll watch the full video. You've looked at over 40 pictures. Read the description. Know exactly what you're getting. Driver seats very clean. No rips or tears. Power driver seat. Carpeting is very nice under the factory floor mats. Power windows power locks and power mirrors. This one does have the automatic headlamps. Factory brake controller. And you can see that this truck has 82,801 miles. You have a compass temperature and mileage display. Steering wheel is in pretty nice condition. Have some controls on the steering wheel right there. You also have your 430 radio which you get AM, FM and serious satellite radio capabilities. Also has bluetooth audio controls and this one has I believe a 28 gig hard drive. So you can put songs and CDs and burn music to this actual player and then you can play it through your speakers obviously. Turned out four wheel drive. Has a six speed automatic transmission and to listen to those songs on you got the Alpine sound system. Factory exhaust brake, tow hall mode, backup sensors. Turn your plug in on. Then it does have a light tire load inflation button too. Passenger seat is very clean as well. No rips or tears on that. Does have side current airbags. Smells very clean in this truck. Be surprised if it was ever smoked in. And we'll take a quick look at the back seats and then we will check out under the hood. No rips or tears back here. Seats are in really nice condition. It does have the latch child safety system. No rips or tears. Has rear defrost. Factory floor mat back here. Does have the in-floor storage which is a pretty neat system. And you do get storage underneath those seats. Under the hood we have the 6.7 liter Cummins diesel. Engine bay is very clean. Road is very smooth. This truck has been fully safety and inspected by our service shop. Has a fresh oil and filter change. All the fluids have been checked and topped off. Truck has been gone through mechanically 100% and is 100% ready to go. Really nice truck at a great price. Hard to find long box. And to see more pictures of this truck or one of our other 400 new and used cars, trucks, SUVs, minivans, Wranglers. You name it, we got it.  Videos of every single used vehicle that we have. All at SummitAuto.com. Thanks for checking out my video. If you want to make this truck yours, give us a call right now<PHONE_NUMBER>. Ask for one of our sales associates to make this truck yours today. Once again that number is<PHONE_NUMBER>. Thanks for checking out this video. If you like it, want to check out more videos like it, go to www.youtube.com. Slash Summit Auto. Remember to like, subscribe, and share on those videos. In fact, in a second you'll see a link to subscribe to our YouTube channel on your left. A link to more heavy duty truck videos like this one on your right. If you haven't been to our website on the bottom, a link to this truck on our website. Click those. Check us out. Check the truck out. And we look forward to helping you with this super clean 2011 Ram 2500 Crew Cab Long Box Cummins Diesel. Thanks again.


What's going on everyone? Sam here with late in sports cards. We're ripping 20 2022 panini impeccable football hobby three box full case break number 46 random teams though There's a look again at your random results as always you can find these on the website under the results tab as well as the link That is currently in chat. So good luck here. Everybody. Let's do it. I want to tick-tock. Yeah It is my fault sin. I take credit for it man. My bad my bad Parts feels like it's in the right place. So want to be back-to-back to back bar cards that were messed up Watts in the 75 AJ Brown to 10 First hits gonna be Devontae Wyatt 21 out of 35 for the Packers You probably have zappy in this no Taekwondo or ampere strong and imagine Got a Mike all-stop four of five nice one there for the bucks on the emerald congrats on that Tampa I Mac yeah, Max got something this yeah, well said said other than Mack Jones Nice one here Vaunted greats is gonna be 49 to 50 Roger Stalback going to the Cowboys. There you go Justin I'm so ready John So ready, dude Nice one here going to the Vikings Jay Jedi's 25 of 25 Justin Jefferson congrats Minnesota Vikings Jera J First rookie on-card is gonna be 57 out of 75 Alec Pierce Nice one there for the that's I think Jersey Gloves. I want to say Off the Colts nice one there close. Oh, it is one hell of a marathon AJ Terrell to 25 Michael Thomas to 75 Ryan Tannehill to 50 We've got a Jalani Woods 10 out of 35 going to Colts nice one there Followed by this one's actually kind of sick Christian McCaffery 47 out of 49 nice one there congrats Panthers That's John F on the combo spot with the CMC run CMC. Yeah, Giants That's gonna be a one Dale Robinson seven out of 25 next up. We've got this is nasty Reggie Wayne 94 out of 99 for the Colts on The on-card congrats Colts Colts doing very well and here you go sin. How about a Billy zappy? 24 out of 35 Two-color patch and a helmet congrats sin. There you go, buddy. Let's go nice one there We'll take that Corner up top. I don't know if it's just the design Like the corner looks okay From there You could tell it's not like bent or anything. It might just be the design But we can send you an empty box and wrapper if you want sin with that one you can magazine that'd be Nice one there Just a little bit bottom rights a little thing to we'll send out the box and wrappers in Top left. Okay. It's bottom right. Yeah, bottom right was soft for sure Yeah, no, it's like that's very typical like like you said very typical of Impactable redemption on the back. Yeah, true Deontay Johnson to 50 that is Patrick Mahomes to 75 Got a Heath Miller 14 out of 99 for the Steelers. That's kind of sick Congrats on that Pittsburgh Anthony M player one Got rookie auto is gonna be a Jeremy Ruckert to 75. That's next one's cool We've got a Fran Tarkent in 10 out of 49 For the Vikings to color patch player warn. I'm turf Tarkenton That's Jersey number two. Congrats Vikings That's one there. Jair J. We've got a Skymore 9 of 99 for the Chiefs Chiefs Scrooge Tarkenton I saw in there for the Chiefs. We've got a Desmond Ritter nice one there 9 of 25 for the Falcons going back to sin again We've got a pure strong junior elegance rookie helmet and glove autos. Congrats on that sin Here's strong junior going to the Patriots bar card We've got Steve young going to the Niners 23 of 25 nice one there on the bar Niners is What's that have a full glove Niners is we're San Fran Ryan V Congrats Ryan nice one there for everybody Get that into a magazine. We'll do a quick recap here We've got pure strong Desmond Ritter Skymore France Harkenton that one's awesome. You got it sin. There's Jeremy Rucker. There's Heath. Heath Miller Reggie Wayne Wanda Robinson Christian McCaffrey Jelani Woods Alec Pierce Justin Jefferson Roger Staubach Mike I'll stop and Devontae Wyatt Mag. We had the Bailey Zappie to 35 Donnie has to sign the redemption you want to sign the redemption person And Steve young yeah, I said Donnie has signed the redemption or you signed the back of it I'll just sign like above the Just sign like up there That'll do it for the break guys. Thanks again for the fill next up. We got divisional


