A raid often is the culmination of an investigation. It has several set procedures that must be adhered to. Federal officers with a search warrant to search these premises. Open the door. This is no impromptu happening, but rather the result of careful planning. If it is to succeed, it has to be. This is the raid leader. He is the key decision maker of the group and is always an experienced officer. He may be the principal investigating officer assigned to the case. Because of this, he has made specific advance preparations that have led him to this moment. In order to legally conduct the raid, he has had to get the proper warrants. Specifically, these may consist of a search warrant or an arrest warrant. Or, as in this situation, both. Needless to say, the legal requirements to obtain such warrants are strict. To make a successful raid, you have to be sure you have correctly identified the location. For this reason, the raid leader checks the area out himself in advance, as unobtrusively as possible. He looks not only at the target itself, he checks the general location around it. He wants to be sure he knows all avenues of approach, as well as any possible escape routes for the suspects. And he has to carefully consider the safety of the public. He also notes who the people in the area are and what the nature of their habits is. There may be an informant among them. But the biggest part of his job, before actually conducting the raid, involves surveillance of those who are under investigation. Here, the agent has found a surveillance point almost directly across the street from his target. It's an easy matter to watch all activity. Every individual entering or leaving the house is photographed. Accurate and detailed descriptions are taken of any automobiles seen on the premises. The model, make, and color of each car is recorded. The license plates are noted, as well as any distinctive scratches or marks. All of this is written down in a surveillance log. This information is necessary in case the car in question is to be seized as part of the violation. It also provides investigative leads and may cooperate court testimony. The car is identified photographically, as well as in writing. Later, at the office, it joins the other evidence that has been gathered on the suspects, their associates, the target, and its surroundings. While the surveillance was going on, the warrants from the U.S. Magistrates Office were received. And now the investigator assembles his raid team and carefully briefs them on all aspects of the job facing them. If any local officers are going on the raid, the raid leader should have them stand up and identify themselves. It is good policy to wear some sort of identifying symbol, badge, armband, baseball cap, or coveralls, so that everybody will know who is on the raiding party. Ideally, the raid team should be made up of individuals who know each other, such as agents from the same field office. Special agents of the Internal Revenue Service may participate on narcotics raids to identify assets and books and records indicating tax violations. Photographs provide a lot of key information at a briefing. But it is not always possible to get them. When they are not practical, sketches may be used. And objects to be seized should be carefully identified. A time at which the raid will take place should be set. The actions of the violators determine just when this time should be. Equipment to be used should be identified and carefully gone over to see that it is in proper working condition. The type of equipment to be taken depends upon the type of raid to be conducted. All agents should, of course, have their own official weapons. Extra rounds of ammunition and handcuffs. Among the other things that might be taken are entry tools, evidence-gathering tools such as a camera, containers for the contraband, sketching equipment, labels, fingerprint kit, and sample containers. Other considerations are portable radio equipment and a good first aid kit to be used in case of injuries. The type and number of automobiles to be used on the raid and their deployment are also noted. The agents are divided into three groups or teams. The first is the entering team. Backing them up is the searching team, which will be responsible for a thorough search of the target. These two groups are helped by a third one, the covering team, who are there to prevent escape and control the area surrounding the target. Now the team members are assigned and any special instructions are given. For instance, the team will have to provide protection for an undercover agent who may be with the violators and be informed concerning the expected actions of that agent. Is any special equipment such as a surveillance vehicle going to be in the area? Is there an informant in the area who may also have to be protected? The raid leader points these things out and goes over them a second time. He then hands out photos and information on the various violators expected to be on the scene, as well as instructions for each officer who will participate in the raid. Any expected resistance is indicated, including whether the violators have a past record of resisting arrest. He defines what contraband and other objects they will be looking for. The specific type, how it could be wrapped, where it could be concealed. The contraband and other evidence may not be familiar to the participating local police officers. They should be shown any available samples and be given detailed descriptions. The raid leader goes over the violators' habits, work routines, associates, and the procedures and timing they use in performing their unlawful acts. He points out any additional evidence the agents may expect to find, such as notes, memos, phone books, financial records. He then explains how each of them will get out to the raid site, what the various car assignments will be, and who will transport the prisoners back to the office. Government vehicles are usually used, but when a large raid is planned, special vehicles may be rented or obtained from other agencies to transport prisoners, contraband, and other seized items. The last and most important factor to be discussed in the briefing is firearms policy. No matter how many raids you have been on, no matter how many raids you will lead, it is necessary for you each time to review the firearms policy of your agency, making sure that every agent and local officer understands when and under what conditions a weapon may be fired. At the conclusion of the briefing, the agents move out to their assigned vehicles and prepare to leave for the scene of the raid. Although cars are being used on this raid, other common methods of approach are by foot, boat, or any other appropriate means. Each raid is different from any other raid. The approach to the target depends on where that target is located. The terrain, the neighborhood, the modus operandi of the violators, all have an effect on the speed with which the raid is executed. Here it is possible to drive virtually to the door of the suspect house. Leaving the cars, the raid squads assemble themselves into teams to which they have been assigned. The covering detail surrounds the house to cut off any avenue of escape for those inside. This is their primary function. Each member of the team is ready to return gunfire from the violators if necessary. The men on this detail also control the outside of the perimeter area. They position themselves so that they can notice and halt if necessary the arrival of newcomers who may or may not be associated with the raid. The raid leader heads up the entering detail. This detail must affect entry, make arrests, and control occupants. Nearby, the third detail, the searching detail, stands ready to rush in with the entering detail. These are the agents with the most specialized duties on the raid, since it is they who must conduct a thorough search of the premises for evidence and contraband. Members usually include a photographer, a fingerprint expert, and any other individual assigned to handle the seized property. On some raids, the members of the searching detail may be the same agents who comprise the entering detail. There is a definite procedure clearly defined by the laws of the United States that must be adhered to if an entry is to hold up in court later on. You must knock loudly at the door. You must announce loudly and clearly that you are a federal officer. You must state that you have a warrant. You must announce that you intend to search the premises. You must demand entry, and you must wait a reasonable amount of time before forcing entry. This length of time will depend on the nature of the objects to be seized and the actions of the people on the inside. These agents were lucky. They had a fairly easy entry. Oftentimes, things are not that simple. A door may have several locks, chains, and bolts on it. The door itself may even be made of steel. Windows may be barred and just as hard to enter by. And there may be carefully rigged electronic warning devices. The whole place, in fact, may be a regular fortress. Complete right down to the lookouts, male or female, to warn the occupants of impending danger. And with a secret entrance that can serve as a handy escape route in the event of trouble. Violators fortify the premises to give them time to destroy evidence and perhaps to escape. Oftentimes, entry can only be affected by the use of one or more tools like these. The sledgehammer, the fire axe, battering rams, eye and