Now, let us discuss the second methodology which is MIP, mercury intrusion porosimetry. So, why you need to conduct MIP, what is the requirement? So, basic understanding is all the geomaterials which are composed of wide range of particles, their sizes, shapes and the pores or the material is porous in media. So, this way of the knowledge of pore structure of these materials is important as it can give insight into both microstructure and the performance. See, there was a time when people used to talk about particle size distribution. Now, particle size distribution is very well understood and its limitations are also very well known. So, present-day geomechanics you know entails MIP analysis to understand what type of pores are present in the soil mass and what is their distribution in terms of diameter, radius and so on and frequency. So, rather than measuring the porosity it becomes more informative if the manner in which volume is distributed with respect to the pore size. So, lot of people you will find are working in this area where they are trying to develop equivalent seepage models for soil mass, where there is a very serious you know doubt or question being raised whether your Heisen-Polsley equation is correct, whether Darcy's law is correct you know. So, these type of studies people are trying to do because these equations do not consider the overall porosity of the system. And in the subsequent slides I will try to show you that when we talk about the porosity I think we are only taking into account hardly 20 to 40 percent of the porosity of the system which you call as the bulk porosity it is not the total porosity. Now for that matter if you look grain of the soil and the pores how they are you know associated with each other. So, there could be some pores which are closed, there could be some pores which are dead ends. So, it is just like driving a vehicle in a lane which ultimately ends up in a dead end. So, you think of water molecules entering the system, but then there have no way out to come out of the system. So, in what way the overall hydraulic conductivity is going to get affected if you have not included dead ends which are present in the pores of the soil mass. Similarly, for that matter you can see some of the pores are interconnected. So, the moment water comes over here gets distributed in two parts and both of them end up in dead ends. So, those who are working into the micro mechanics of the system they require these type of analysis much more and this is where the energy concepts are becoming very important in geomechanics because using the energy concepts particularly the law of thermodynamics you can analyze what is happening inside the porous material. Now most of the time we talk about the pores which are through and through like these are the pores you know these are the passing pores. So, any water which enters into this simply comes out of the system and we call it as a short circuiting effect. That means, the water has tendency to short circuit the sample itself it is not entering to the sample it is passing through the pore through and through without taking into account the complete porosity of the material. So, this is where most of the time people have given a thought that how total porosity of the system can be measured and that is where mercury intrusion porosimetry becomes quite important. In western countries they do not use it because of the reason that it deals with mercury and they are too much scared of you know mercury as a poisonous and toxic material, but anyway we continue over study using these things. So, whatever porosities you have till now talked about look at this grain there is another grain like this of the sand or the clay or whatever there is a agglomeration of the grains, suspension and there is another grain like this. So, if you want to understand what is meant by porosity the first type of the solid is known as a non porous solid it will not have any tendency towards fluid no attraction clear nothing can pass through this. So, this is extremely low surface area most of the sands will show you this type of a porosity this is where we talk about their surface porosity. How about this system these are the porous solids they have high surface high pore volume and high dimensions because of all these protrusions and the interest which are present in the system. Now, this is a particulate structure where you have particle size and the surface area which are quite high and this is a very interesting type of a porous material which is sometimes also named as catalyst. So, on the particle you will see that lot of ions cations or the foreign bodies have a tendency to get bugged. Now, this process we will discuss later on under sorption desorption capacity of the material. So, basically these are the activated sites on porous systems which are normally present in powders or very fine-grained materials. So, we talk about the porosity the whole idea is to distinguish between this to this to this to this type of grain which are present in the soil mass. These are the shapes of the poles which are present in the soils they are cylindrical in nature they are the slits. So, a material will pass through like this it will come over here again pass through like this and so on. This is slate structure conical pores spherical or ink bottle type of pores you have. So, enough permission can take place through this ultimately there is a dead end in this form and everything gets accumulated over here and sometimes you have interstitial interlinking of different types of pores. So, these are the basic models which people have come up with when they talk about the porosity of the system. Now, how would you identify a pore is a million dollar question. So, that again is a very intricate thing. How would you differentiate between these type of pores? Versus of MIP and its results are required to be from that basically we can understand which are the of course. Yeah one of the examples I will show you how to differentiate between the two types of pores at least. Any question doubts? That is what I said these are the assumptions these are the people have assumed that these type of pores will exist and they have done mathematical modeling and they try to collaborate the results from the experimental results and then they show whether this type of system has cylindrical pores or slit type of pores or ink bottle type of pores or interstitial diseases and so on. Lot of research is going on in this area and not believe this, but this is the micro analysis of the soil samples and for understanding the interaction which we have been talking about you have to understand these type of phenomena and the mechanisms. Then only you can talk about how the contaminants are getting you know interacted with the soil mass. So, when you start talking about interaction then you have to go into the micro mechanism. So, roughly if you characterize or if you classify the pore sizes and the parameters which you can obtain from this type of analysis there are three types of pores micro pores, meso pores and micro pores. I think now you can understand in which zone you normally talk about when you do classical geomechanics. These are all in nanometers range. So, when you talk about micro pores they are less than 2 nanometers. Most of the zeolites, carbon, silica fumes they will have this type of pores. Meso pores they are from 2 to 50 nanometers, alumina, polymers, catalysts they will exhibit this type of pores. And micro pores are the pores which normally you talk about when you do your porosity test to obtain the porosity and that is where I say you only you know talk about one third or one fourth of the porosity of the total system ignoring the micro porosity and meso porosity for which you require either helium gas or mercury. So, that under pressure these fluids will enter and they will reach up to these pores water molecule cannot reach up to this pores. So, that is the difference why you require some non-wetting fluids like mercury and helium gas to do pore structure analysis. Now these are the parameters which normally one will look for from the analysis bulk property apparent and real density, percentage porosity, pore volume pore size distribution that is the pore volume versus pore size. So, rather than particle size pore size is more important this is what I am trying to emphasize over here is the pore volume versus pore size not the particle size. The total pore volume in total volume divided by per unit weight of the material average pore size a specific surface area of the material and particle size distribution that is relative percentage versus particle size. So, this information you should be getting from a typical mercury intrusion porochymetry. Anything else Sneha which you can think of getting from this test or this is a complete system. In your hydraulic conductivity models what are the parameters you have used to define k hydraulic conductivity normally you say k is proportional to e upon 1 plus e or e square upon 1 plus e or e cube by 1 plus e, but there are lot of coefficients which get multiplied to this. What are those coefficients shape factor tortuosity factor sorry diameter that is for coarse grain materials yes. So, shape factor tortuosity these are the two important things. So, we have been always assuming or ignoring these factors we never talk about shape factor and tortuosity, but slowly and slowly when you go to the modeling of contaminant transport you will notice that the tortuosity factor becomes much more important. So, you can still use these techniques to obtain shape factor c parameter and tau parameter this is the tortuosity. I hope you understand what is meant by tortuosity factor that is effective length divided by physical length of the sample square of that. So, that is why tortuosity factor could be much much higher than 1 and hence your hydraulic conductivity gets affected because of tortuosity of the particles. So, there is a lot of scope of doing research in this area. Then comes the characterization schemes and here I am going to just introduce a bit of gas adsorption because later half of the lecture is going to be associated with the gas adsorption techniques for finding out surface area and so on.  