Hey guys, it's Nate, AKA the Foot Accountant. Welcome back to the channel. I wanna talk to you guys today about once to watch cards and what the best time to buy these once to watch cards could be because we are entering the end of the once to watch promo. I think we have two or three days left. I think these cards go out of packs like Monday at 6 p.m. U.K. The squad building challenges will end around that time as well. And the objective for Mr. N. Dombele will end at that same time as well. So the once to watch stuff is literally gonna be done. I think, yeah, one day, 22 hours when this is over. So we might have a few more hours for the actual cards and packs still. But make sure you guys are getting that objective done if you're going for it. And if you wanna do these SBCs with the promes or with the player pick for Sanchez and McIterian, get those done as well. And yeah, as you're watching this video, it's probably Saturday. And Premier League games are starting up for the weekend. Now, I have some games over here that I pulled up on SofaScore for Saturday. There's not very many once to watch players that are actually playing on Saturday. A lot of the players are playing on Sunday this week, which is kinda interesting. But tomorrow we do have West Ham, Crystal Palace, we have Holler in there, N. Dombele's objective card. And then a couple guys from Real Madrid, obviously. Then we have some Dortmund and Bayern Munich cards as well. And then other than that, maybe we have the PSG, the Cardi, and then Ben Jeter. So there's not a lot of ton of action for once to watchers on Saturday. There's a few cards that we could watch. And as you saw, I have a couple Hollers on my transfer list just to see if we can maybe get some hype there. But I wanna talk about kinda the price fluctuations for these guys and what I'm gonna see happening over the next couple of days. As we near the end of the promo, a lot of people wanna know, hey, let's say I want this once to watch Griezmann for my team, 590K, he was 550 earlier. When's gonna be the best time to pick up this card? When's gonna be the best time to pick up this Lasano or Ben Jeter? A lot of people want this Ben Jeter card. So I wanna kinda address that today because these are special cards. They were in packs obviously for 10 days this year, so it is a bit more than team of the week. But they're special cards. They're gonna rise out of packs, most of them will. But again, they're still in packs now. So I think the best opportunity to get some of these cards is gonna actually happen this weekend. So for the cards that play today on Saturday, what I want you guys to look for is a lowering in price to sell off after the game. So we'll use Ben Jeter as an example. Right now he's 125,000 coins. He is inflated a little bit. He was 115K earlier this evening, but he's definitely inflated rising up into his game today. He plays again. They play Montpelier in the afternoon, my time today. So Ben Jeter's price is rising. People are know that he's been performing very well. IRL for Monaco. He's been scoring a lot of goals. And that's why they're investing in this card because they think he could score and they can make some money on that card, possibly get the inform, all the hype, all that kinda stuff. So that's why this card is up. But let's say Ben Jeter does not have a good game today on Saturday. Let's say he does not score any goals, does not have an informed worthy performance, and you see this card's price drop down. You're gonna see a lot of selling after that game, which is what you normally see with ones to watches. But these cards are have a lot more supply than they had last weekend when they were first out. So the panic selling, not panic, but they sell off after the game from people who invested in this Ben Jeter card should be more significant and more severe because more people have that card on the market, more people are trying to get rid of it, more people are currently investing in this card right now at 125K. So I think, excuse me, I think you're gonna see a little bit more extent, excuse me again, extended and maybe more extreme panic selling on some of these ones to watch cards this weekend because they have more supply, which allows more people to invest in them, more of their cards on the market, allows their price to drop a little bit more. And I think that's gonna be the buy time for these Saturday cards after their games if they don't have an inform worthy performance. So let's say you want this Ben Jeter card for your team. I would not be too afraid to say that I think you could expect to see him close to 100,000 coins flat. Maybe he rises up to 130 right before the game. You might see him be panic sold down to 115 really quick and then maybe some undercuts and some open bids right around 100,000 coins. I think that's kind of your buy range for both Xbox and PlayStation. Somewhere right around 100,000 coins for this card would be good. But that's the whole idea. I think the lowest point for these cards this weekend for Saturday games especially would be after their game finishes. So again, Ben Jeter plays against Montpelier and after his game finishes, you probably will see a sell off on that card like what we saw here from last weekend he played drop down from 125 to 110. Obviously last weekend he was only in packs for two days before he played a game. This week he's got even more. But the hype is on this card. He's got a lot of hype. There's an inform this week. Gullivan's gonna link to this card. A lot of people like this Ben Jeter card and he's very good in game and he's been performing very good IRL. So this is a hyped up card as well. Any other games that play on Saturday? If you're a guy who wants to watch Coutinho which a lot of people like this card, I think you're gonna look at the same situation.  His card I think even went up a little bit. Even though he already had a wants to watch it was in packs. He really literally couldn't get an inform on the team of the week three. His card price still went up because it's a wants to watch, it's a live item. People saw that he was playing well. If you want this wants to watch Coutinho on your team I think this weekend might be the opportunity to get that card in your club as well after their game. Right now it says 215,000 points for this card. He does have the inform already. The upgraded stats from his 86 to the 87. So I think that any guy that plays on Saturday I think that by time is gonna be post game. Usually about two hours post game is when you see the lowest point for that card because you see open bids for cards that people just wanted to get out and try to get coins from. And then also people undercutting. So that's when you can really get the good deals in that second hour after the game is over people will be undercutting. People will be listing cards for open bids. And then after that the panic selling kind of stops. People realize the card's low and it kind of jumps back up maybe 5% in price. And then it continues to go up as it reaches its out of packs time on Monday. So that's what I like for these Saturday cards. Cards that maybe have a game on Sunday I think we might have a couple different buy windows. Obviously you have Pepe plays on Sunday. You have the Manchester City with Rodrigo. You have Joe Ellington. You have Wambi Saka. Not sure if some of those guys are gonna be playing or all of them are gonna be playing. But then you have Barcelona, Barcelona Sevilla. That's a big game. So you have Griezmann as well to watch for that one. Any of these other teams down here. I think like yeah, Inter and Uve play. So that's a pretty solid game. Couple of ones to watch is in that one. So that's a card or a game you could watch as well. So Sunday actually kind of has more marquee games for a lot of these ones to watch cards. For most of them at least, not all of them for most of them. So you can watch the prices on Sunday too. Probably watch for some panic selling. The same thing on Saturday. But also, I think you could see maybe another opportunity to pick up on those cards. If it's a later game in the day, like let's say on Sunday we have Inter and Uventus playing at 1500. So it's like 3 p.m. my time here in the USA. So it's a late game for you guys in the UK. It's kind of a later night game. That's kind of getting closer to squad battle rewards. So after that game finishes, yeah, you know what? It might take like a couple hours, maybe three