lever bars. The key thing to remember is to use only the amount of force needed to enter and no more. There may be a better entry route than breaking down the front door. Windows and any other doors should be checked to see if they are open and afford easier entry. The idea is to attack at the weakest point of the premises, wherever it may be. One of the first things violators are apt to do when they realize a raid is underway is to try to destroy evidence and contraband. This must be prevented immediately. The other thing on their minds is to escape. Stopping them from doing this is the most important thing the agents must accomplish once entry has been obtained. The violators must be subdued as quickly as possible and the premises swept through to find any persons who may be in hiding. The primary responsibility is to control the occupants. The persons named in the warrant should be arrested and anybody else found in the area should be kept under control. Everyone should be frisked for weapons. Order should be maintained. The violators must not be allowed to become the masters of the situation. Once the place has been secured, the occupants of the premises are asked if they have anything that is of value, including any large quantities of money. The agents take anyone who does claim to have valuables along with them as a witness when they go to pick up such items. The agent should ask all persons whether there are any additional valuables on the premises. The valuables are then taken to an open area where their owner can watch them throughout the search. The search team should use a systematic plan to search the premises. The search may proceed in a clockwise direction, a counterclockwise direction, or in quadrants. After each agent has searched his particular area, another agent searches the same area. Using methods like this ensures that all areas will be searched at least two times. Do not touch evidence when it is first found. Call a second agent to witness the discovery. The evidence should then be photographed. It's location sketched. Large amounts of cash and other assets found during raids, especially those involving narcotics violations, should be reported immediately to the Intelligence Division of the Internal Revenue Service so that tax effects can be evaluated and the money applied to taxes due. And custody is taken by the person who is assigned to handle all the evidence. He should label and mark. It is then usually placed into a larger container that is kept for all the evidence found on the premises. It is packaged, retained, and protected by the agent assigned to watch over the evidence. The chain of custody must be maintained at all times. From the beginning, the raid leader has been coordinating and supervising the activities of the raid officers. After he is satisfied that the raid has been finished, he completes an inventory of the items seized. This list is written on the back of the warrant. If items not covered in the warrant are seized, these must be listed on a separate receipt. A copy is given to the occupant of the raided premises, or if no one is there, it is left in a conspicuous place. All the violators are then removed and transported to the U.S. Marshall's office or the agent's office for processing. Prisoners should be taken before the U.S. magistrate without unnecessary delay and the evidence logged and placed in a safe storage facility. The raid leader will see to it that the premises are placed in good order. If there is any damage to the raided building, it is the agent's responsibility to nail up or otherwise secure the premises. When this is done, a post-raid critique is held which points out those techniques that were successful and those that were poor and did not work. The object is to clear the air so that future raids may be improved. We have been watching a raid in a typical urban area. However, not all raids take place in such congested conditions. Outdoor raids in rural or open areas present different kinds of problems. Approach procedures are more restricted. You must know the terrain and dress to blend in with the natural cover that is so vital to the security of your approach. Agents must be on the alert for booby traps like this one. Criminals hiding out in remote locations are apt to have all sorts of devices rigged to sound warning of the approach of strangers. And most important for outdoor raids is a first aid kit that includes materials for treatment of snake bites and other animal bites. Once at the house, the basic procedures apply that are used in raiding similar size premises in urban areas. The same division of the raiding party into three teams. The same statements to those on the inside, the same search and control procedures once entry is obtained. And the same danger. Remember, any raid is one of the most important and dangerous parts of your investigation. Study the proper raid procedures. Practice them until they become second nature to you. Your life may well depend on it.


This is Witspace news for Friday the 19th of February 2024, I'm CMDR Buur. In Elite Dangerous News this week, Ram Tarr drops a surprise partial solution to the Titan anti-Guardian field, some in-depth supercruise overcharge community analysis has taken place and are the lights being turned off at Galnet again? You know how this bit goes, please like, subscribe and ding that little bell so that YouTube shows you all our content and if you'd like to directly help our work here at The Burpit you can also support us through Patreon, links to that and everything else are in the description below. The Titan Euer has been completely stripped of supporting systems by a concerted community effort after it pulled a surprise gaggle of authorised interceptors out of its hat a couple of weeks back. As a result, as of this recording, its in-game defence level is shown as completely vulnerable, it is under sustained Nanite torpedo attack right now and its hearts are dropping like a box of bricks out of a plane. If you are looking to collect your Titan decals and ship kits etc do not wait to get your 2 million credits worth of damage to its thermal core, we do not expect the beleaguered Titan to last into Saturday UTC. Likewise if you haven't yet seen a Titan explode or your fancy catching another one it is happening this weekend probably on Saturday night. If you want to track the damage to the Titan while you are away from the game we've linked to the excellent DCOH tracking website below. And those hearts are set to take different if not more damage from here on, as we were going to press today the in-game inbox was hit with a message from the pilots federation noting that the engineer Ram-Tar in the mean system has found a way to protect guardian weapons from the anti-guardian fields that emanate from thargoid titans. The message specifically states that once the weapons are shielded they can be used against all thargoid threats including titans. As of this recording there doesn't seem to be a solution to any other guardian modules beyond weapons but honestly Oya isn't going to live long enough to share an opinion on that at this point. We're assuming that the protection extends to AX operations in HIP 22460 as well where this horror story all started but we've no specific science to back that up currently. The hybrid SCO frame shift drive a blending of human and thargoid technology that was released into the commander sphere a couple of weeks back has been subjected to some significant testing and analysis this last week while the player base attempts to ascertain exactly what the perfect use case scenario for the module is. In case you missed it the drives feature what essentially equates to a boost button in supercruise that accelerates the user to thousands of times the speed of light in the matter of just a few seconds. The downsides to the drive other than it's only available in grade C and it can't be engineered are that it generates huge amounts of heat. It absolutely chews through fuel at an alarming rate while it's boosting and the resultant ride from using the boost feels something akin to an interdiction tether. Kind of like wrestling with a large live salmon while you've got olive oil soaked hands. When oddity did surface this week in relation to frame rates and heat generation in the module it appears the module generates a lower heat signature if the PC running the game has a lower frame rate but generally speaking with the use of heat sinks coupled with the rate that the drive chews through fuel which is by far its major limiting factor in normal gameplay this bug is unlikely to impact anything of any significant consequence. Whilst we've seen opinions on the usefulness of the SCO drives admittedly unusual abilities swerve in exactly the directions you might expect there's also been some serious attempts to pin down the drives performance high points and best case use scenarios. I myself have been using a completely unengineered python this week packed with fuel tanks, heat sinks, collection limpets and an SCO drive to farm some high grade emission POIs for an engineering project I'm working on at the moment. It's absolutely perfect for reaching those signals really deep in the system that are about to expire. I wouldn't have had a hope of reaching those signals before the SCO drive and honestly the brief rides in the supercruise equivalent of white water rapids in between signals are really good fun. Commander Alec Turner recommended a superb forum post based analysis