You require gas adsorption also sometimes because of finding out let us say surface properties. So, if you are interested in finding out low high specific surface area then gas adsorption is a good technique. Micro mesopore distribution that means, further differentiation between the pores which are present in the system, micro mesopores which are in the total volume and of course, helium gas spectrometry which will give you the real density of the system. This is part clear. So, we have discussed about MIP quite in detail. Helium gas technometry instrument you must have seen in the lab where you can pass helium gas and you can get the real density. About gas adsorption I will show you what is the application and how these techniques are used for characterization of the geomaterials. A bit of the MIP details. So, mercury intrusion porosimetry is regarded as the standard method for macro and mesopore distribution analysis and since this technique is conceptually much simpler it is experimentally much faster and this is unique because of its ability to evaluate a much wider range of pore sizes than the alternate methods like gas option, calorimetry, scanning electron microscope and thermoporometry. How much heat gets diffused in the soil mass from one place to another place? This is what is known as thermoporometry and this technique is used not only to determine the distribution of pores in various materials of the soils, but is also to find out the changes which a system undergoes during loading conditions. One example is that compaction process. So, from dry to wet of optimum when you compact the soil how your pore structure is changing can be captured by this technique. This is the basic concept of porosimetry. A typical wetting fluid will show you this type of meniscus and the angle or the tangent between the surface and the meniscus will be theta value which is going to be lesser than a non-wetting fluid. So, in case of non-wetting fluid because of the surface tension this is how the fluid will sit each drop of the fluid. Now, using this concept I can pass it through a pore of size d by applying certain pressure without breaking the drop clear. So, if you think that this is a tube which is nothing, but your capillary tube you have done this analysis that if this is a surface tension force. So, T times multiplied by cos theta into the area of cross section is the uplift force. T sin theta component gets nullified and this force is lifting the fluid in the capillary that is the volume multiplied by density. So, from there you can get the equation which governs the law of mercury porofimetry is known as Washburn equation I will show you slightly later. So, the characteristics which you use are mercury is a non-wetting fluid for many solids and it is forced to penetrate into the pores and penetration pressure is related to the pore size. So, this is the pore size the amount of pressure which you are applying from outside they are correlated with each other that means, a certain pressure will take care of a certain pore size. So, I will show you a typical MIT result which will be self-explanatory and to show you how this type of analysis can be done and you can achieve some conclusive results. Another interesting thing is that the volume of mercury which is going into the pore is directly related to the pore volume. So, here we are showing a pore in this way this pore could be cylindrical ink bottle type slit type or anything as per the previous models. Now, this is what happens when you are trying to intrude mercury into a pore because imagine as if you are parking a mercury droplet into a pore by applying some external pressure and the condition is that this mercury drop should not break clear due to the external pressure. So, it is a basically synergy between the between the pore and the fluid which is trying to enter into it. So, the more pressure you apply here what will happen either the pores will change or the droplet will change. So, this type of contradictions will come sometimes when you do this type of analysis. So, I would like to show you one trigger. Now, this is the basic model which is used to understand a wetting and a non wetting fluid. If you have a system of particles where the pores are you know concealed by a layer of the liquid what happens mercury will not be able to enter into this. However, there could be a system where if you apply more pressure what will happen this mercury has to enter into this. So, this is the basic concept of choosing a pressure and how this pressure is going to result in intrusion of mercury into the pores of the system. So, basically this becomes a interesting phenomena what pressure should be applied for a given pore. So, that these pores of a certain diameter get built up. So, this equation you can derive easily by the mass balance that is a subsistension T cos theta r is the radius of the pore or the capillary and P happens to the pressure. So, this is how you have computed suction pressure also in the soil mass by using the same equation and theta is the contact angle. Now, this is what is known as Washburn equation. So, T is known for mercury and theta is known for a soil mercury system 130 to 140 degree and T is 0.48 dimes per centimeter I suppose. What it leads to is a typical mercury intrusion porosimetry characteristic curve. So, if you look at this curve what you will notice is on the y axis is volume of mercury which is getting entered into the system or coming out of the system with respect to pressure on the x axis. So, how would you read this graph is if you increase the pressure what will happen the mercury it has a tendency to go into the pore. So, this becomes an intrusion curve. So, the black one is intrusion curve as you increase the pressure applied the more and more volume of mercury goes into the pore of the soil mass. So, this way you can complete all the pores by applying a very high pressure. Now, what is going to happen when mercury is entering into the pores of the soil mass can you speculate something it may it may break the pores itself. So, there could be a collapse of pores. So, now, this is what you are going to see here it is just like your consolidation graph you know where this is known as intrusion curve the mercury goes into the pore and if I retreat back the mercury by applying suction. So, what is the graph which I get this is what is known as extrusion graph that means, if I can extrude the mercury which has entered into the system by decreasing the pressure or by applying some vacuum this is where you end up. So, some volume of the mercury remains in the soil mass this could be because of the destruction of the pores and this phenomena is normally known as hysteresis. Now, hysteresis is becoming a very big question mark in geomechanics everywhere we talk about hysteresis. If you remember in your electromagnetic courses there you talk about hysteresis and based on hysteresis you have classified the material you agree or no a material which stores more of the magnetism has more hysteresis. Now, this concept can be utilized in geomechanics also in characterizing the materials and differentiating between two types of materials and the type of pore structure which is existing in the system is this part ok. So, this is what Sneha is trying to study and she will be presenting a seminar on wetting and drying curve where she will be talking about hysteresis associated with wetting and drying. Now, that again is a capillary action that is what you are trying to study. That is what Seema is trying to answer in her thesis and she talks about soil water characteristic curves during wetting and drying. So, why they are different or why they are similar? So, these are three examples of hysteresis which normally we talk about. Now, NC2-OC response in classical geomechanics is also nothing, but hysteresis. So, how do you define hysteresis? There is nothing, but the amount of energy which gets stored into the system. Here what is happening? The amount of mercury which is getting stored into the pores. So, there must be some force which is capturing all the mercury into the pores or this mercury cannot come out because of several reasons. One of the reasons could be collapse of capillaries. So, Sneha this is the challenge. Later on maybe when I talk about hysteresis in drying and shrinking phenomena, there you can notice that your proctor compaction curve in wetting cycle will be different than the proctor compaction curve which you obtain in the drying cycle. So, these are the you know effects of environment which are causing drying and wetting of the material when moisture goes into it or comes out of it. So, these type of tests which we are discussing like MIP are nothing, but a good simulation of a natural phenomena in terms of quantification of its pore structure and the alteration in the pore structure because of some process. Is this part clear? If pores were perfectly elastic, what would have happened? Come out exactly.  That is right. So, no loss of mercury, no loss of pores and so on. That is what I said. The way you characterize your ferromagnetic material, nonferrous materials, nonferromagnetic materials, what is the differentiation? It is just based on the amount of magnetic energy which they store. Exactly that is what we are doing. That is what we are trying to do and that was the reason of telling you that the consolidation theory should be revisited by using energy concepts. Just by applying mechanical loads, you cannot find out the volumetric deformation to a precise limit. You are ignoring lot of mechanisms which are going on in the sample and you are just measuring something which is not very accurate. I think now you can correlate it better. So, similarly somebody may ask you to develop a model based on energy model for stress strain relationship of materials. Why you get peaks in OC material? Why you do not get peak in NC material? Why do you get a peak in heavily compacted sands and you do not get any peak at the time of shearing in loose sands? So, everywhere you are finding this is the packing of the grains which is getting affected by the particle arrangement. So, lot of things are going on inside the particle which we are not capturing to the many test details. And that is where this type of thinking and philosophies you know is going to be quite helpful in answering the mechanisms which are very close to the nature. Good. So, since that today they have followed things. Is this okay? Any other suggestion? No doubt. One more additional this thing means about the cisterosis. Another reason could be you know this entrapped mercury it is because of the pore shapes which sir has already shown. For example that ink bottle type. So, while including it will get entered but while extruding it is not possible to come out all that mercury because it got entrapped into that bottle shape. So, that could be another reason means even if the pore structure is intact but because of the pore shapes it is possible that mercury will get entrapped and it is not possible to come out. Or in another word it means what you can say it is soil contaminant interaction how it going to affect the pore structure. Correct. That we can understand from this. The degradation of the pore porous media because of interaction it becomes a reverse problem. You got it it is a very good thought which you are giving that is right. So, you can see the after effect and then you can back trace the effect. This is also known as back analysis. So, degradation of the material, materials response to external disturbances you can study easily. I have included one slide what he was talking about and I hope it should be clear when I show you that slide. So, what is the information which you get from this type of a relationship. So, basically what you are doing here is you are developing a incidentally the way you look at it is nothing but your consolidation curve is it not your pressure sigma prime versus void ratio e versus sigma prime curve. So, e is nothing but there you talk about the compression of the grains sorry compression of the pore structure void ratio void ratio keep on changing. So, the same graph what information you will get from is this the pore size distribution surface area equivalent pore size critical pore diameter distribution of total porosity and free porosity under trap porosity. This trap porosity which it was discussing. Now, this is a typical intrusion curve which we got for one of the samples which we had analyzed. So, where you have pore diameter versus applied volume normalized volume. So, the more the pore diameter what happens more and more volume of mercury is going to get intrusion system. Now, could you answer this question that you find here one bench what is the reason for this bench formation. That means, the normalized volume does not increase with the pore diameter clear mercury is a non compressible fluid. So, there will not be any time lag it shows the porous structure