hours in total for the game to be completed, let's say like two and a half hours. By that time, you're at like 17.30. So that's like 5.30. So then you have two hours of panic selling after that. And that leads you right up into squad battle rewards. So you might see some panic and another opportunity to invest with some of those later game cards on Sunday with squad battle rewards with more supply coming on the market, open bids, et cetera, et cetera. People are playing squad battles. People are getting the packs anyway that they can. So that's kind of how I feel about the wants to watches. You know, you guys might ask, well, they're going to be in packs for another day. The only chance that would have these cards possibly drop even further is if the Saturday cards were panic sold, you bought one. And then on Sunday, they drop an SBC with like a 50K pack that would supply these wants to watch cards. I don't really see that happening. I think it's good. I think it's the best time to buy these cards is going to be after their games when they're getting panic sold this weekend. If you want to put one in your club, if you want to invest in one for the future or put one in your team rather, I think that's going to be your best time to do that right there because these wants to watch cards are awesome and they're hyped up and they're pretty good wants to watches this year, man. We have some pretty good guys in here. Griezmann, I mean, Lukaku's playing well. Koutinho is playing well. De Young has an inform already. You know, and then Pepe, Jal Felix are exciting players to watch. Even guys like Joe Ellington getting a lot of quality playing time. Thorgan Hazard, Brant, Lozano. Wants to Watch this year is very exciting. And like last year, it's kind of similar to like Feet to 18, how I feel at least. So that's how I feel about the buy time for these wants to watch cards. And overall the market this weekend, you should be seeing a dip down in price for the Weekendly sell off as well. So that's going to help your card prices on Saturday night and Sunday night as people are playing the Weekendly, as people are finishing their games, maybe selling some cards to get coins out of their club. So that's why I think that your wants to watch buy time is this weekend. I think these cards will rise out of packs. They are basically informs. People will be getting more coins and say, hey, maybe I have right now, maybe I have the informed De Young, is 170K or whatever it is. Maybe I'll pay that extra 30K to get the live items De Young. People love these live items, especially like a card like De Young they want to put in their squad or a Griezmann or a Rodgery or a Quattino who's going to be a staple in their squad for a while. And they want to rock with that card. Or a high player like Joe Felix that card's really good in game. They want to get those cards in their club. So that's what I think the best buy time for these wants to watches will be. And I also want to kind of talk about, everybody wants to know, why is the market so low? Why is the market not exploding? Well, we know it should be like it has been before. What is going on with the market? And I think it's pretty obvious. People don't have coins. And you want to know why people don't have coins. Well, the SBC content for EA Sports, it's been tricky. It's been conniving a little bit. They've just kind of been dinking and dunking. Or just a little bit here, a little bit there, taking coins away from people on the market through these SBCs, the wants to watch New Beginnings SBC that you get. What is this? Show a high group rewards. How do I see that? Can I click this down? No, I can. I can, yes I can. So the Sanchez and the McTarian. How much do you have to pay for this? Footbin says, this is 20,000 coins to get one of these. And the wants to watch promas is 36K. So if you did both of these SBCs, you're looking at almost 60,000 coins that you just rinsed right there to get two cards. Two untradable cards. Maybe you did Markey Matchups. That's another 18K. So you're looking at almost 80,000 coins right there. And so many people are doing this National Pride SBC. People are addicted to SBCs right now. And it's obvious because the price of these SBCs are staying high. But people don't do this SBC. It costs you 120K. And the packs that you get back aren't even worth the cost of face value. This is like one of the worst value SBCs that I've seen on FIFA in a while. Especially for an advanced SBC. A lot of these other ones are decent. Maybe you can do it with some of the cards in your club. But if you are just doing this SBC from scratch and you're paying anything over 50K for the whole entire National Pride SBC, I'm not about it, okay? So if you're working on that one, I would say just set it aside, wait until later on in foot when you have more disposable coins. But right now, EA is doing a fantastic job of controlling the market taking off because they keep dinking and dunking with these little SBCs, 20K here, 30K here. And that's just a lot of people that maybe only have 100,000 coins. They're like, oh man, this is a good deal. This is a good card. So once the watch item gets live, it's gonna get upgraded throughout the year. I'm gonna do it. Doesn't fit in their team, but they're gonna go do it. So now all of a sudden, instead of 100K, they only have 50K after doing those two SBCs. And that's why I think you're seeing some of the market not rise as much as it should. Also, next Thursday, people think that the market's gonna be going up again because we're gonna get the first foot champions rewards. I think there's a lot of people in the same boat as me. A lot of casuals, if they started on Friday especially, they didn't have time to grind to 2,000 weekly points. So next week's foot champions rewards might not be a full bore or full reward week, kind of like it was this week with rivals. So yes, the market could go up next week. I bet it will, but it might not be that big boom that everybody's talking about. But then again, right now it does seem to be dipping a lot. Malinkovic Savages, you know, I saw this card at 10K on Wednesday night and I thought, okay, this card's a pretty good buy. I read under 10,000 coins. I got a bunch of them at like 9.5K. And right now he's around 8,800 coins. Malinkovic Savages just under 9K. It's kind of ridiculous. Like that's a good card that people will use in this game. It just seems like we need some more reward sets to kind of turn this game around. And honestly, more objective content from EA. If we see this next week, if we see less SBCs that are gonna require like 20 to 30,000 coins and more objectives from EA, then I think you will see the market rise up because they keep killing people with these SBCs because people are addicted to SBCs. They can't say no, man. People cannot say no to these SBCs. And that's the biggest problem with why this market is low. But again, a little bit of market talk in the end for you on that video. But again, once to watch cards, buy after the game is my opinion, especially if you just wanna get one, put it in your club.  