of SCO fuel per hour and speed rates across all of elite ships created by commander Oscileron which you'll find linked below it comes complete with a google sheet listing all the numbers involved and there's a very competent review of the SCO drive by youtube channel dry heat and sand that balances the drives performance intra system as well as inter system one quite clearly being way more useful than the other that video also offering up some usage scenarios at the end. Ultimately the overall picture that we're getting here is that the drive is very useful currently at least in specific scenarios but not well placed outside of those scenarios a bit like trying to build a barn with a watermelon instead of a hammer. It can't be a coincidence that the drives arrival in the game coincides quite nicely with the community bearing down on those thargoid titans that are placed much deeper into the systems that they inhabit and that usage in those environments might help negate at least some of the many interdictions that come with travelling in thargoid controlled space. The in game galnet news service has seen a shift in its cadence of late that is starting to gain the attention of the community as a result rather bizarrely I have to report that this week it may or may not have been updated with a short piece acknowledging the distribution of the new achilles aerospace frame shift drive I'm not being deliberately facetious in my uncertainty there unless you're specifically watching galnet like a hawk these days it is genuinely quite hard to tell. The cadence of updates to the news network has changed significantly in recent times to the point where you could happily park a beluga lengthways in between them and the dates printed on the top of those updates rarely seem to relate to the date the item is actually published and sometimes differ depending on where you look at them. This in point the in game version of the story I'm speaking of specifically here is dated the 8th of April that's 11 days ago as I speak these words it doesn't yet appear on the front and centre web version of galnet news at elitedangerous.com. Commander Gravitas deficiency made us aware that it does appear on the older and as best as I can determine no longer officially in use pages at community.elitedangerous.com from frontier but there it's dated the 10th of April we're guessing all of this is symptomatic of the entire writing staff having left frontier around the start of the year when redundancies were sweeping the company. As a side note to that fdev started recruiting again this week for some of the other roles that they let go just two months ago and if you're keeping half an eye on frontiers back and forth in the gaming press this week then you will have seen the understandable backlash that is causing them. As far as galnet is concerned the cadence and indeed quality shift that the service has seen of late is quite palpable there are significantly fewer articles on the feed these days sometimes there can be a week or two between updates whereas we had become used to two or three updates a week at least. It's possible that what we're seeing here is simply just another symptom of fdev's well documented financial woes and the elite project having no writing staff as a result. But we have been pondering here if indeed this is an all part of a larger plan the company has in mind for elite in the future. Historically the game has always generated its own background simulation, event and numbers driven local pseudo news feed that is viewable in every station and starport in the galaxy. The feed which is viewable in station services will tell you what and how many ships have been through the system recently, the status and major events related to the factions present in the system as well as details of any player bounties local to the system and a report on any power play movements. It's all very dry and very clinical however lacking as it does any human touch. There are no unnecessary words, no colour to the stats presented and no greater context is offered with it. However the system was implemented around a decade ago and since that time technology has evolved in some quarters that evolution is happening at a rather terrifying pace. The video card giant Nvidia for example is now a world leader when it comes to implementing genuine AI into a game space to the point where they are now worth trillions of dollars. The world's stock markets are always on the lookout for the next big thing and AI is currently the recipient of that particular money hose. Frontiers boardroom have mentioned on one of their publicly broadcast earnings calls before that they are actively looking at how AI could be leveraged to benefit their business as are I'd imagine all the major publishers and developers. Elite Dangerous has always been a very statistic and event driven environment. It generates huge amounts of data on a daily basis covering player movements, changes in the BGS and the rise and fall of economies etc. So the political back and forth of power play are ultimately all numbers and event driven. It doesn't strike me then as a huge leap to wonder if perhaps a chat GPT like system couldn't be plugged into the data stream generated by the game and in particular the new power play 2.0 and then leveraged to interpret and display that stream with a somewhat more human like slant to it. In an attempt at least to supplement, if not replaced completely, the frankly irreplaceable the biological neuron driven feed from the previous generation of Galnet. Are you planning on wailing on the Titan Oya before it's too late? Will you be protecting your stock of Guardian weaponry and just what do you think is happening to Galnet? Let us know in the comments below. That's it for now, thanks very much for watching, we'll be back later this week with more videos, until then O7 commanders follow the greens on the way out and do keep clear of the toast rack, we very much look forward to seeing you next time.


Thank you very much. I'm really glad to be here on unfortunately I can't say the whole week, but I'm looking forward to today and tomorrow. I enjoyed today. I'm looking forward to tomorrow very much so I'm going to attempt to sort of Give a talk where I put a few details on the slides, but I'm gonna also draw on the on the board So I think if you if you what I'm drawing on the board should be on the more understandable sides if the slides are too too technical, but feel free to interrupt and so to set the stage I I want to talk about Constantine curvature surfaces, and so I don't hopefully it's since it's such a big deviation from what we had this morning I wanted just to find the basics. So Can you read that? Okay? So the isoprometric problem is sort of a very old geometric problem in various guys's So what we're going to mean by the isoprometric problem is that you say that a set Omega in a man in a Riemannian manifold say is going to be isoprometric if So a set is going to be called isoprometric if it has the least area the boundary area For all regions of the same volume. So I wrote n but really for today You can set n equals 3 so in a 3-manifold you when I say volume an area Then it makes then everything is fine. So you want you want to enclose a fixed amount of volume with the least area Okay, and I'm just going to ignore any issues of issues of regularity of which there are many and quite interesting story but not for today and so what I Wanted to talk about today has to do with critical points for this variational problem So you can ask for the global minimum, but also you can ask for just a further first-order critical point that means that to first order the set minimizes the area for fixed volume and You can also ask that to second order it minimizes area. Okay, and so What I'm going to say is is a surface is constant mean curvature Okay, so a surface is going to be a first-order critical point if it has constant mean curvature the mean curvature is just the trace of the second fundamental form and Stability I won't write it down, but I won't write down the condition Okay, and so stability can be measured along the boundary of the surface I'll always write the boundary of sigma and so it turns out that your second-order stable You're a second-order critical point for the isometric problem if and only if you have the following Inequality for all functions with mean zero. Okay, so here a will be second fundamental form squared and so This condition that that you require that seed have mean zero That's like saying that you preserve the enclosed volume and now you're asking that you don't you can't decrease the area While while enclosing a fixed volume to second order at least Is that okay? Are we good till there? So I just mean that okay. Let me write this over here Yes, this is just Omega if you have any family of surfaces With this being the original one and I I want to fix the volume then Then I just want that the derivative at that time equals zero is Zero okay, and then similarly when I say second order I want a non-negative second derivative at time zero okay, and so The study of coming curvature surfaces is is sort of geometric analysis setting I think and It in the set in the for the isometric problem That's a very old problem and more recently people have studied sort of the critical points and so you have the following uniqueness Results, so if you have it embedded compact constant mean curvature surface in R3 Then it must be a round sphere, so that's proven