property that the pore diameter of this range are quite prominent. So, it is just like please free flow of fluid into the system. So, with a with no even increment in the pressure the entire mercury goes and sits into the pore spaces, but then I just just wait a minute please and then if you want to further overcome the resistance offered by the force you have to apply more pressure. So, truly speaking as the pressure increases you know the normalized volume keeps on increasing which is being mapped over the pore diameter. So, this is a good way to see what type of distribution of the pores you have in the material and how easily the pores are getting filled up with the mercury because of certain pressure. So, this type of diagnosis you may do by looking at this type of graph yeah what you are saying because of the type of the pores that means, from pore sizes of let us say 2 to 0.2 the most of the resistance is not coming in the picture. So, these are the pores which are good enough for mercury to flow just like this very easily you do not require any external pressure. So, if in other words there is a predominance of the pores of this size in the sample this is the resistance offered by the system and this is the resistance offered by the system. So, you can very easily make out that this is the range in which the pores are present in the soil mass or a porous system. So, this is how you can diagnose what type of pores and their frequency and their magnitude and their diameters are present in this system. Present day MIPs have softwares which are included in them. So, they analyze everything for you based on the curves which normally you get by doing an experiment. Those of you who are interested in learning MIP they can contact switch it and whenever he is doing his experiment next time you can come and sit with him it takes time. So, you please fix up with him and you can demonstrate to them how it works. Now, this is another interesting relationship which you will get out of this exercise mean pore diameter as a function of void ratio alright. So, as the void ratio increases the mean pore diameter also increases that is understood. So, but this void ratio is the total void ratio which we are talking about which includes all sorts of pores micro meso macro which otherwise you would not be able to obtain. That means, the material and the grain porosity also you are considering into the analysis. Now, this answers your second part of the question when you are talking that how these studies can be employed for soil contaminant interaction. You will notice in the subsequent lectures when sorption desorption takes place there is a lot of parking of the cations which is taking place on the grains of the clays. So, unless you know exactly how much is the surface area which is exposed to the environment or the contaminant you will not be able to estimate how much interaction is going to occur. Now, this is what actually such it was trying to explain. You may have a system where the mercury gets entrapped inside and there are both the ends which are choked. So, less orifice on both the end, but more cross-section which is available for mercury to get filled up. Now, other way of understanding this would be there is no difference between this type of pore and this type of pore. So, truly this is a limitation of MIP. You cannot really map the pore structure because this is equivalent to this. All the mercury which is entrapped in this portion can be you know drawn an equivalent with this type of a analogy. So, two systems which will present almost the same response, but it is very difficult to differentiate between two type of pores. You have to think of something new for differentiating between these two type of pores. For civil engineers this may not be very important at this moment, but those who are working in synthetic polymers, synthetic zeolites catalyst for them these studies are very very important particularly those who are may I came across a sponge iron sample where people wanted to do MIP. I hope you can appreciate why MIP should be done on a sponge iron. How much amount of energy is required to melt it? For that pore structure is required to be studied and lot of raisins, polymers, catalysts which are being fabricated by the industries require these type of studies and they contact us for doing this test for them. Some more interpretation on the results which you get from mercury intrusion porosimetry with this is the complete tomography of the sample. You cannot come across things better than this. This work was done by my another PhD scholar Dr. Vibhuti Das and we studied here the concrete specimens. Like in your particular distribution curve you use lot of terms as C C, C U, D 15, D 85, D 30, D 60, is it not what for, for what purpose. So, that you can characterize the material better. Where do you use C C and C U term in classification of the soil coarse grain materials? For fine-grained materials you have another classification scheme, liquid limit, plastic limit, plastic D index, Atterberg limits and so on and then drawing the A line. So, the question is that after doing MIP how I am going to differentiate the materials? How I am going to use the parameters to differentiate between one material and one material? So, if you look at the first relationship which is the volume of mercury which is intruded in the sample as a function of the pore diameter alright. So, as the pore diameter increases what you will notice is that the volume of mercury dropped down. Now, if you do a bit of construction now this type of construction you have done to find out the creep and T 90 if you remember 90 percent consolidation in the soil. So, the mechanism remains same. So, this is the pore diameter versus volume of mercury graph will give you a parameter which is known as DT. So, DT is nothing, but this pore size you know there will be a sudden increase in number and the cumulative volume of the pore. So, this parameter becomes very important characterizing the geomaterials. If you plot percentage volume intruded of the mercury versus pore diameter there is something known as mean pore diameter Dm which corresponds to 50 percent of the pore volume. So, if you consider 50 percent of pore volume if you obtain Dm this becomes another parameter which can be used for characterizing the geomaterials. And the last parameter is DC this is known as continuous pore diameter. This is what I was talking about in the previous slide that therefore, which are continuously staggered or continuously present in the system. So, this is the term which is known as DVH that is increase in volume of the mercury divided by differential changes in the log of the pore diameter. So, if you plot this index with respect to pore diameter wherever you get a maxima. Now, this maxima corresponds to DC. So, this is the continuous pore diameter the maxima of the curve which corresponds to the group of the largest fraction of the interconnected pores. So, this gives to the answer to the point which you are raising that when the pores are interconnected you do not require much pressure to push them from one pore to another pore to another pore conductivity is very simple. So, based on DT, Dm and DC they are your equivalent terms to D50, D30, D60 and D85 and D15 and then you can try to see what is happening to the material. I thought of showing you this relationship which you will appreciate which shows that how curing of the concrete can be checked you know by using these three parameters. What you want concrete to become after 28 days much more durable that means, the pore sizes should be as small as possible. So, if you plot DT, Dm and DC with respect to days of curing what you will notice is as days increase there is a decrease in pore diameter and that is what you wanted clear. So, it is a very simple application of MIT in checking the pore media characteristics clear. So, this is how you can go for synthetic concrete as well by using different type of pozzolonic materials and making a good grade of concrete. In the next class I will discuss the specific surface area determination.


Ever wonder where your suppliers are getting their products from? How much they're paying and what you can do as a dropshipper to skip all of the middlemen and buy from the cheapest and best suppliers from the top of the line? Those suppliers are called wholesale dropshipping suppliers and that is exactly what you're going to learn in this video. So quick intro and let's go. What's up everybody, hope you all enjoyed your day today and hopefully now you're going to enjoy it even more. My name is Lee Wan from AutoDS, I'm the content manager and I've also been dropshipping for the last several years and in this video I want to talk to you guys about wholesale dropshipping suppliers, these are the guys who are buying your products or the products that you're selling on your store, they're buying them straight from the manufacturer and they are paying the cheapest price for these products. Wholesale suppliers usually sell in huge quantities and us as dropshippers we usually do not buy huge quantities and we do not hold any inventory at all, we usually buy just one quantity or sometimes two when a customer buys more than one and we ship it directly from the supplier to the end customer. So if the wholesale supplier does not want to ship out one product or two products at a time, how can we work with them, skip the suppliers in the middle and make more profits on ourselves, that's exactly what we are going to go over. So how exactly does this work? First we know that we have the manufacturer, this is the one who actually creates the product from the start to the finish. Then we have the wholesale suppliers who buy from the manufacturer and again they buy in large quantities. Everything that the manufacturer creates is sold to the wholesale supplier or distributor. Then the wholesale supplier sells to retail stores also in stock, not in huge large stocks like the wholesale supplier buys from a manufacturer but still retail stores need to hold stock. That's why we usually when you go shopping for pretty much anything there's usually more than one product in stock because they are buying stocks from their manufacturers. And from the retail store you have the end customer who goes to the retail store and buys the product or when your buyers are buying from your store they are the end customer. So that's how it works. You got the manufacturer, the distributors, the retail stores and the end customers. Now many of the suppliers that we are working with while we are dropshipping are actually retail online marketplaces like Amazon, Aliexpress and so forth. And those online marketplaces are actually buying from the wholesale distributors who are buying from the manufacturers. So now that you have a good idea of how the hierarchy works and what an item goes through from the point where it gets manufactured all the way until it finishes the whole chain of getting down to the end customer what can we do as dropshippers to work with wholesale suppliers who simply put do not want to work with quantities of one and two. We're going to get to that in just one minute but before that I want to talk about eBay's dropshipping policy and how that works with wholesale distributors or wholesale suppliers. So here is eBay's dropshipping policy and I took a little snippet from their policy page. Dropshipping also known as product sourcing is when you buy stock from a supplier and work with them to send items directly to your buyers without ever handling them yourself. All of this we already know as