So a guy like Sarabia, a guy like Joellenton, a Pulisic, even a Barela or a Jovich as well. And maybe a Holler too, like a McGuire even. Just buy one, throw it in your club. It's basically like discard, inform, investing. These are live items. Somewhere down the line, probably United's gonna have a game where they hold a clean sheet. McGuire has a good match rating. Maybe he gets an inform, goes to an 84 or an 85, whatever the 82s go to. You might be able to sell that Harry McGuire card. You bought it for 10K during the promo. You might be able to sell it for like 18 or 19,000 coins. So it's basically like discard, inform, investing, banking on that some of these players will get one or two performances in the next couple of months where their card shoots up in price. But again, these cards are special cards. They're going out of packs. They're gonna rise because they have the cool card design. They just pop, they're like wow to the eye. They're cool looking, and they are live items. And people in FIFA Ultimate Team love themselves some live items. So again, I think getting some of these guys, the discard ones that are close to discard. You can't go wrong with that. And again, buying after the game seems like the best thing to do in my opinion if you want one as an investment or in your team. So do what you will with those and make sure that you are using the SofaScore app. I love this app. Make sure you download it on your smartphone. Go to the app store and just search SofaScore. It's on there. It's easy, set up notifications for ones to watch players so that when you invest in them, you get notifications on your mobile device when they score and when they do good things. Even getting the starting lineup, you get a notification for that and you can sell those players into the hype before the game. So watch my other videos on that on the channel. Peruse around the YouTube channel. There's a lot of other videos out there as well that aren't just for one period in time. They're for kind of how-to videos. Later this week, I'll probably be posting a video on icon trading. That's a very highly requested video. I wanna get that out to you guys as well. So be on the lookout for that. And of course, the usual market outlook on Monday as we center minds for the next week of FIFA Ultimate Team. So be ready for that stuff. Streams as well. Check the link down in the description on live streaming multiple days per week on twitch.tv backslash, The Foot Accountant. Check my other links down there as well. If you enjoyed this video, smash the thumbs up on it. Comment down below if you have any questions. And of course, subscribe to the channel if you are new. It's been Nate, The Foot Accountant. Catch you guys later. Peace out.


So I mean this is related to Dima Schlaktenko's talk and I want to talk about random matrices and their limits and the limits are given somehow by operators usually in this context. But one of the main points of my talk is that I want to go over from polynomials to rational functions, non-commutative rational functions. I will tell you what is this. And I will also somehow look on unbounded operators. OK, so let me start with random matrices and operators. And OK, so I mean I'm talking essentially on the macroscopic limit of eigenvalues of random matrices. And the typical phenomena in random matrix theories that by concentration we have in the limit a deterministic behavior. OK, and this deterministic behavior quite often is also interesting, so it's worth to look on what it is. And for operator algebra people it turns out that actually this limit is related to very interesting operators, or maybe more fancy C-style algebras and phenomenon algebras. But essentially it's operators on Hilbert spaces. OK, and I mean this is somehow the fundamental observation, one of the basic things in free probability theory, which makes this relation between random matrices and operator algebras. And this goes back to Dan Waikoulescu, who created free probability theory. And one of the big results, the main results there, is that the limit of random matrices can very often be described by NICE and also interesting operators on Hilbert spaces. And he was, one still is, actually interested in the von Neumann algebras, which are generated by those operators. OK, but so I mean let me be more concrete. What do I mean with that random matrices converge to operators? So let's say I have my random matrices. Also I have N by N matrices. And I have M of them. And I'm claiming almost surely they converge in a limit to some operators. So those are guys which are living on a Hilbert space, bounded operators on a Hilbert space. And in order to give a meaning to these convergence, I also need a state. I mean for my matrices I have the trace which contains information about eigenvalues. And in the limit I also assume that I have a canonical trace there. So that's somehow the probabilistic flavor of the whole thing that actually is convergence. I mean convergence of moments. And so we talk about convergence in distribution of those guys to those guys. If I'm taking any polynomial in M non-commuting variables, I take this polynomial at my random matrices and then calculate the trace that this in a limit converges to the same polynomial applied to my operators and then taking this functional tau, this trace tau. That's the definition of convergence in distribution, which I mean you will see more of this in the talks of Dima about asymptotic freeness that's really doing exactly this. OK, so that's the basic kind of convergence in free probability theory. And again, I mean I should really stress that I mean even though we are talking here about operators, in operator algebra you usually have very different kind of convergence. I mean this kind of convergence, convergence in moments is change of perspective in operator algebra. So people in operator algebra usually are not looking on this. And so maybe free probability, the idea was really we should have this more probabilistic point of view on this whole thing and looking on moments. OK, but then in recent years, it has turned out that actually in many interesting situations we have a stronger form of convergence, which we call, let's say, strong convergence. I mean this goes essentially back to the paper of Harger-Rubin-Torb-Johnson and then there are many follow-up papers. And I think this naming is strong convergence. This goes back to Kami Mahler. OK, but anyhow, so what is it? I mean it means I have convergence in distribution, but I have more. Namely, I also have that the operator norms converge. So I'm taking any polynomial in my random matrices. I'm looking for the operator norm of them. But the operator norm of them is nothing else than the largest eigenvalue. And I require that this converges to the operator norm of my polynomial applied to the matrices. And so my operators are living in some Hilbert space. So there I have the canonical operator norm. So this norm here is well defined in the limit. OK, and it turns out that very often I have a situation like this. OK, and maybe I want to show you, I mean, yeah, give you maybe the basic example where you see this phenomena. And I mean the best example which we have is that what happens to the limit of independent GUEs, independent Wigner matrices, they converge to free semicircular elements. OK, so I suppose, I mean, this is what Dima will show you probably in this next lecture. And I think you have seen what free semicirculars mean. OK, but anyhow, so I mean, before I really show you, maybe more concretely, let me point out that actually, of course, there's a difference between the one matrix case, because this is more or less the classical situation, and the case of several matrices, which really is the non-commuting case in which we are finally interested. So in a one matrix case, this notion of convergence, which I have, the convergence of all moments, means nothing else that the classical distributions converge. So this is really just a convergence of probability measures. This is really in a classical realm. And that I phrase this in a way that x and convergence on operator, this is just a matter of language.  