by alexander of now. There's some other proofs as well If it has genus zero even if it's an immersed then it still it must be around sphere And finally if it's stable then it's also also around here So in particular along with sort of an existence result the symmetric problem This tells us that because in order to find the minima. We found critical points right so in particular The isometric problem in the Euclidean space The solution is the round the round ball right so the round ball enclosing a fixed area has very Enclosing a fixed volume has the least surface area among any such set Okay, so that that statement was known before these do it directly by by a more sort of Sematization techniques or you can sort of classify the critical points and use a existence result for isometric reasons and so If you've taken a sort of a course in in Riemannian geometry where you do you go beyond the definition of of Curvature once you start to look at what does it mean to have certain sorts of curvature? You learn that that Ricci curvature is a thing that controls volume Great, that's sort of the fundamental property of Ricci curvature at least for me if you're a Kaler geometry Maybe you don't agree with me, but so for for comparison geometry really volume is coming with is related to Ricci curvature Okay, so Bishop Gromov. There's also some very I think you don't learn this in your first Riemannian geometry class But it turns out Ricci curvature and the isometric problem have sort of an obvious link You can give some easily bound way the isometric regions behave by knowing something about the Ricci curvature and so What I wanted to talk about instead is the scalar curvature So just in case you don't remember the scalar curvature Will be the trace of the Ricci curvature, which is itself the trace of the sectional curve Or the trace of the correct appropriate sectional curvatures or the curvature tensor and so To start looking at examples of manifolds with various sectional curvature or scalar curvature behavior You start to realize that you don't expect to be have too strong of a control on an area and volume for scalar curvature Okay, so sort of the things that are true for Ricci curvature is definitely not be true for scalar curvature Well, it's it's a much weaker addition and so However, it turns out that for small volumes. So if you're interested in very small regions Scalar curvature does play a certain role. Okay, so let me draw a try to draw a picture and so So what my picture is supposed to be is you supposed to imagine a Compact manifold where the scalar curvature has up as a maximum at this point. Okay, so Okay, and so what it turns out is that then the point where the scalar curvature is the largest is where the small isoparametric regions turn out to concentrate. Okay, so There is a blue so if I ask on this in this manifold, how do I enclose? point zero zero zero one Volume with the least area. I'm going to do something like like this and so Heat so you don't know anything about where these regions are for large volumes I can't say anything. Well, I may be in a rotationally symmetric example You could say something but for very small volumes that answer is actually very simple is that ice for regions and actually more generally stable CMC regions like to concentrate around points of maximal scalar curvature or locally maximum It's stable the stable CMC problem okay, and I'll just point out that there's there's a big difference in the Stable CMC case and the isoparametric case because let's say this was the global maximum But this was a local maximum if this is the local maximum. You could find Stable CMC surfaces which were not isoparametric Okay, so stable CMC surfaces just feel the effect nearby But to be isoparametric you have to really beat every other surface Because that's like being a global minimum versus a local minimum And so the the real key to this sort of result is that on small scales Remania manifold look flat Okay, and so it turns out that when you start to study this problem the scalar curvature is telling you What's the deviation from flatness in a certain sense? That's very vague explanation, but the The reason that scalar curvature can control the area and volume is because of the additional input of flatness in some sense That's sort of a big explanation Okay, so what I want to talk about today is You take this problem as an idea you say, okay, I sort of understand the behavior of these sorts of questions for manifolds which are flat on small scales and I that that lets me understand small regions So then the question is what about manifolds that are flat on large scales and Let me understand look at large regions. Okay, and so These sorts of examples have sort of a completely different story Coming from general relativity, but I'm not going to start I'm not going to tell that story all and I'll just tell it from the geometric point of view okay, and so For today the key example of a manifold that's flat in some sense on large scales is For me it's going to be the Schwarzschild metric and So the exact form of the metric is not so important, but what you should know is That it forms a family of rotationally symmetric scalar flat manifolds and If you look at the metric and so for me bars are always going to be Euclidean so The metric is going to be some conformal factor to the Euclidean metric and for it the distance from the origin very large The conformal factor is going to go to one right so this metric the Schwarzschild metric as you go towards infinity You go toward G bar Okay, and there's some parameter here M Which has some some physical meaning it's called the mass but for us again We can just think of it as just a parameter describing these metrics Okay, when M is zero you get Euclidean space, and so it turns out There's also there's a long story relating scalar curvature in this number M But it turns out that M will always be positive otherwise the metric is not going to be well behaved in the compact and so it's going to turn out that Not only does scalar curvature have an effect, but also the mass M is going to have an effect on the positioning of large isoparametric and CMC regions and so What I wanted to talk about today now that we're sort of to the real topic is so what happens to large Stable CMC surfaces if you're asymptotic to the Schwarzschild metric so that means that I'm going to consider like manifolds with metrics, which are this Schwarzschild metric which is like Euclidean plus some correction and then I'm going to allow some either even a further correction to perturb things a bit So you're not the the manifold the the metrics will not be exactly rotationally symmetric and in the compact part of the manifold You won't have any real control so you sort of imagine them as Out here They're looking roughly like this, but then there's something quite confusing going on and You could have some some boundary for me for technical reasons if you're an expert I'm going to assume that boundary is minimal and there's no other closed minimal surfaces and so So for me, I cut the Schwarzschild at the I cut it off here and I don't worry anymore and so the the first result in This direction proved by his skin now and His getting out proved an existence result and I'll later talk about a uniqueness result that they prove And so what they prove is that so in this manifold. It's not clear That you can find any CMC large CMC regions or large stable CMC or isoparametric regions Okay, so it turns out even the existence of the isoparametric region You can try to fix the volume and min this area Even the existence for that problem is a bit difficult because you could have some loss of mass at infinity Right, there's there's some non-compactness to the problem So you could have like this usual picture where a minimizer would rather just run off to infinity in the limit There's nothing that's something you're you're a priori worried about. Okay, so it's not even clear that There exists any CMC surfaces Nor clear that there's just any that you you know what they look like, but it turns out that okay There do exist stable CMC surfaces and you know exactly what they look like and I'll draw that Here, okay, okay So it turns out that you can find a Foliation near infinity by stable CMC surfaces Okay, and so notice in Euclidean space if this was exactly Euclidean space. This is easy I just take very large balls and take bigger and smaller ones But in Euclidean space there's no uniqueness for those balls So I could take a large sphere and move it a little bit And it's also CMC with the same mean curvature and same area And what's gonna be the question here is is it true for these spheres? So what happens if you move these spheres a little bit? Can you can they remain CMC or? What happens if you move them a lot can you find another one which is CMC and it turns out the answer is going to be no So that's what I'll come to next So but for the existence result we do know that there are candidates for CMC Surfaces and so and in some sense they're centered Okay, so the if you look at sort of what is the center of these spheres? Obviously you're in a manifold so it doesn't make sense But you're nearly Euclidean in the region where the spheres are and so you can define some sort of Euclidean Center and the Euclidean center is going to be roughly the center of the manifold whatever that means so these spheres are not very far off Okay, so they enclose the center and their center is roughly the center and What I