dropshippers. Dropshipping where you fulfill orders directly from a wholesale supplier is allowed on eBay. Remember that if you use dropshipping you're still responsible for the safe delivery of the item within the time frame stated in your listing for the buyer's overall satisfaction with their purchase. That has to do with eBay business policies we have more than enough content on that and that is stuff that we already know. But here what I want to show you is that eBay fully supports working with wholesale dropshipping suppliers. So this is a very important thing to note. A lot of people are getting suspended on their eBay accounts when they first created they make a couple of mistakes and then they have to start proving a whole bunch of stuff to eBay. One of those things is that you are actually working with wholesale suppliers as dropshippers because we know that they support it. Keep this in mind know that eBay definitely supports working with wholesale dropshipping suppliers. As you know AutoDS has over 25 supported suppliers that you can work with all fully functional when it comes to price stock monitoring and more. And we also have order fulfillment services. But when it comes to wholesale suppliers we have two suppliers that you can work with today. And of course we're always working on adding more. But if you're asking yourself the question who are these wholesale dropshipping suppliers and how can I start working with them. Let's go over those two suppliers that we support today. Starting with one of my personal favorites which is CJ dropshipping. Now recently we released a video and a full blog article explaining how to work with CJ dropshipping every step of the way why you want to work with the supplier besides one of the biggest reasons on them being a wholesale distributor which eBay does support. So CJ dropshipping has free US inventory which means you can ship out your products from the US to the US and get really fast shipping times. They also have a print on demand service so you can actually offer something that other dropshippers have no idea how to do it. And a lot of customers are buying print on demand products so you can customize t-shirts, clothes, necklaces and many other things. Now there's so many advantages when it comes to CJ dropshipping. I'm not going to go through all of them now but that is a wholesale distributor where you can even buy stock. Once you have a product that is selling well you can ask CJ dropshipping to give you a quote to source these products for you. If the product is only being sold in China and it's selling well for you simply ask them for a quote. They will tell you how much it's gonna cost to get 50, 100, 200, 300 units to their US warehouse and then you'll be the only person selling it from the US to the US with fast shipping times. You don't need me to tell you what's gonna happen to yourselves and profit once that happens. So that's another nice thing that you can get working with CJ dropshipping and on top of everything again it is a wholesale dropshipping supplier which as I've showed you eBay does support and you will not have any problems working with the supplier and of course integrating it with AutoDS for price and stock monitoring and more. So CJ dropshipping is the first wholesale dropshipping supplier that I want you guys to know that you should work with as a wholesale distributor. I will leave a link to our CJ dropshipping article and video right below this video so go ahead and get started, watch that, implement it and good luck with CJ dropshipping. The second supplier that is a wholesale dropshipping supplier that you can work with today that also is supported by AutoDS is China Brands. Now China Brands similar to CJ dropshipping also has warehouses in the US so you can chip out your products really quickly to your US audience. Not only that but we have a partnership with China Brands so this partnership is actually going to give you a dropshipping agreement which is something that eBay may ask for from time to time or any other selling platform that you're selling on. Sometimes you may get a request for some agreement that you have with your suppliers so that the selling platform that you're selling on can see that you really do have agreements with your suppliers and you're not just adding products from any random suppliers and doing work that they don't want you to do. So on top of being a wholesale distributor which eBay supports having thousands of trendy items that are good for the dropshipping business model because they completely support dropshipping and that is what their platform is for. China Brands will also be more than happy to supply you with the dropshipping agreement between you and them. As you see here in front of me there's an official partnership with AutoDS and China Brands and that is what's going to give you this certification letter showing that you have an official agreement between you and China Brands as a dropshipping supplier. So those are the main reasons why you do want to work with China Brands and again I'm going to leave a full article on how to work with this supplier along with CJ dropshipping right below this video so you guys can go ahead and get started right after watching this video. Start working with those dropshipping wholesale suppliers and get your dropshipping business to the next level. Now I want to remind you guys they are wholesale suppliers that are selling in quantities of one and two. They want to help you with your dropshipping business. This is costing them some money because it's not really profitable for them to sell only one or two units but they do know that when they get a mass amount of orders per day from plenty of dropshippers then they can make this business model work and it is working. That sums up this video for the wholesale dropshipping suppliers what they are, who they are and which ones you can work with today on your dropshipping business. Again I'm going to leave the links for all of the videos and articles that you need to read in order to know how to work with these suppliers and work with them step by step and really build your dropshipping empire with the help of these wholesale dropshipping suppliers that will make your dropshipping life an easier one. Thank you for watching. Do not forget to subscribe to our YouTube videos if you are new. This is the kind of content that we're always giving out to you guys along with product finding videos, suppliers, marketplaces, case studies, interviews and so much more. Our goal is always to help you succeed in your e-commerce business because our success is mutual. So let me know if you have any questions, any comments regarding this video or any other topic regarding dropshipping and I will be more than happy to personally answer your remarks. Thank you for watching and see you in the future videos.


Hello and welcome to the Grand Line review, your source for everything one piece. Today we have a manga review of chapter 936, The Great Sumo Inferno Tournament. And so I think the thing we mostly all predicted has come to fruition with a deathmatch of sorts being put into action by Queen, which is finally giving us a taste of his more sadistic side with the color and everything. And the best part of all of this was any time that Luffy interacted with Queen, because Queen is just ridiculous enough to get caught up in Luffy's idiocy, and I really really enjoyed when Luffy called him balloon guy. In doing so, Luffy also set his own victory conditions for The Great Sumo Inferno, even if it isn't set up to be a contest that one can actually win. It's more about delaying death or simply giving up. So it seems that we're going to send in wave after wave of increasingly stronger opponents of video game style for Luffy to trash, which is quite convenient really, because I imagine that after a certain amount of time pretty much every relevant officer figure within the prison of mine will be rendered out of action, thus making the eventual chaotic escape significantly easier. Realistically speaking though, without the Seastone Cuffs it's got to come down to Queen entering the ring himself, because surely there's nobody else here who could handle Luffy. And from there we have a few possibilities. The most likely one in my mind is that their conflict gets interrupted by the Big Mama escape team, although given how goofy Queen is, I also wouldn't put it past Oda to craft a more comical ending to the tournament, where Queen is accidentally forced out of the ring somehow in a shocking turn of events. But the tournament does begin this week, and there is an absolutely beautifully drawn panel of Luffy activating Konkurasaki, which seems so simple, you know, it's a straight on shot of just half of his face, but Luffy's expression is just terrifyingly perfect. Like if you ever see someone smiling at you like that, then you know you're in for a bad time. I guess the other thing to flag here is that Kaomatsu has a connection to Yogoro, so he is very potentially an Exyakusa himself. Once again he remains completely enshrouded though, and I find it quite interesting that Oda is going to such great lengths to keep him hidden. It's really building the anticipation for one hell of a big reveal of this character, which can go one of two ways really. Either we're going to be introduced to some tragically maimed and malnourished individual with some heavy, heavy shock value, or we're going to be introduced to another completely absurd looking citizen of Wano, possibly the most absurd looking we've seen so far. And I know that a lot of people are hoping for Kaomatsu to look like an incredible badass, but at this stage I can definitely see the latter option occurring. Another unexpected highlight of the chapter for me though was any time Raizo was present at all. I feel like I've said this before, but this ninja has really grown on me. When he was first introduced during Zo' I was pretty disappointed, but his comic value just cannot be denied. I loved the part in the beginning where he was stealthily speaking with Kaomatsu, but as soon as the cart behind him moved away, his gigantic and not at all classically ninja form was put on full display and immediately spotted by the guards. He also had another great moment where he claimed that he'd put in a lot of work to get the key to Luffy's handcuffs as they were being taken off him. So yeah, at the moment he is far and away my favorite member of the Kinamon gang, and the saddest stuff about the potential of the Prisoner Mind stuff ending is that we won't be able to see any more of Raizo's madness in there. Alright, on to the next half or so of the chapter though, and we are back at the bath house. I spent some time last week arguing that what we saw was completely unnecessary, as well as the fact that I'd gladly eat my words if Oda made it relevant to the plot. So I'm going to concede this week that the bath house, for better or worse, was very relevant to the plot. I am still really conflicted though. On the one hand I do make a point to defend wacky moves by Oda, because that really is the core fabric of One Piece. On the other hand I don't think what happened here was, you know, quite wacky enough to justify so easily evading two members of the worst generation. Like sure, Drake can't handle naked women, that's fine. That doesn't damage his character any more than it damages Saesange's character. In fact I'm quite happy that we finally actually learnt something about the guy's personality. Hawkins is very much a different matter though. I'm still not entirely sure what happened here to be honest, because he was on the verge of capturing or wounding or whatever in Nami, and then as soon as her towel slipped off he just disappeared. He doesn't seem to have been knocked out with the happiness punch, and it's just really unclear what happened from that point onwards until he reappeared when Drake came in. Initially what I thought had happened was that Saesange got sent flying back into Hawkins while he was still invisible, but yeah I just, I don't know and I think the whole scene in general is just a bit clunkily put together. Another example is that we immediately cut from Saesange on the ground in a bad situation to him skywalking with Nami, Robin, and Shinobu.  