OK, in this multi-matrix case, if you are saying that, let's say, a pair of two matrices converges to a pair of operators, by definition, this means the convergence of all moments. But I mean, those are non-commuting moments, because my guys don't commute. I mean, I cannot extend this collection of moments to a probability measure on R2. So this is really something non-commutative. And I mean, it's really one of the problems is to say, what is really a non-commutative distribution of a tupper? I mean, the simplest thing is, OK, it's the moments. So we apply our state to any non-commutative polynomial. But giving more analytic structure to this is something which is not so clear. OK, so this means it's hard to see anything, but you can go back to the more classical regime by trying to understand the convergence of x and y and to x, y by just applying sufficiently many functions to your operators. And then, of course, this means any function, let's say a polynomial, at least, of this pair converts to a polynomial of this. But the polynomial of this is just, again, a classical object. And again, you can look on pictures. OK, so let me make this clear. I mean, here is the classical Wigner's theorem of the semicircle that everybody should know. Yes, I hope.  So it's a n by n matrix where the entries are chosen independently. And it's the same distribution. And in the GUE, we take the normal distribution for each of them. In the Wigner case, we can take different ones. But for this, it doesn't make a difference. OK, so here is the picture. And I mean, this is the classical, OK, this is what was done by Wigner in classical probability theory. But the point, my point is, that actually this limit, OK, in classical theory, you describe the limit by the semicircular curve. OK, but the point is, I think which was already in Dimas' talk, is that actually, this limit distribution is given, is a distribution of a very important operator, maybe the most important single operator, namely, it's a real part of the one-sided shift. So you take the one-sided shift. So this is one of the most important famous operators. So in your Hilbert space, you take a basis, which you index by the natural numbers, let's say 0, 1, 2, 3, and so on. And then the one-sided shift just shifts the basis by 1. So E0 goes to E1, E1 goes to E2, E2 goes to E3, and so on. And then you extend this linearly. And then the adjoint of this operator shifts backwards. So E2 goes to E1, E1 goes to E0. E0 doesn't have anything to go to, so it goes to 0. OK, so that's the adjoint. And then if you take, essentially, the real part, L plus L star, so this is a self-adjoint operator, then this operator has, with respect to a very canonical state, I mean, we need a state, if you want to talk about moments. And I mean, there is one state, which is somehow special. I mean, namely, a vector state. There's one vector, which is special, namely E0. OK, so if you take the vector state, this is back to this, then we can calculate moments of this guy x. And it turns out the moments of this guy are actually the moments of the semicircle. So in this sense, the GUE converges to this operator x. Yeah, OK.  I mean, this is Haymors and people. I mean, this is an operator about everybody. An operator algebra taught a lot. But calculating the distribution of this, I think this was nothing which anybody was interested in. And I think it was, this is why Kulesku, that we really had this change that actually, I mean, first of all, this guy has very simple and nice moments. And actually, it's a limit of this thing here. OK, good, so I mean, so the theorem of Wigner, I mean, in this language, we can say that xn converges to x to this operator. Of course, in the classical theory, of course, Wigner didn't talk about x. He just said it converges to the semicircle. OK, but so this is the usual convergence and distribution. But then also in the classical theory, there's some strengthening. I mean, what does this convergence and distribution tells us? It tells us that the average behavior of the eigenvalues goes to the semicircle. So we are talking about the average behavior of eigenvalues. But this does not really address single eigenvalues.  So Wigner's semicircle law, I mean, would be compatible with the fact that there might be very large eigenvalues somewhere. So the largest eigenvalue of the GOE could be, I mean, here in this usual normalization, it should be 2, I mean, the boundary of the spectrum. But I mean, this does not follow from Wigner's semicircle law, but I mean, there could be an eigenvalue at 10, let's say, which just disappears in a limit. OK, so OK, but one can strengthen this, and this was done in random matrix theory, that actually the largest eigenvalue of xn really converges to 2. And 2 is actually the operator norm of x. So this is this strong convergence, which I talked about in the beginning. So this is really, we see this in a classical context. OK, good, but now the multi-matrix case, that's what we really are interested in. Now let us consider not one, GOE, but two. And OK, the simple situation for choosing two is I'm choosing them independently. And then it turns out that actually in a limit, again, this converges to essentially two copies of this one-sided shift, which I had before, in different directions. And I mean, this is given by creation and annihilation operators on the full Fox space. And I think Dima showed you some things like this. OK, and this again, those operators, so those are now non-commuting operators, and they generate, again, some of the most important C-star and von Neumann algebras which are around. So if you don't take the sum, then this is related with the Kunz algebra. And the sum, they create the three group factors. That's really the von Neumann algebras in which Waikoulescu was interested. And again, I mean, there's a canonical state that a vacuum state. OK, and so I mean Waikoulescu's theorem, which Dima will prove in one of his classes, is that actually a pair of these independent GOE converges in distribution to this pair of x, y of this creation and annihilation, or sum of creation and annihilation operators on the full Fox space. So that was the basic observation for Waikoulescu. I mean, another way of formulating is that they are becoming asymptotically free, and we have the free-ness in the limit. So OK, so this is the basic result of Waikoulescu. But as I told you, I mean, this here, OK, it's not clear what this means. We don't have, you don't see it. But you can see it even if you are looking on polynomials or functions. So to see something, I mean, let us take a function, a polynomial in x and y, xy plus yx plus x squared, for example. And then, of course, this convergence distribution means that in particular, the polynomial of my x and y and converges to the polynomial of x, xy. And this is true for any polynomial. OK, and then, again, we have this tells us that if I take this polynomial, plug in my Gaussian random matrices, calculate the eigenvalue distribution.  So actually, I mean, what I have done here, the histograms, I have taken one realization of this situation. So maybe my random matrices are maybe 5,000 by 5,000 random matrices. So this is the histogram of the 5,000 eigenvalues of this matrix. OK, and then I compare it with the distribution of this polynomial of those operators. And this is this curve. And in free probability, we have developed methods for calculating this distribution. I mean, of course, it's not a non-trivial thing, really, to get this distribution. But that's what we are able to do in free probability theory. No, no.  But if you go over to more complicated polynomials, OK, maybe you have hope. But I think there's no hope of really getting explicit formulas. So it's really more an algorithm which allows us to calculate those things. Good. OK, so we have this in distribution. But then, again, it's in the classical case. I mean, this picture doesn't tell us anything about the largest eigenvalue. Again, there could be an eigenvalue at 100, which survives sitting at 100, and doesn't converge to 10. Close to 10, where it should go. OK, but then we have this important paper of Harger and Torb-Johnson, who actually showed that in this situation, we have the same as in the classical case, namely the largest eigenvalue of the polynomial of my random matrices converges to the operator norm of my polynomial in x and y. So it really converges to the boundary of this distribution. OK, so we have here the strong convergence. And I mean, there have been more papers which do this for other situations. OK, but what I really want to do is I want to go further than polynomials.  