just said is going to be important for my description of the uniqueness results Okay, so the theorem that I wanted to talk about today is the following so if You're asymptotically short shield in the sense that you're a perturbation of short shield a lower order perturbation with six derivatives Who cares and you will assume that you have positive mass because obviously if you're going to prove a uniqueness theorem You want to exclude Euclidean space so Euclidean space has zero mass. That's just there's no extra terms So I want to add an extra term. So once you're not Euclidean space Then if your scalar curvature vanishes identically Then a large stable embedded CMC surface is here Okay, so in particular there's no So there's no such surface for example over here. That's large stable CMC Okay Is that there are any questions about? Yeah, so so these are the only large stable CMC surfaces in the in the in the manifold okay, and so You you can't do anything you can't have any hope besides saying things for large surfaces And this is sort of like what I was talking about before with the small surfaces You don't expect to understand the medium surfaces in such a manifold Because they could live entirely in the piece which is just compact is doesn't have anything to do with Euclidean and okay, and so What's that so If you in short-shield if you if you look at the doubled short-shield for example Then there are definitely Extra CMC surfaces that you sort of don't expect and so I don't know if there are large CMC surfaces you don't expect But you sort of you don't imagine that Surfaces that go are allowed to go through the the boundary They could behave very very poorly. I mean, I guess that's not totally understood This is sort of this is sort of the smallest manifold in which to prove it you name this result in some sense You could try to you could try to enlarge your manifold improve a different a stronger you think this result. Okay, so again for The experts You you might people you might have assumed that this has this theorem is true If you say non-negative scalar curvature instead of zero scalar curvature and that turns out to be false So You can I can construct an example with non-negative scalar curvature which violates this theorem I could I could change the hypothesis on the scalar curvature to a longer sentence And then it would still be true But it there's no nice way of saying the exact hypothesis which what we can prove And so again if you try to weaken asymptotically short-shield to asymptotically flat So here we're sort of assuming a sort of asymptotics if you try to do something slightly weaker It's also false by these examples of curl auto and chain And so what I wanted to talk about for my remaining time Is what goes into the uniqueness result in particular? I should say what other people have done before me because this builds on several a list of several results by other people so um the Essentially the way the story goes Is that people proved uniqueness results for these surfaces Under various conditions on the surface So you assume that you have a large stable cmc surface and it satisfies x Additional assumption Then it must lie in the in the canonical foliation or then it does not exist Right so and then what we did was finish the last the last list of of conditions and put you put everything together And you got a uniqueness result okay, so what Husky and yaw prove in their their original paper is that if You're centered in a certain sense If you're weakly centered then you're you lie in this foliation Okay, so let me try to draw a picture of this so what Husky and yaw were able to prove is that if You contain a ball of a certain size related to the mean curvature Then this picture is wrong and actually you're in the in the canonical foliation Okay, and so this sort of assumption Is essentially assuming something about the inner radius of the manifold compared to the mean curvature Okay, and that that will come back when I talk about what we proved um Oh, I'm sorry, and then this Condition was subsequently weakened weakened by ching and tian to just assume To say that there exists a set Which is very large say but fixed and once you contain that set Then you're in the in the foliation. Okay, and so I'll I'll say a word about how you might prove such a result in a minute, but let me just let me go through the the um Results and then so we were able to shrink this set down to a point. So if you contain a point then That's enough to force you into the into the foliation Any given point if you contain a point and you're very large So but but very large depends on the point so and so somehow What what we prove is that if you contain a point Then you eventually miss this compact like we prove as you eventually miss any given compact set and so what the these three results Tell you is that if you have a counter example to the uniqueness theorem Then you don't look like this but you look like this Okay, so The sphere and its center are very far to one side the manifold Okay So i'll come back and talk about these these guys Okay, and so there's been several works related to this and so um What I wanted to talk about first is how do you sort of how does such You prove sort of these theorems. I'll be a big brief here But the general idea Is the following quite simple identity Which is remember for me bars mean euclidean and no bars mean this other metric, okay and so Assume that you have a constant mean curvature surface sigma in your manifold Then you what you It is for so for the husk and yaw or the ching and tian arguments You're going to the surface of the the surface will lie very far out in the manifold So you can say what's the difference between the euclidean and the g mean curvature Okay, so it's quite a nice exercise In terms of how does mean curvature could change other conformal change And then because there's extra terms you can add those in So it turns out you can compute that the difference of the euclidean and the G mean curvatures has something to do with this quantity m And then there's this r to the minus three times and x dot the normal vector, okay and um Okay, so but on the other hand we have a way of getting zero Okay, so Both of these terms are going to give me zero So what i'm going to do is i imagine the first term This is like saying what happens to the the euclidean area when i move In a fixed direction a so i'm right. This is the first derivative area if i just move the surface in a direction a So for euclidean space, that's a isometry so that obviously doesn't change area And if you work it out the mean curvature times the speed Along the normal speed which is that is is going to be that first derivative. So that's the first term The second term is just the divergence theorem Right, so if i integrate New dot a over the boundary i can use the euclidean divergence theorem to bring it inside and the divergence of a constant vector field is zero Okay, so putting that together i get That the integral of h bar minus h times this new dot a it has to be zero precisely Okay, so that's coming from and there i've used the fact that you're c mc Right to pull in the h Few paying attention so that's one of the only places you use it in an obvious way in some other places You'll use it in a more subtle way and so If you assume that you have a sphere which has radius r And center r times a fixed vector so that that that's sort of like saying that if you rescale the picture So it has radius one the center is a Okay, so variant notion of center And so what using this this estimate for how the The mean curvature changes between the two metrics What you can do is you you have this thing which you know is zero I don't know if you can see that this thing, you know is zero, but then you can compute it Okay And now here if you're really bored you can figure out how to compute this integral and so You're using here implicitly that sigma is quite round and that's a sort of technical Note, but it turns out that what pops out is a Okay, so in some what we find The zero in order for you to be a quite round c mc surface Okay Is that clear so the idea is to use this fun Argument that I described before to have an integral which on one hand is zero The other hand is the the size of a in some sense Okay, that tells you that you have to be centered and then from there you can use the implicit function theorem to tell you that you actually Delay in the filiation You're you're near in the filiation. So then you can you can use something much sort of more basic in some sense So, all right, there we go And so just one It turns out that the the step from replacing sigma by the sphere is quite Because some of these terms are a bit singular so there's like R to the minus three term and that that could play So if you if you don't Investments on how spherical you are this argument might not work Okay, so and ching and tian what their contribution was is they were able to improve this approximation Technique and that's that and in this can you have this this Additional assumption that the inner radius was somehow under control and ching and ching and tian were able to handle The the argument even if the inner radius was not under control in a certain sense Okay, and so then i'll be very brief here, but if the inner radius is not very large Then you need a sort of a different different argument and just i'll just say use an argument related to the positive mass there Okay, so I won't I won't explain that so now to get sort