And yeah I'm sure that's something that the anime will expand on, but it felt a bit weird in the chapter. And I can't help but feel like these little oddities are all for the sake of a bathhouse scene, which you know, delivered on its promises I guess with a very, very naked Nami. But whether or not that was worth it, I'm not so sure. I did enjoy that both Drake and Hawkins were able to recognize stealth black though. They probably won't be able to put together that it's Saesange because they seem to have been fairly isolated as of late and they probably aren't aware of the whole Vinsmu connection. But it would be interesting if they say reported to Kaido that the German were present on Wano and then they got embroiled in everything just by association. You know, if they're I guess even still alive after Holkek Island that is. And the final piece of this chapter moves us to the mysterious wanderings of Zoro, which I quite like because when you think about it, the chapter mainly focuses on three characters, Luffy, Saesange, and Zoro. So it felt like a nice catch up with the Monster Trio. But in regards to the Zoro section there was a great panel on the last page where Zoro has his evil smile on.  But as suspected the Shusui has been taken. So for now Zoro is a neat audio user. Although I don't think that's going to last particularly long given that we have Mr. Weapons Collector over here. Although the interesting thing is that Zoro doesn't seem overly concerned with losing Shusui, which you know he's held and mastered for two years. So it may very well be much easier than expected to get the Nidaki Tetsu into his hands as well, which I'd be incredibly hyped for. Zoro testing out and getting to know new blades is always fun. Plus I should mention that Zoro's entire environment at the moment is just stunning. There is nothing more picturesque than a battle between swordsmen on a bridge in the snow. As a result I do hope that we see more of the fight, but this does seem set up so that we can just cut to the results of the conflict at a later chapter.  But all in all this was a fairly solid chapter. Things are moving on Wano. In fact I didn't even mention the whole heart pirates being captured and that lore is about to be activated in a big way and there's also the idea that was suggested by Shinobu that their plan was leaked implying that there may be a traitor amongst the alliance which is incredibly intriguing so there is a lot going on here and I love it. Overall it was really enjoyable. Overall it was really enjoyable and I think it was very wise to put the bath house stuff in the middle of the chapter because it had a strong beginning and a strong ending with some clunky stuff in the middle which structurally leaves me with a very good impression of it. But that pretty much does it for chapter 936. If you enjoyed this video and the content this channel produces in general then please do consider donating to the Grand Line Review Patreon because the support of all of your amazing people is what continues to make this channel possible. Also do check out my Teespring store if you're interested in shirts, hoodies and other miscellaneous items but the proceeds going directly to support the channel as well. And if you'd like to join the fun at any time then please do head over to my Discord server where a wide array of shenanigan retakes place on a daily basis. And finally please do comment with your thoughts on the chapter. This has been the Grand Line Review and I'll see you next time.


Rechargeable batteries are everywhere. They're in our homes, in our cars, and even in our pockets. Even as battery technology has matured, however, the physical and chemical processes that unfold inside of a battery as it delivers power have remained largely hidden from view. But thanks to advancements in electron microscopy and methods for handling materials on the nanoscale, scientists and engineers now have front-row seats to the action. Over the past decade, tremendous progress has been made to push the resolution of the Transmission Electron Microscope, or TEM, to smaller and smaller scales. As a result, scientists can now routinely image individual atoms in many materials. But it takes more than high resolution to catch a glimpse of what goes on inside of a battery while it is operating. One of the biggest problems is size. Even the smallest coin-shaped batteries found in cameras and toys are too big to view under an electron microscope, and even if they could fit, slicing them open would necessarily compromise their function. To address these problems, scientists and engineers have devised various ways of miniaturizing rechargeable batteries and making their key components visible under a TEM, all while preserving battery function. Collectively referred to as in C2 TEM, these techniques are helping researchers tackle some of the biggest questions in battery research. What causes rechargeable batteries to fail? How do the various electrochemical components of a battery interact? How can batteries be made better? The simplest design features a single nanowire as the working electrode, an ionic liquid or lithium oxide as the electrolyte, and a lithium-based metal oxide as the counter electrode. With such small active components, the open-cell configuration can be easily integrated into the small grids used to hold TEM samples and can be assembled relatively quickly. And in addition to supporting atomic-level imaging, this configuration allows scientists to study how lithium ions are shuttled into and out of the electrodes as a battery is charged and discharged. But while the structural response of the electrode materials adequately simulates what goes on in a real battery, this open-cell layout mainly serves as a simple model of the much more complex structure of rechargeable batteries. The design is therefore limited in many ways, one of the most important being the limited contact between the electrolyte and the electrodes. To address this shortcoming, scientists can assemble a closed-cell configuration in which both electrodes are bathed in a liquid electrolyte. A typical cell of this type features the electrodes and electrolyte encased in layers of silicon to create the sandwich-like structure commonly found in computer chips. A silicon nitride window at the center of the chip allows an electron beam to go through and capture lithium transport in action as the battery is charged and discharged. This type of cell has allowed scientists to better understand one fundamental battery process in particular, the formation of the solid electrolyte interface. This layer between the electrolyte and the electrode plays a major role in how lithium ions move into and out of an electrode and ultimately affect battery life and performance. Despite providing an unprecedented new look at the behavior of rechargeable batteries, the current state of in-situ TEM for battery research is still limited. As researchers look to improve these techniques, they must account for the effects of the electron beam on the electrolyte, the less-than-optimal image resolution that can be achieved through liquid electrolytes, and, most importantly, the limited number of times cells can be charged and discharged under a microscope.


This is the story of how Sai discovered his friend had narcissistic behavior and the surprising lesson he learned about self-love. Sai has just changed high schools because of his mom's new job, and Sai was the first to be nice to him. He remembers it like yesterday. He was used to his small town and tiny school back home, but this school was terrifyingly different, with 500 kids per grade. But Sai was the one who looked him right in the eye, smiled, and invited him to sit with her when nobody else had. She has it all together. Perfect grades, perfect clothes, the latest technology, and friends who idolize her.  They immediately become close, bonding over their shared love of anime, Harry Styles, and trying to stop self-sabotaging their happiness and practice self-love. They hang out every day. But things start to change for the worse a few weeks into their friendship, and Sai worries he has misjudged Sara. It all changed when Sai visits Sara at work. During calculus, Sara begs Sai to come to see her at the local coffee shop she worked at. She pleads that her shift is boring, that the people there are toxic, and that she needed him. Sai agrees and goes to visit her during her break that evening. He waves through the glass as he approaches the door, but Sara didn't wave back and looks away. When Sai sees her standing at the till, she looks up at him with annoyance and asks why he would come to her work. Sai is so caught off guard by her response that he doesn't know how to react. He holds back tears and apologizes before quickly walking away. As he walks off, he hears Sara giggling with her co-worker, whispering about how embarrassing and tragic Sai is and why he has nothing better to do than stalk her. The next day at school, Sai knows he has to face Sara in homeroom. Sara strolls in confidently and unbothered as always. She starts to talk to Sai as if nothing had happened as they prep for their English presentation. She confesses that she hasn't read the book and asks Sai to leave the book summary and Q&A. When she reassures him, they'll be fine because she's read the cliff notes. Sai agrees as he couldn't lose marks on this assignment and needs to keep his grades up for the class, plus he has already done all the work. The presentation goes off without a hitch. Their teacher, Mr. Jacobs, compliments them on their work, especially on the creativity and insight displayed on their poster board. Sara proudly thanks Mr. Jacobs, bragging that Sai didn't want to do a poster board, but she was happy to do it. Mr. Jacobs smiles and then talks about where they could have improved. Sara applies before Sai could speak and throw Sai under the bus, explaining that Sai didn't finish his part. The teacher then looks at Sai and tells him how he expected more from him. Sai runs home, avoiding the bus as he can't spend one more minute with Sara. As he gets home and opens his phone, an article from Twitter pops up. People who practice self-love acknowledge their flaws and are thankful for who they are. Narcissists display the opposite behavior. Narcissists believe that no one will bring them contentment, simply because they need constant recognition and admiration. Connected family services. Sai feels comforted after reading that and feels bad for Sara. Her insistent need to be admired by everyone, how she humiliated him and never apologized. As she took credit for his work, it all started to make sense. She wasn't practicing self-love, she was being selfish, and that was the difference. What would you have done if you were Sai? Let us know in the comments and until next time remember, don't ever believe that you only matter because someone else doesn't. Everyone matters, including you.