That's OK, but usually, I mean, you want the convergence of, let's say, continuous functions or whatever. And in many situations, you can go from one to the other. So if I have one random matrix, I mean, the things which I had before for polynomials are also true for continuous functions. OK, and in non-commuting variables, of course, this is now a problem.  But then what? If you want to go further, it's not so clear anymore. So I mean, so what can we do? And I mean, of course, can we go to continuous? I don't know. I mean, I don't know what is a continuous function of non-commuting variables. As Tim already mentioned, there is a theory of analytic functions of non-commuting variables, which is being developed at the moment. And there's a lot of progress on this. So this is called free analysis. And so in a sense, at the moment, seems there is a nice theory of analytic functions. But still, it's not yet at the end. And at the moment, I don't really know what to do with this on my random matrix level. OK, but what I do a little bit about is something in between going a little bit further than polynomials. And the next thing is rational functions. I mean, classical rational functions is you divide one polynomial by another. OK, and this is something which actually can be done in a non-commutative. But actually, it's non-commutative. Rational functions are much harder, but also much more interesting than in a classical case.  Because I mean, this is independent of what I told you before. I think this is a very nice subject, which is worth to be well known. OK, so non-commutative rational functions. So this is a quite old subject. So they were constructed by Amitzou in 1966. And then Kohn did a lot on this. I mean, he wrote a lot of books. So I mean, he made quite a living out of this. So this is really part of non-commutative algebra or ring theory. And so I mean, what is a rational function? Principality is clear. What it should be, I mean, a rational function in my non-commuting variables, y1 up to ym, they are not just formal variables, which I assume not to compute. So this should be anything which I can get from the algebraic operations. But I also want to take inverses. So I do everything, including inverses. For example, something like this. So this expression should be a non-commuting expression. OK, but then, of course, one has to be a little bit careful. Because first of all, if I write down an expression like this, I mean, I could do algebraic manipulations and write it in a different form. And I should be able to identify whether this is the same or not. OK, and related to this is, of course, that if I invert things, I mean, one thing which I'm sure you cannot invert is zero. So I should not invert zero. But it might be that zero can appear in a very complicated form, and it's not clear whether it's zero. So it's not obvious to decide, for example, this guy here is zero. So the left-hand side. So if you get somewhere that the left-hand side looks like a good expression, so maybe you're tempted to invert it. But because it is zero, you cannot invert it. It's clear. But the problem is it's hard to see this.  But it's not obvious. And one of the main problems is that rational functions, there's no canonical form. In the classical case, every fraction will just divide a polynomial by another polynomial. In a non-commutative, this is not true. I mean, you see here, for example, what I'm having here are really nested inversions.  I mean, this is basic, but that's a nontrivial statement. But if you are adding inverses in a non-commutative and invert again, usually you cannot reduce it to just having one division. OK, so there's also no canonical form of writing such a thing. And that makes the whole thing a bit complicated. And I mean, it's not really an easy task to construct these rational functions. But in the end, I mean, all this can be done and was done by those people. And what you get is a skew field on division algebra. So a skew field is a field which is non-commutative. And it's the same as a division algebra. Some more operator algebras, I think people call it more division algebra. So this means everything which is not 0 has an inverse. OK, so there exists something like this. And this usually is called a free field. And it's denoted by this. I mean, I think this goes back to corn, this bit strange notation. OK, so this is the free field. And I mean, there's one thing which makes working with it easier. And it's somehow the replacement of not having a canonical representation. Namely, it turns out you have a canonical representation if you go over two matrices. So I mean, if you're working in a ring, let's say in a ring of non-commuting polynomials, and if you just try to stay in this ring and do everything in this ring, things are very hard. But if you include in your arguments also arguments of matrices over the ring, so you go to matrices over the ring, then suddenly you have much more possibilities. OK, so that somehow seems to be a general message, which was an operator algebras people are aware of. I mean, for non-commutative algebras, you should also consider the matrices over this algebra. If the algebra is commutative, it doesn't contain new information. But in a non-commutative, there is a lot of new things there which are much easier to see on this level. And so for the non-commuting rational functions, it turns out that every rational function you can actually write as the inverse of a matrix, and you multiply by u and v, which essentially means you take one entry out of this, where this matrix contains polynomials, which can be chosen with degree less than 1. So you can do this one inverse, but on a level of matrices. And maybe here is the example, the guy which I had before. You can also write it in this form. And this is more or less the sure complement formula for inverting a block matrices.  And you see this matrix is very simple. This only contains polynomials. And actually, you can take them linear or f i. Only degree one is showing up here. So this means I mean, this here looks hard to deal with. But with such things, you have much more possibilities to work. And this representation, I mean, this is also true for polynomials. I mean for polynomials, maybe it's not so clear what it's good for, but for polynomials, if I have here polynomial, you can also write it in this form. And actually, the entries are linear. This is what we call linearization. And this was more or less what Harger-Robin-Torr-Bjonsen introduced in our context. And which was really the basis of many advances which we have made for calculating, for example, distributions of polynomials in three variables. OK, so Harger-Robin-Torr-Bjonsen essentially introduced somehow that we can write a polynomial in non-committing variables in this form. And so I mean, we had a lot of tools for working with polynomials.  