of to the stage of what I want to talk about today is What we're left with so i'll just to recap we use this sort of flux type argument You compare euclidean to g mean curvature and you use this funny argument to show that if a The center a was sort of you're sort of centered Then you had to actually be in the in the foliation And so thus the thing that's remaining is that you're really quite far out Okay, so you look like this And so it turns out that you could try to run the same argument you say oh i'll just check the same integral But it turns out that These sort of flux integrals that you used before vanish So you can show they vanish just by this funny like first variation and divergence theorem argument But then you get that it's equal to something in terms of a But then you get that that's equal to zero. So you haven't proved anything So the the previous argument doesn't work for in that in that case is what i'm trying to say Yeah, you you get f of a you know that f of a is equal to zero you'd like to say that implies But if they is zero That's that's not E zero for all a bigger than one in some sense. So you don't get any information and so It turns out that that's not so i mean After the fact that's not so surprising because there exist counter examples So it the problem is now in for these guys the scalar curvature and the mass Play a sort of a similar role Okay, in the previous results the mass was this quantity m was everything But here now the scalar curvature starts clawing its way back into the problem And you turns out that if you just assume non-negative scalar curvature you can construct You can construct those guys The double piece has a different problem, which is that they go through the compact part in a certain way Is that the answer? Okay, so um it turns out that in some sense these sorts of integrals can't work out but if you do sort of a very Careful what's called liapunov-schmidt analysis In some way you can you can rule you can show that vanishing scalar curvature is enough to rule these out So i also don't want to talk about that because It's it's a bit hard to describe okay, but What it turns out Is what you need is that Analysis to work You need to know something about how the inner radius and the mean curvature behave So mean curvature is usually like one over the radius so for a sphere in euclidean space Mean curvature is one over r two over r depending on how you measure it, okay, and So this sort of theorem needs some sort of a prior input that the mean curvature and the inner radius are of the same size so that's like saying that this distance And this distance whatever that exactly means Which i'll write say one over h that's another sort of way of measuring the radius of a sphere c mc sphere This this theorem needs it there of the same size So what's missing now is proving that they must be of the same size And so that's what that's the theorem that i wanted to finish by by talking about, okay, so Under in the assumptions that we've been talking about actually this theorem itself only needs not negative scalar curvature or whatever We don't really talk about that but You have this a priori estimate that says the the inner radius the distance to the sphere And the mean curvature Are roughly of the same size You're not so worried about this being very large. You're worried about it being very small So what you're worried about Is that this sphere is getting very large But drifting off very slowly, so it's like getting very large But only drifting to infinity very very slowly And that that turns out to to really hurt your most of the analytic techniques that you have because the error terms are just going to dominate Right because if you integrate something like one over r Maybe you bound that one one over r cubed You might end up trying to bound that by the inner radius, right one over r is is Smaller than one over r not right because it can only it only gets better far out But then if that if that term you don't understand you have you have a big problem and so um Yeah, so where's that you is it used? so so this theorem is false if you don't assume asymptotic to short shield, um, so Which asymptotically short shield that's a stronger So I assume that i'm nearly euclidean, but then the next term is m over r And then I allow any any terms and it's actually this isn't this is not true if you if you just assume yeah and so um sort of the key Input in the following theorem, which I think is one of my favorite It's one of my favorite theorems Is that so if you have a stable cmc surface in a three manifold Then it turns out that you have the following relation Between this integral of the mean curvature squared And some other terms and these terms You can think of as just being non negative. So we were gonna we're interested in scalar non negative This is a trace free second final form. Just throw it away. It's not it's a non negative term Okay, and that tells us that integral of h squared is smaller than 16 pi okay, and if you're If you're good at computing things in euclidean space say so for the realm sphere in euclidean space The integral of h squared if you've normalized it like I have is exactly 16 pi okay, and so The proof Some sort of conformal balancing argument, which appears in many related related problems nowadays But what I just said is essentially this so if If you have any closed genus zero surface Then 16 pi minus integral h bar squared. So the euclidean version of this term is negative right so This is this is related to the the wilmore inequality not the most not the recently proven wilmore inequality But sort of the classical wilmore inequality, which says L2 norm of the second of h like the integral of h squared in euclidean space is always at least 16 pi okay And so the idea of the the sort of The estimate that I Let me bring the estimate back The idea of this estimate to get Somehow this this estimate you want to play these two things off each other. So obviously This is not a contradiction because the things which are positive and are negative are different right one is euclidean One is g but we've seen that it's quite quite a good idea to try to change The barred to the unbarred and pick up this m term. Okay, and so, um, I'll I'm nearly finished. I'll just sort of Tell you briefly the idea and so I'll put some I'll put some formulas on the board. So I'm sorry, but I'll get a point out which term How the terms work and there's one there's one final conclusion about the structure that I wanted to make Okay, so If if we're going to use this this this formula, which I had before so that says the The h mean curvature is the collinear curvature plus some term Which is like x dot new with a certain scaling factor and here m is as usual this this all important quantity m mass and so Okay here. You just square this great and so now Okay, I didn't do anything except So I've squared h Then this quantity I said is negative and in particularly you can write it exactly It turns out to be the using gauss-bonnet and the gauss equations It's negative l2 norm of the trace-free second fundamental form Okay, so that and that term will turn out to be important in a second And so This term Is going to tell us something about the inner radius Okay, so this term has a sign. It's everything is squared Okay, and so that means we can bound it from if we put it on the other side We can bound it from below so it doesn't matter exactly you should think of that as a good term but The argument seems quite hopeless because if you compute the size of this term it seems really big okay but you notice that This term would vanish if you knew the euclidean mean curvature was constant And that has something and that has to do with it, right if you delete Then this is that you can use the divergence theorem to the inside and this is exactly the thing which has Laplacian zero Right, this is the great the gradient of the green's function But the is not inside of the surface So there's no there's no delta. You don't pick up a delta. That's where you're far out. Okay And so now what's funny is that in order to to deal with the fact that This euclidean mean curvature is not constant you have to use this sort of Sure type inequality so the shirt like sure's theorem says for example that if you have something who's Trace whose second form has is pure as a Zero trace free part so it's pure trace Then the mean curvature is actually constant Okay, so that's that's this this says something like this in l2 And they are these two terms play off of each other and you can you can complete them there. Yeah Here Yeah in in this This is for the manifold and so yeah, I've suppressed some amount of like changing back and between euclidean So I'll I'll stop there. Sorry if that end was a little technical so The thus the in some sense what happens is that So you you want to So the problem is to a stable cmc condition only feels things along the boundary, right? That that says the mean curvature is constant and some integral Expression along the only I'll go back to the big now everyone's going to get sick So yeah, so these two things cmc and stable cmc only feel the boundary So if you don't assume something like Asymptotically short shield it turns out that there's these examples by carlotto and chain Where in some piece of the manifold? It's exactly flat sort of in a half space So then you can just just look over here and you can be stable cmc In this flat space and you you don't feel the rest of the manifold at all and