Oh Audiences on YouTube seem to have a fascination with comparisons $1 spoon vs $1,000 spoon $1 ice cream vs $1,000 ice cream $1 burp vs $1,000 burp I thought I would create a video about this fascination Focusing on illustration and art as the subject So here is what I did I created six different artwork concepts and also listed some illustration styles that I was interested in seeing I gave this information to a friend of mine along with a budget of $250 Australian dollars and told them to get all of these ideas made by different artists This would ensure that I haven't seen any of the images prior to recording this video Very important My friend then compiled these finished artworks into a PDF and we're going to scroll through them together for the first time ever today I really hoped my money went to good use and I hope these artists were nice to me and my character After I've reviewed them all I'm going to attempt to guess how much each of them cost I apologize in advance to the artist if I completely butcher that bit I'm sorry Later in the video I will reveal something top secret that I've created with one of these artworks so stay tuned to find out what it is I'm super excited for it Okay So these are the individual costs $6.66 The little devil $23.92 $33.25 $39.91 $45.49 $71.25 Making a grand total of 214 and 9 cents AUD Not too shabby on the budget Let's begin Okay so I have the file open now I've been told that there's going to be a blank screen between each of the artworks So Oh my god That's so cute I didn't know that they were going to add like the sketches and stuff in it as well I'm a really big fan of the colors All shades of green that I really like The little butterflies They're so cute I really do like the trees in the background I feel like it gives the artwork depth The way they've like adjusted my character with the hair and everything I'm a big fan of that The butterflies are so cute I really hope this is a reoccurring theme with all these artworks how these artists have adapted my character into their style It's going to be real disappointing if someone's just traced my character and not adapted it at all Let's hope that doesn't happen In terms of price If this would sit on the scale it could be anything honestly So I guess it's time to move on to the next one and see how it compares It's the lo-fi study style It's so good There's a lot of things in this picture that are actually in my room I mean, the jelly's not in my room But pretty much everything else is and I can't stress enough how accurate and amazing this is So with this background there's actually a lot of jelly just props and stuff in this so you could probably recognise the curtains the dreamcatcher the lava lamps the lemonade They're all things that in every single video And now the things that are actually in my actual room are the little dog His name is Davis He's a childhood favourite And no, it's not a real chicken leg I've got a pop plant and my Blue Yeti microphone And the headphones And see these little guys over here They're the wobbly boys A.K.A. you I'm a really big fan of this because it's a relaxed sort of chippy style And all the colours and everything together kind of just blends in and works So they've really nailed that lo-fi study vibe It kind of sums up my whole personality and all my interest even the chicken leg Coming up in a future video this chicken leg will have its green time Please wish him well in the comments The lo-fi design was so on brand I've made some slight adjustments to it and you can get it as merch Woohoo! On my store right now you can get this exact design on a t-shirt and hoodie It's available for a limited time so get yours fast while they're still here I really like this design on the more aesthetic colours but I made sure to include plain black and white too if you're not into that We're off to a really good start and again I have no idea where this would sit on the scale so let's continue with the video I see the text and it says chippy style That is so cute! Ok first I really like the jelly surrounding me because that's the colours of my intro and this goes to show that you don't need heaps of detail to make art look good because that is cute! As you can see they have adapted the character very well and they've changed a few things here and there but it's still very recognisable and it's still really cute! I don't know how many times I need to say that I also really love the shines in my hair and the little blushies on my face I have a feeling this one is probably on the lower end of the scale just because of how simple this is but we're saying that I would pay good money for this because cute! Scrolling, scrolling the next one I see is anime style I'm very excited! The detail in this I really really really love this one but I really love all of them so far so I can't say This one is really really cool This is exactly what I mean about having a character adapted to their art style Look at how many changes this artist has made with his own intuition and yet it's still really recognisable as my own character Look! I have ears! He's completely changed my outfit which I will explain in a second He's also detached the hoodie so everything kind of works together in his piece and it's kind of like a little beanie in this which is really cute He's also interpreted the fringe or bangs if you say really well in his style which is completely different to mine but it works just as well If not better! I also really like the pink and yellow highlights throughout the hair and clothes I think that's a really cool touch Also how the hair and eyes match the sky in the background that's just a MWAH! 10 out of 10! Okay so let me just explain the concept of this Quite a while ago I actually got some fanart from someone who made this on the screen right now It's a jellybender! So I took the concept and sent this fanart to my friend who sent it to this artist so he could interpret it himself So that's exactly what you're seeing here when it comes to the outfit and the floating bubbles This looks like it could be from a real anime So a big shout out goes to ForceDodo for the inspiration of this piece It's amazing! Scrolling, scrolling, scrolling, scrolling I see the text for pixel style Oh my god it's so cool Look at the little enclet!   So I wanted to see another artist reinvent the design This has been made really accurately despite only using pixels He's not only made the gradient look consistent but it also still looks like I'm in the jelly This also really gives me some old school video game vibes This is the final one and I'm scrolling and I see cartoon slash manga style That's so detailed I absolutely love this artist style I'm seeing my character looking directly at the viewer As you can see the hair looks pretty different The artist has done a really good job at translating this to their style Also I wish I could hold two plates of jellies Speaking of the jellies I really like how the colors are desaturated so they don't distract too much from the actual character It's also a really minor detail but I do like the color because it matches well with my skin tone and hair color Normally if I draw my character holding some jelly the plate is usually silver but I feel like this works out better The eyes Oh my god they are so pretty and they also match really well with the rest of the piece Look there's even purple in there Honestly I can't think of anything that needs any sort of improvement with this piece It is just amazing There's no other word Overall This was not how I expected things would turn out I thought maybe one or two artworks might be like outcasted from the rest I'm really happy with what I got for my budget and however it is split up it is definitely worth it and I Honestly I'm just speechless Speaking of budget let's try and guess which one belongs where So I've actually got a tier list maker right here and I'm going to guess which one belongs where This is going to be really hard so wish me luck and to the artist if you're watching this I am very sorry if I get your prices wrong Okay so the one that I feel like I have right is the chibi one and I feel like that's probably going to be the lowest tier the $6.66 just because it's a simple design so I'm just going to place that little boy there Also if I got a really good price with the pixel art I feel like that could be an option in this tier level as well so I'm going to put the pixel art in the $6.66 tier as well just because I'm a bit unsure of where where he's going so I'm just going to pop him there So I think it might be easier if I try and guess the most expensive one and my gut is telling me it's the jelly bender one so I'm just going to move that one up to the $71.25 tier so now it's these three bad boys left and I am stuck I want to put the holding jelly and the lo-fi jelly artworks in the $45.49 tier but I'm not sure which one will go lower so I'm just going to place both of those there and I'm probably going to put the children illustration in the middle okay now I'm very stuck so now I have to move one up and one down I'm going to move the pixel art to the $23.90 tier and with the other tier no idea even though the lo-fi one has a background in everything I feel like it's a very chill sort of art form so maybe they might it might be $39 I'm just going to slide it there but I am still very very very unsure and this is my final tier list now let's see if I'm correct all of the artists commissioned in this video did an amazing job and are going to be linked in the description below they were all kind enough to let me use their art publicly like this and they're all super talented so if you need any illustration or art related services give their gig listing a visit and I'm sure they'd be happy to help