I mean, of course, as I just told you, it's actually this theory of corn and so on. But it appears in many contexts. And it was maybe rediscovered many, many times. It has different names, or it goes in parallel. And maybe, I mean, the oldest one I know of is also called Hickman's Drake. So this goes back to 1940. OK, so in our context, it appeared with this paper of Harger-Robin-Torr-Bjonsen and Greg Anderson give another version of it. But slowly, we became aware that actually you can go back much in time. And we became aware that actually, instead of just looking on polynomials, we can look on rational functions. I mean, before we didn't even know about rational functions. OK, so this means now I should come back to my random matrices and operators. I mean, I have shown you these non-committive rational functions somehow as an algebraic object. But of course, I want to think of it as a function. I want to apply it to operators. OK, and so I mean, there are a couple of issues. One has to be a little bit careful about. So first of all, I mean, one has to notice, which maybe, if you see it for the first time, is a bit strange that not every relation which you have in this free field holds in any algebra. I mean, a free field, OK, in a free field you require everything which is not seriously invertible. So this gives you something. And here's an example. I mean, in the free field, you have this relation. So this is, I mean, the inverse of this. Of course, the inverse is the product of the inverse in the other order. So this is a valid relation in the free field. But I mean, it's not true that in any algebra this is satisfied.  So I mean, if you multiply its visits a joint in one direction, you get one. But in the other direction, you don't get one. Then if you plug it in here, then it's not valid. And I mean, the problem is not that you're not allowed to plug it in. Because I mean, you have to take here the inverse, you take the inverse of one, so that that's okay. But so you get that if you plug it in here, you get V star V, but this is different from one. So this means this relation, which is true in the free field, is not true in this specific algebra. Okay, and I mean, but corn, I mean, this already goes back to corn, shows that this is more or less the only problem that you have. So maybe the problem that you have here is that the left inverse is not the right inverse. And in the free field, you should have that the left inverse is the right inverse. So if you have an algebra where this is not the case, then okay, you cannot plug it in. And also if you go over two matrices, you should have left inverse is the right inverse. But if you have this, then everything is okay. And actually, I mean, so those guys where you have this property, called stately finite algebras, and actually also an operator algebras, I mean, they also are the ones which appear as the finite for Neumann algebras. And in particular, if you have a trace for Neumann algebra context, then you are in this situation. Okay, and in our situation, usually we have a trace. So this means we are really okay. Okay, so we are not dealing with type three for Neumann algebras, because then we would have problems. But in type two to one, this is fine. Good, okay, but then, of course, there are more issues. I mean, of course, if you want to plug in, you have to take inverses in the free field, you can take the inverse of everything which is not zero. Of course, for operators, this is not true anymore. So this means if I apply my rational function to some operators, first of all, it could happen that for my operators, I have some relations which are not there in the free field. So I mean, I could have an irrational expression which is not zero in the free field, but if I plug in my operators, I get zero. Okay, so something like this can happen. But then it could, of course, also be happen, could happen that if I plug it in and I get something which is not zero as an operator, it doesn't have to be invertible. I mean, not every operator which is different from zero has to be invertible. Okay, good. So this means I have to be a little bit careful if I plug in my operators. And possible solutions are, of course, I just plug in operators in rational expressions where all the inverses make sense for my operators. So I stay away from inverting operators which are not inverting. Okay, but actually, I mean, if I allow unbounded operators, then I can invert more operators. And so I might also consider the possibility of allowing unbounded operators and then I can plug in more things into my expressions. Good, okay, so let me first look on the first situation and yeah, in this situation, you can extend these strong conversions of random matrices from polynomials to rational functions. So this is a result of Sheng Ying. So he's a PhD student of mine and he's also here. So I mean, so let us, so the situation is we consider random matrices which converge to operators in a strong sense. Also, by definition, this means if I take a polynomial in those guys, then the distribution, the trace of those guys converges to the trace of this and also the operator norms. That was our definition of strong conversions. So we assume we have a situation like this and we know, for example, we have it if I have a GUEs, independent GUEs. Okay, and then the statement here is that then this kind of convergence remains also true for rational functions. So namely, if instead of a polynomial I consider now rational expression and of course, I don't want to deal with inverting things which are not invertible. So I only take an R such that if I plug in my limit operators, then this makes sense as an bounded operator. So whenever I have to take inverse, it should make sense as the inverse of my operator. Yeah, okay, and then if this is, if I consider such a thing, then I can also, at least for sufficiently large N, plug in my random matrices into this rational function and I get what I expect to get, namely that also the distribution and the operator norm of these rational functions of the random matrices converges to the limit, to the corresponding limit contribution. Good, okay, and the proof I mean is essentially by recursion and the complexity of the formulas with respect to inverses and essentially you only have to control what, when you take the inverse, okay. But because we can control the norm, we have the strong convergence, we can control taking the inverse in kind of uniform way for the approximating matrices and the limit operators. Okay, so what we have here somehow, if we start from convergence for polynomials, we can extend this to the convergence for rational functions on a strong level, which means if I can control the operator norm for polynomials, I can also control things for the rational functions. Of course, one could ask the question, what terms if I only can control the distribution but not the operator norm on a level of the polynomials and then it's not so clear, then I cannot really go over to the rational functions because then I might have some eigenvalues which prevent me from inverting things and it's hard to deal with them. So it's not clear, so I'm going from convergence in distribution from polynomials to rational functions. If I have no control on the operator norm, then this is not so clear, so we cannot do this. So this is really a theorem in a strong convergence and here's an example. So here is this rational function which I had before and now I'm plugging in again my GUEs and my limit operators. So I'm taking independent GUEs which I know converge to X and Y which are given by these three semicircular GUEs which are concretely realized here as two copies of the one-sided shift. Okay, and I mean I have chosen here such a rational function that I can plug in those GUEs. I mean X and Y, the spectrum of them is between minus two and plus two. So I have chosen this four here so that things are away from zero. So these inverses are not no problem with those GUEs and then the theorem tells me again now I can plug in for sufficiently large N, I can plug in the GUEs, I can draw the histograms and this again converges in distribution to taking this expression here in the X and Y. And furthermore, again, we have no separate eigenvalues. The largest eigenvalue.