so What assuming what the the stronger assumption of asymptotically short shall does is it sort of smears out this The the thing that's going to help you so that the mass which is what helps you the m over r Is sort of everywhere rather than rather than just potentially in the half So so so then if there's no m over r term then the manifold is flat if you have non-negative scalar curvature That's the positive mass there So m over squared of r. We don't know so the m over r to the The one half plus point one Whatever that is, right? So so those I don't I don't know exactly what happens here um So we can say something Which is that if you're interested in the iso parametric problem So you assume you impose a stronger condition on your surface in exchange for a weaker condition on the metric So if I ask not just what are the second order critical points, but what are the minimizers? okay for the minimizers then You can prove that going off like this no matter what the metric is this is bad For the minimum for the for what's the least Area in closing that volume and it turns out that the canonical foliation is indeed the minimizer No matter what the metric does But there could exist other critical points That that that answer your question Okay, so so that So for the result that I talked about at the very end you don't you don't use it but it turns out that in In this sort of result. So once you know that the Inner radius and the mean curvature are comparable Then you can do sort of a Lyapunov-Schmidt. I don't know if you know it a Lyapunov-Schmidt redot You can sort of perturb off of euclidean space in some sense You know that this sphere is round in this year a cmc with respect to euclidean And then you say put this new metric which is nearly euclidean and how does that change the mean curvature? Let me do the best I can to account for that by wiggling the surface slightly And then it turns out you can What the effect of that is and then you can say Is it possible to pick a sphere? Which then becomes exactly constant in curvature Okay, and so it turns out that when you say is it possible that has to do with a certain function that you can compute And that function turns out to have have a from both the scalar curvature and the mass And so by by looking at those two things together It turns out that you can see there's no real geometric I don't think there's like a geometric way of seeing this but Just by computing this function you can see that the curvature could beat the mass term in a certain sense If it was allowed to sort of bump do some bumps it could like go like this and that would allow large cmc spheres


Hey, this is Brett and this 2016 Ram 3500 CUCAB Short Box Single Rear Wheel Laramie is stock number 13294 ZA. I am here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used heavy-duty truck and Ram headquarters. This 2016 Ram 3500 has the 6.7 liter Cummins diesel engine paired up with the 6-speed 68 RFE automatic transmission. This truck has been fully safety and inspected by our service shop per the state of Wisconsin inspection process. It has a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100 percent ready to go. I'm going to go all the way around in this video inside underneath. Start it up and take a look under the hood to give the most accurate representation that I can of the vehicle. Really nice truck all the way around. Brilliant black crystal pearls of color. I shoot all my videos in 4k. If you like the video, you can subscribe to the YouTube channel, click the bell notifications and get updates on the videos I do each and every day. As well as having access to one of the largest catalogs, vehicle and heavy-duty truck walk-arounds on YouTube. This one comes with the painted alloy wheels. It's kind of a polished aluminum but they have paint over them. It's a clear coat and it has Lofen LT27570R18 tires, Lofen X-FID tires. These tires are I would say 90 percent, 80 to 90 percent of the tread left on those tires. Very new tires. Frame and underbody is exceptionally clean for a 2016. This is a one-owner clean title history, clean car facts and it's been owned in Kansas and Nebraska its whole life. Front fenders in great shape. Projector lamp headlamps, LED running lights, factory fog lights. Front bumper is in excellent condition. I didn't see any dents or dings on there. It does have the front bumper parking sensors. You get the chrome trimmed grille which is in really nice shape as well. And the hoods in really nice shape. Didn't see any major dents on there. Passengers side front fender looks really good as well. And the passengers side front wheel. No major scuffs or scrapes on there. Brilliant black crystal pearls. Got a lot of metal flake in it. A lot of blues, greens, purples, yellows. Really a neat color. Very cool looking. Look how nice that paint is. As you go down that this side of this 2016 RAM 3500 take note of how clean the body is, how reflective and mirror like that paint is. I take these HD videos so if you're far away or even if you're close by and you just cannot make the trip down but you're still interested in purchasing the vehicle you can see the truck here the truck and have confidence in the vehicle that you're looking at before you even get here. So when you do get here there's absolutely no surprises. You can make a smart and informed buying decision from wherever you're at. Now if this video helps you make that buying decision let your salesmen know that you saw the video that it was helpful and that Brett sent you. Back wheels in excellent shape as well and the back tires are just about as new as the front tires maybe just a hair bit less tread more like 85% of the tread left back here. Framing the underbody looks really good for 2016. Has all the remaining factory exhaust so it hasn't been altered in any way. Lower rockers and cab corners are all in really nice shape as well and it does have the really nice wheel-to-wheel side steps. Passenger side fender on the box here looks good. Rear bumpers in great shape but I didn't see any major dents or dings in there. Back up parking sensors full towing package which includes a receiver hitch four pin and seven pin wiring. Look at how clean that tailgate is. Very nice condition. Comes with a very nice spray and bed liner. Fifth wheel and goose neck prep package seven pin wiring and you do get LED bed lighting back here. Bed's in fantastic condition and that spray and bed liner goes on to the tailgate. Shuts nice and solidly and as you go down the driver's side just as clean as a passenger side no major dents or dings on the box and for full disclosure this back wheel just as nice as the rest. Down the rest of this side of the truck cab and doors all look really good. This one does have the heated fold up till mirrors built in directional signals they fold up like so and in like that. Take a quick look at the back seats. Nice tan leather back here no rips no tears on the seats latch child safety system power sliding rear window. Seats are in nice shape.  Storage underneath there in floor storage with removable containers for easy cleaning you can put ice and drinks in there it's like you have too many coolers wherever you go or if you're not in Wisconsin just extra storage space you do get child safety locks on the back doors and the inside and bottoms of the doors all look really good. I want to show you the VIN sticker here no Canadian trucks here we have a lot of competitors that sell Canadian trucks we try not to tire and loading information sticker right there guarantee this truck wouldn't look this good if it was from Canada. Inside the Laramy package gives you the tan leather seats 40-20-40 split bench seating in the front both these front seats are heated cooled and power and you get the Laramy embossed into the backrest memory driver seat with lumbar factory all-weather floor mats up here auto headlamps power windows locks and mirrors and these mirrors do power fold in I always like showing both sides so you know that both sides are working properly hop inside check out the miles the radio and everything that this truck has to offer on the interior you can see you get the seven inch LCD display there digital spinotter compass time range to empty trailer brake gain you can change all those corners to read whatever you want instrument cluster is very nice and clean comes with the heated leather wrap steering wheel cruise controls on the right bluetooth and information center controls on the left there are audio controls in the back of the steering wheel and other than just a little wear at the top of the steering no rips or tears on that steering wheel comes with the six speed automatic transmission with the optional tap shift this one has the 8.4 3c radio you can see it does have the factory navigation system and there is highway 41 so that is working nicely and FM and Sirius XM radio capabilities they're your heated seats cooled seats and heated steering wheel controls you also have your backup cam and your cargo cam which you can see what's going on in the bed and both of those are working nicely you also get all your different apps on here and then up here is your alpine badge letting you know you have the nice sound system down here are your more tactile volume tune and climate controls your turned out four wheel drive factory brake controller stability control tow-hull mode factory exhaust brake and your front of your parking sensors you can turn those off and on does have a 115 volt 150 watt plug-in and