Okay, so let's have a look at a very interesting topic and let's cosets. Cosets. The emphasis here is on sets, we can have a set. And there's a few things, this goes somewhere which is quite important but as per usual it takes a while to get there. So we're going to define a few things. Again we're going to have a group it is going to be a group and it contains a set of elements and some binary operation on that. And we're going to have a group H which is a subgroup of group G. I'm going to use that less than sign as subgroup. I'm saying that as a subgroup. I'm also going to have a relation and we're going to have, we're going to use this tilde squiggly line and they are left and right cosets by the way. So we're going to just concentrate on the left for now anything we do you can just do in the reverse and you can show the right as well but let's stick to this relation and the relation is going to be on elements A and B elements of G such that or if and only if A inverse binary operation B is an element in H. That is how I'm going to describe my relation. I'm going to take two elements of of G and I'm going to say that relation is only for if I take two elements there and I take the inverse of A binary operation B that that product is and I use product some group composition remember binary operation can be anything is an element of H and then furthermore I'm just going to state the following. I'm going to state that this is an equivalence relation and if it's an equivalence relation I have these equivalence classes on G and if A is an element of that I'm just going to say I'm just going to write it like that that's an equivalence class on this group G and it contains the element A. Remember I take its inverse binary operation with B and I say that's an element of H that is how I define this and my claim my theorem in the end is going to be that this equivalence class which is a set remember it's a set of elements is equal to the set of A binary operation with H such that H is an element of my subgroup. I'm stating this is a set and I'm stating that's a set and in the end I'm going to call them cosets and in the end I'm going to call this a left coset. Okay first of all before I prove all of this and if I say these are two are equal to each other I've got to prove it in this direction and I've got to prove it in this direction. First of all is this an equivalence relation? This video is just going to be about is this an equivalence relation? For this to be an equivalence relation we have to have the properties the reflexive property. Reflexive property let's see if that holds I'm going to say in other words I'm looking at A and A. Now is that is that true what does this mean? Well it says what I have to do here is then if this is my relation I'm saying A inverse binary operation A. Well I set this up as a group if A inverse is there then definitely A has to be there and this is just the identity element E and the identity element we know is inside of H because it's a subgroup it must have that same identity it must have that identity element so the reflexive property clearly holds E as an element of H. The symmetric property symmetric property does that hold if I have A, L with B does that imply the B equivalence relation with A is that so? Now what I'm asking here is if I have this relation remembers A inverse and B that is an element of H that is how I set it up this chalk is flowing right to my eye anyway if this is in that set then it's if that is an element there its inverse must also be an element of H and remember how we define an inverse we looked at this before I take the inverse of the second one and then the inverse of the first one that must be an element of H and lo and behold B inverse the inverse of the inverse is just A and that's an element of H so what do I have here well I have just shown that if this holds then that holds because this is nothing other than saying B this relation on A so we're shown that the last one is the transitive property transitive property what we have here I'm going to say if A this relation to B and I'm just using set notation and B this relation to C this implies A's relation with C C so can we show that what are we saying here we're saying A inverse B and we are saying B inverse C we're saying that's an element of H we're saying that's an element of H well if they're both elements of H if I take the binary operation between two of them by the closure property that should obviously also be there that should obviously also be there so if I have A inverse B and that with B inverse with C and I say I claim that that's an element of H and by the associative property of groups I can do this first that gives me the identity element which leaves me with A inverse C as an element of H therefore I'm showing that there is A this relation to C and that's an element of H so all of them hold the reflexive the symmetric and the transitive and the transitive property so really I have shown that this is an equivalence relation and you can do it the other way around as well when you do R it's B inverse A everything swaps around it's easy to prove that that's an equivalence relation so I have really shown that this exists it is a set here with elements A in it that's how I've defined it it is an equivalence relation it's an equivalence class and now in the next video we're going to show that this is a set well this is a set but that it's equal to doing this it's equal to this set and I'll show you how to do it in this direction and then you take this and end with that or you take this and you end with that because if you want to prove that two things are equal to each other the best way that we are going to do it is if you want to show that two sets are equal to each other remember these are two sets is to show that A is a subset of B and B is a subset of A and if that is so then A equals B and that perhaps by the way kids you can see if you can if you can set that up very easily I'm just going to show you how it starts you're going to take X as an element of this A and then you continue and the same you're going to do with this side and then get to that side but we'll get to that video first of all we've defined this we're showing that this is an equivalence relation and we're going to end up with this set which we call a coset and then we're going to call this a left coset and then also you get the right coset and the right coset well we also write this as a h h and you also I'll check that out and you also get the right coset let me not get into that now before I get too confused we'll look at all of those once we've proven once we've proven this this is by the way this is the left coset because the A which forms our equivalence this class here is on the left and then it's going to be on the right which we just write as h as h a and this is a h but we'll get to that that's not important we've shown that this is an equivalence relation


Welcome you back once again here on Yankees Hot Stove as we share some reflections on Tommy LaSorta who passed away last week at the age of 93, larger than life. His love of the game showed everywhere he went. Everybody he spoke to, a great ambassador of the game, Jack and a man who by his own account bled Dodger Blue. Yeah, I think of that word ambassador when I think of Tommy LaSorta, Bob. And I actually had the good fortune of meeting him while I was still in college. I'm a junior at Fordham University and Tommy is giving a speech on campus. So since my buddy Mike Zuccarello and I were the school sports editors, I had the opportunity to interview him and meet him beforehand. That was good enough. He was a major league manager who with the Dodgers had those back and forth with the Yankees. That was terrific to just even speak to him. Well, then he gives the speech and in the course of giving the speech, he talks about Frankie Frisch who of course he knew the Fordham Flash. He talks about Vince Scully, who was revered at Fordham when you were a sports journalist like me. And then he throws my name in the mix and starts talking about me as enthusiastically as he spoke about those two icons. So I was never a big man on campus like Flash was at GW. But for those five minutes when Tommy LaSorta name dropped me in the middle of his speech, I was, I've been a fan and he was a great man ever since. Well, I can honestly say that I've never met Tommy LaSorta and Tommy LaSorta probably never mentioned my name in a speech like Jack. So congratulations on that. But when I think of Tommy LaSorta, I think of the iconic managers in the game. Sparky Anderson, Earl Weaver. When you walked into a major league clubhouse and they were leading your team, you knew exactly who the boss was, right? There weren't at a Linux departments. There weren't the computer guys in the clubhouse. It was Tommy LaSorta making out his lineup and motivating his team. And if you go on YouTube and you listen to stories about Tommy LaSorta, it's all about motivating his team, almost making them better than what they physically actually were using some information from the media to get it into his clubhouse to get his team fired up. I think about 81 beating the Yankees after going through some hard aches at the end of the 70s. And I think about that 88 team with Kirk Gibson and that amazing run to a World Series title. Tommy LaSorta was able to motivate people and just a great character of our game. And again, in that 88 World Series, you could have made the argument as much as teams are protective of players now. Kirk Gibson had the bad left hand, the bad right knee was not supposed to play. And you don't need analytics or anything. All you need is motivation and a speech to say, this guy has something left in the tank, put him in and he won the World Series for him. A memorable home run off Dennis Eckersley and the Dodgers sail from there. They beat a team that people probably didn't think they could beat. And to Flash's point, even in the previous round against the Mets, in our buddy David Cohn, Ghost wrote a column for the Daily News and criticized the Dodgers. Who do you think made sure that that column was on a bulletin board? Tommy LaSorta and Coney has said that when he went out there and pitched, his legs felt like Jello. That's how nervous and tense he felt because everybody at Dodger Stadium was against him. That was inspired by LaSorta. Well, in the speech he delivered at his Hall of Fame induction. LaSorta said that he would go to sleep as a child. He dreamed he was pitching for the Yankees, playing with legends like Bill Dickey, Lou Gehrig and Joe DiMaggio. Though he never wore pinstripes in the majors, he became synonymous with a Dodgers franchise equally steeped in history and tradition. LaSorta will forever be remembered for his huge personality and the impact that he made upon the game he loved so much.