What's up, everyone? It's your girl Kenzie here from Leighton Sports Guards, and I'm repping some personals for Antoine G We've got two 2021 Panini Immaculate Football Hobbies Two 2022 Tops Dynasty Baseball Hobby Boxes and three 2023 Bowman Baseball Jumbos All right Antoine. Thanks as always for your orders. Let's see we get you We're gonna start with the Bowman Baseball again. No paper-based ships out of this. You'll get everything else Good luck nine autos Bowman coming at you and believe those it'll last two. I'm a football box as we have to so Don't I feel like we haven't seen a quarterback out of that yet. So man It's a little big big RPA out of that. That would be something First up we have for the Mets Hazer's bias first auto Mets Cossus rookie to your favorites Jackson holiday top 100 See Big Drew Jones come on paper Valera Simon one Lawler Cheetahman. Yeah, fuchsia paper of Yoshida rookie. That is 262 of 299 Red Sox Cam Collier Chrome first Harrison Kevin Perrata rookie Garrett Mitchell may he have prospects Seah Cole Young Bella and Brady house Sights on September Soda Strom We have fuchsia first of Kyle Harrison for the giant 71 of 199 Xander Ramirez Light coming up. It's gonna be an Ellie Dela Cruz for the Reds. That's one there prospects Lawler Saying we've got a Roman Anthony on the Lunar Lunar Glow. Nice one there Marcello Meyer boxes with a nice Roman bread for a second. 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We have a you on hell a ponte first blue jade On the beast first auto Adley rookie to your favorites Xavier Isaac Menzardo refractor and he pages media Pedro Leon we have pink border to 175 JJ blood day rookie for the Marlins Montecino Merrill Raza Munoz We have a wow a pearl first three of ten Dylan O'Rei for the Brewers very nice three out of ten Brew crew there you go It's a really nice one there I'm not seeing it Painter rose gold. Sorry thinking pearl Solano Wells it looks like the same exact tone as the pearl packs using We do not tops. No, we did not have any of that spotlight for Washington. It's gonna be the carol fellow Ponte de Paula first Saying we have a paint and gram on the lunar globe Muncie Riley green rookie to your favorites Elijah green collier first chrome Of those Elijah green top 100 next auto we've got a Samuel de la Rosa on the green grass 30 out of 99 Third baseman there for the Cardinals on the green grass I was talking to Donnie about it last night. I was like who wakes up in the science Let's do a green grass parallel. It's a real. I like it. I do don't get me wrong, but it's like where does that come from? and Zalas By as Jordan Walker Nice tops. Yeah, we we don't have any of that. Unfortunately, but yeah, I've seen some really nice hits come out of that stuff We've got Cardinals rookie spotlight Nolan Gorman Brady house Drew Jones base and Luciano One more auto I believe here Alvarez rookie We have purple killer Watson. That's 149 of 199 purple border Brook sleep Jordan Walker bias Got Brock Jones base and Oswald Parazzo Last pack jumbo a number two Okay, but I thought I didn't have a trash bag in the first. We have a And Ronnie Simon for the rays on the atomic 18 out of 100 There you go I sit there Atomic first auto. It's looking autographed there, too For the raids Dibromatina's and Drew Romo now we'll do it for box two box three here First hit up we have Astros.  Yeah, I've heard the blasters are pretty far Haven't haven't seen any We go any pages, right? I never get lucky when I wrote retail Costs a stela cruise or rip anything for myself, honestly, it's always for y'all You know the clean refractor Jordan Lawler Chef Simon almost and Hannah and Alcantara See a red Red auto Spotlight rookie for the Mets is gonna be Francisco Alvarez Christian Hernandez CN We've got lunar glow of Coulson Montgomery white socks Refractor first Colby Thomas 240 of 499 Rimmels Going good so far today. See how? Pulling some nice cards. Yeah, Garrett Mitchell. Sky blue to 499 Kumar rocker Rangers Ben Scum Jordan Lawler Curtis Mead Jackson holiday prospects his Montez first chrome and hence No, I don't think so. I was saying that yesterday. 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Let's see a big RPA out of this one Manzada that cleat or soul First up we've got Packers 3375 Devonte Adams Here's one of my favorite Alex. How about the sideline towel rookie 10 of 15 Anthony Schwartz for the Browns? It's pretty cool 10 of 15 there Now we've got Curtis Martin on the patch 8 out of 10 player worn use material on that one They've got eye black auto 65 of 99 of Russ Grimm Russ Grimm redskins throwback auto there inscribed Hall of Fame 2010 Nice And we have another eye black this one's five of 99 Frank Gore five of 99 Well, Antoine, we don't have a quarterback But honestly this one was probably probably be better than quite a few of the quarterbacks from this class. Oh My this is a true RPA Jamar There you go Beautiful hit We'll get that one right in a mag for you. Wow Well, that'll do it for your personal there thanks as always Antoine congrats on that we appreciate all your support We'll get these cards right out to you