dual glove boxes passenger side floor mat and seat are an excellent conditional rips or tears on there you do get these speakers and the ceiling the headliner is in really nice condition i don't think this truck has ever been smoked in you get map lights power slide rear window button and your home link buttons for your garage door security systems and lighting systems 911 and assist buttons in the rear view mirror and you do get three cup holders on that center console there that can flip up we'll start it up and take a look under the hood starts right up no check engine lights or anything like that i would personally like to thank you for checking out the video today and hopefully from this hd video you've been able to verify the quality condition options and of course cleanliness of this truck all the way around inside now all the lights are working nicely really a nice truck for the miles and age on it under the hood we have the 6.7 liter Cummins diesel engine and jimbe is very clean runs very smooth once again this truck has been fully safe and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off shocks are doing a really nice job pulling that hood up there is the emission sticker didn't see any corrosion on the hood which is always nice and uh i can't say this is about too many 2016's but i would highly recommend this truck from a quality and conditions standpoint i'd have no problem shipping this one to texas new york florida california whoever's going to get this truck is going to be thrilled with the condition on it and ship it back to kansas nebraska wherever whoever's going to get this truck is going to be very happy and to see more pictures of this truck or one of other 550 new and used cars trucks sv's mini vans wranglers half tons three quarter tons one tons you name it we got to go to the website right there summonado.com full pictures and descriptions of every single vehicle all at summonado.com if you'd like to check out more hd videos you can go to youtube.com slash summonado click the bell notifications get updates on the videos they do each and every day as well as having access to one of the largest catalogs of vehicle and heavy duty truck walk around on youtube almost 9 000 videos in county in fact in a second you'll see a link to subscribe to my youtube channel the upper left they link to all the ram 3500 truck videos i've ever done in the upper right a link to this vehicle on our website on the lower left and a link to one of our latest youtube videos on the lower right click those check us out we're super excited to help you with this ultra clean 2016 ram 3500 crew cab short box lary me single rear wheel and brilliant black crystal pearl thanks again for checking out the video remember to like subscribe and share on the youtube channel i really appreciate it thanks again


Good morning faculty members, respected delegates, I am Dr. Sushmit Afle, 3rd year resident from DIY particle medical college, Navi Mobile. Today's my title is muco-microcytes in COVID-19, it's a systemic review of cases reported in DIY particle hospital in correlation with the co-morbidity. Coronavirus disease is caused by the severe acute respiratory syndrome, coronavirus 2, it has been associated with wide range of opportunistic bacteria and the fungal infection. Muco-microcytes is a spectrum of invasive fungal infections that is caused by the mucarils, order that belongs to the surfylon, muco-microtina, rhizoporus, mucar, rhizomucar and the leastimia. It has been associated with the wide range of opportunistic bacteria and the fungal infections. This fungi may present in a wide range of multiple clinical syndromes with sinuses, orbital, cerebral, pulmonary and the gastrointestinal involvement. The germinate forming angioinvasive hyphae that was in function of the involved tissue giving in a dry gangrene appearance, the angioinvasive capability of the organisms that can lead to direct infiltration to the blood vessels and the thrombosis or embolism at present as acute ischemic stroke. Several risk factors are described including the diabetes malitis, malignancies, solid and the bone marrow transplantation, iron overload status, steroid mediated or background cohabititis. Other shared risk factors includes prolonged hospitalization with or without mechanical ventilators. Diabetes malitis stand as the strongest risk factors giving rise to the 36% of patients with invasive muco-microcytes where diabetes in present cases reviewed in 929 cases. While long-term use of corticosteroids have often been associated with several opportunistic fungal infections that includes the asperagealysis and the muco-microcytes, even a third course of corticosteroids has recently been associated with muco-microcytes especially in people with diabetes malitis, aims and objectives, aims to know its temporal association in relation to comorbidities and with drugs being used in the COVID-19. Objectives to analyze the patient characteristics associated comorbidities, location of muco-microcytes, use of corticosteroids and its outcome in patients with COVID-19. Materials and methods patients present with the COVID-19 positive status with comorbidities, COVID-19 positive status with periorbital and facial swelling, case presentation, case for, or 60 years old diabetic male presented with respiratory distress, left orbital pain and swelling, left nasal congestion and discharge with fever of short duration. RT-PCR from the nasopharyngeal swab for COVID-19 was positive. Here on the axial images, left etymodal sinusitis with ill-defined medial wall of the left orbit and hypoenzymes foci are also seen involving the flow of orbit with this discontinuity. Case two, a 40 years old female presented with right orbital pain and swelling for five days. Patient had passed history of severe COVID pneumonia for which she was hospitalized three weeks ago. She was treated with remdesivir, oxygen support and intravenous methylprednisolone. On axial and coronal images, polypoidal mucosal thickness is seen involving the bilateral maxillary, etymoid, spinoid and the frontal sinuses with smooth expansion of the sinuses. On coronal image, the extra coronal muscles and the retroorbital it shows T1 hyperintense and T2 hyperintense areas within the purposes of the right glom. Case three, a 51 years old male presented with right sided weakness for seven days. RT-PCR from the nasopharyngeal swab was positive. Here, the polypoidal mucosal thickness is seen involving the left maxillary, etymoid and the frontal sinuses with T2 hypointense areas within. On coronal section, the few areas of cortical bridge are also seen involving the left riviform plate with suspicious intranational extension of the legion. Areas of ultrasonic signal intensities appearing as hypointense and T1 and hyperintense and T2 involving the anterior inferior and the basic frontal region and crossing the midline. Histopathology evaluation of the nasal discharge reveals broad aseptic like fungi hyphae on QH weight more. Case four, a 45 years male presented with respiratory distress and pain in abdomen since one week. RT-PCR from the nasopharyngeal swab was positive. On axial images, there is circumferential wall thickening of the terminal ilium, illusical junction and the wheat mite adjacent phytostanding. Here on the coronal images, there is circumferential wall thickening of the terminal ilium, illusical junction with mild adjacent phytostanding. Discussion. Mucomycosis is an opportunistic fungal infection which causes angioinvasive disease leading aggressive lacrosis and infarction of the involved tissue. Rhinoorbital mucontagusis involves the parancel sinuses and orbit orbits and may extend into the cerebral paranthema. Underlying feed supposing factors that includes the uncontrolled diabetes malignness, immunocompromis status, systemic use of corticase steroids, pre-existing respiratory pathology, cancers and steam cell transplant. Among these, diabetes is one of the most common etiology. Results. In a recent systemic review conducted until 2020, almost 2021, out of 27 cases, 21 had involvement of the parancel sinuses and 4 had extension of infection into the orbital compartment, one with the intracranial extension and one with the extension into the gastrointestinal tract. The findings of 27 suspected mucomycosis cases in people with COVID-19, diabetes malignness was reported in 70.3 cases while 88.8 were receiving the corticosteroids. These findings are consistent with the case series of 27 suspected mucomycosis in COVID-19. The 69% had the diabetes malignness and more than two-third deceives the corticosteroids. Collectively, these findings are familiar at the familiar connection of mucomycosis and the corticosteroids induced in patients with COVID-19. Conclusion. Imagining findings of the mucomycosis includes the mucosal thickening or the obfuscification of the involved parancel sinuses. Majority of the lesions that appear hypotensin T1 and variable to hyperintensin T2 images. Low signal intensity of the fungal elements on T2 vented images along with restricted diffusion on the DWI may be seen. Hypertrophy of the nasal terminus with the nasal secretion is seen with the nasal involvement. Discontrast enhancement can be seen in the thickened mucosa and involved tissue. However, the areas of non-enhancing soft tissue may be seen within the affected corbinates or the paranasal sinuses and it's also known as the black-corbinate sign. Designs helps in the early detection of the nasal mucomycosis. Thank you.