Hey guys, welcome back to my YouTube channel Daniel Rosal here this YouTube channel is all about everything to do with living in Israel and Jerusalem and bringing you this video today a little bit hungover and that is because it is Yom Ha'atzmahut Israel's national day. It's 75th birthday, which is just crazy There are plenty of people walking out there on the streets that are older than the state of Israel has been in existence But Israel has turned 75 and the Independence Day is a big celebration in Israel The Israeli Air Force do a flyover on the night of Yom Ha'atzmahut And that's the thing about the Jewish calendar. It starts on the night and ends at the night So Yom Ha'atzmahut started last night. So there was lots and lots of fun in Jerusalem city center lots of parties lots of drinking lots of music Thoroughly, thoroughly enjoyed it and today it's more typical for folks to do stuff like Barbecues, that's like the big classic Yom Ha'atzmahut pastime. So I'm getting ready to tend to Quiet barbecue in a few minutes, but I thought as an act of national service on the 75th birthday of Israel I would talk about 10 things that are great and good about living in Israel. So here's my list Okay, so starting this off in no particular order and not ordered by Significance, I'm gonna go with that Israeli wine as my number one choice because it's one of those things You know, we're gonna get on to the heavy stuff about Israel being the only Jewish country in the world Let's just start off with something almost everyone can appreciate and that is good wine It used to be an oxymoron to say Israeli wine. It was terrible there was kind of kiddish wine in the Jewish world and that's what people thought Israeli wine was but Everything has changed dramatically in the period since and now Israel is pretty established as a Wine terroir if I'm saying that correctly of growing importance on the international scene And you can go visit wine tasting is a popular pastime here So lots of the wineries the smaller ones at least will allow you to come into their place And they'll tell you about their wine and it's amazing where where you can find wineries in Israel We went down to the Egyptian border their videos are on my YouTube channel In fact, I have a playlist about the wineries I visited in Israel I'll put a link to it But something I'm realizing after living here for eight years is you need to kind of stack the positives of Living in a country as far as possible And I think one of the big positives about living in Israel is the Mediterranean lifestyle that you can have here It's such good weather and I think that alcohol and moderation wine in moderation Can definitely be can definitely be a nice a nice part of that I think So there's lots of good wine here in Israel and unlike so much in Israel. It's relatively affordable You don't need to spend generally more than 30 shackles 40 shackles Which is like eight or $10 to get a very drinkable bottle of wine now I'm far from a wine expert, but I would like to think I know a good Rose from a bad one. That's my favorite color of wine and there's lots of good wine in Israel And we're seeing a growing trend of wine bars opening up Which I'm very excited about because I think it's wine bars are wonderful And if you needed a recommendation for a wine bar in Jerusalem or Tel Aviv drop me a comment I'll be happy to send you to some cool places Second pro positive about living in Israel the country is really small I did a video recently comparing the size of Israel to Ireland I think I got the fact that Israel is something like 200 a little bit over 200 square kilometers I could be totally botching that figure, but it's a very very small land area one figure that I that I know I'm not botching as Ireland is like three to four times bigger than Israel and Ireland's not a very big country That's where I originally come from so the fact that Israel is super small Can be a disadvantage because it can feel a little bit claustrophobic here at times, but I also think it's a major advantage It's it's a small country, but it varies so dramatically like the parts of the country when you go up to the north of Israel You're in this like lush forest is area with spectacular views of mountains the mountains stretching up to Syria and Lebanon and then you go down into the then you have like Tel Aviv and the whole kind of like coastal plain Which is very sort of hip and fun Lots to do there are great beaches What have you and then you can go to the south of the country and you're in an arid desert Right stretching out for hundreds of kilometers literally and actually one of my favorite places in Israel are at both ends of the country I love Matula on the Lebanese border. It's not perhaps you could say the most spectacular place The town itself, but I don't know. I like it. I love exploring borders And I've had some good times in Matula and Mitzpehramon in the desert is that also one of my favorite places? I think it's a lot nicer than a last and definitely a cool place to check out okay positive three and This would actually be this is really the number one positive for me But I'm trying to sort of order this video so that it's not just from a let's say Jewish perspective but the whole reason I moved to Israel is because I am Jewish and Living in Israel as a Jewish person. There's really nowhere else. I would rather live my life I love about being Jewish in Israel is that it's integrated into the state and it's the only Jewish Majority country in the world, which I think again, it's kind of like sometimes you could say that's a bad thing You've only got one option if that's if you want to live somewhere where you're not in a religious minority and the other on the other Respect its advantage because you don't really have a difficult choice to make you've got basically Israel What I love about Judaism practicing Judaism in Israel is again as they mentioned it's integrated, right? It's not like you need to live in a specific Neighborhood and like there's a list of kosher restaurants now. I live in Jerusalem. So it's a bit more You know there's more kosher Let's say food than other places in the country but there's tons of kosher food options here for every type of a culinary interest whether you're into Asian food or You love just a good greasy shawarma. You've got to cover it The national religious days and Judaism are public holidays in Israel. So you don't need to use up your Vacation time just to observe your religion because during those religious holidays Jews religious Jews abstain from work and using even electricity So that makes it very difficult to you know, too. So that's nice It's baked into the country and there's just a great feeling from not being a small minority like growing up in You know in the Cork Ireland I was like sort of almost the only Jewish family in the entire city And what I love about Judaism in Israel is you get to transcend your Judaism because we're most of us Who come from different parts of the world to move to Israel what you call in Hebrew making aliyah because most of us I think made that decision for that reason we can define ourselves in ways that don't involve just being Jewish Reason for the diversity of the food in Israel firstly the food is if I can say so great There is a falafel now These are the foods that I enjoyed a lot more and enjoyed so much that I had to get an organ cut out of me I'm talking about my dear beloved departed goldbladder. So I have I'm training a bit more healthy now So stuff like falafel is slightly off the menu for me, but I still I still a falafel You know talking about more healthy foods fresh salads was a huge emphasis in Israeli cooking on Using fresh ingredients and the use of preservatives here is also not a big thing You'll even see this when you buy bread from the supermarket that if you keep it out on the counter in the hot summer It'll start like going very very badly off like growing mold in at two days It's just they don't really use preservatives and the just the amount of fresh ingredients One particular food and it's it's kind of a melting pot the Israeli cuisine It's sort of a melting pot from Jews from all over the world So you've got Jews coming from you know, Arab countries like Tunisia Introducing amazing dishes like shakshuka into Israeli cuisine. Of course, you've got falafel classic Middle Eastern food And there's also even a substantial Russian population here of Russian Jewish immigrants to Israel, which means of course There are good Russian bars where I spent Probably a little bit too much time and money and Last night there's good Russian bars in Israel and there's Russian foods as well Russian restaurants So yeah, it's definitely And I want to say one one another food stuff that is very you wouldn't associate with Israel necessarily is Ethiopian food there are again a lot of Ethiopian Jewish immigrants to Israel and they bring with them their cuisine So Ethiopian foods amazing. It's become my second Favorite food. I would only put it after maybe Indian and Nepalese food and I don't even know sort of which way I'd have to order those two But I love I love those foods I've come to really love Ethiopian food You get a flap breadcull in Jera and you scoop it up if you haven't tried it When next time you're in Tel Aviv or Jerusalem put Ethiopian restaurant into Google Maps And you'll be surprised to see how many options there are and just pick one that gets a good rating and go there And you might also become a convert to Ethiopian food Reason five to love living in Israel. Tel Aviv has great beaches and that's not to be taken for granted Tel Aviv is not the only place with beaches in Israel Israel has All the way along its western coastline down to the Gaza Strip and up to the border with Lebanon There are beaches the southernmost beach in Israel the one right by where the Gaza Strip starts is called Zikim It's actually a pretty cool beach. There is surfing in Israel, which I really need to get back into because it was one of my biggest hobbies growing up in Tel Aviv You have a lot of tourist beaches and it's a great place to to hang out Pal Machim is a really nice beach that I want to recommend to people It's a little bit more quiet than the beaches in Tel Aviv. It's a public nature park So you do need to pay an entrance fee But I find it much more pleasant less people blasting music and it's just a more laid-back vibe So that's actually my favorite beach in Israel. Habonim in the north is also a really nice beach that I can recommend Habonim I'll put a little sort of like graphics To check out so don't limit yourself to checking out the beaches of Tel Aviv If you have a car or you're renting a car go up and down the coastline because it's cheap and it's quick hyphes You can got a couple of of beaches and of course I can't forget the Dead Sea which has beaches as well There's Cali Beach in the north and other beaches along the coast of the Dead Sea The Dead Sea is a very different experience because during the summer it is crazy crazy hot there You can't really swim obviously because it's you know the Dead Sea and it's like salty So I personally for the it's kind of like a novelty I I personally prefer going to the beaches on the Mediterranean with some people really like the Dead Sea It's supposed to be very good for stuff like asthma and skin conditions and I actually have asthma So maybe I should be doing more Dead Sea expeditions random Thing number six on my list easy access to to be shishima and I was putting together This list today. I was thinking from back to last night. I was thinking what can I say is so great about Israel? There's so many things not on this list like the diversity of the population if you are Jewish and you're looking to You know to marry Jewish how easy it is good options within both Gender is whatever gender you are but then I was like, you know the little things as well to be shishima. It's so good it's this Israeli spirit based around citrus and It's a uniquely Israeli product is made here ginger. It's got like ginger Lemon, it's just amazing to be fantastic. Unfortunately, to be has a reputation among Israeli bartenders for being a drink for students Which is just terrible. It is so much more than that. I love fruity stuff. I love fruity cocktails More than they love me back But that's actually one of my favorite drinks as well and you can make very simple cocktails by taking a bit of to be Shishim Shishim in Hebrew means 60 a little bit of ice and tiny touch of water and beautiful Reason 7 is the sunny weather. I mean, it's hot in Israel It gets really hot and the summer is really long what I find interesting about the climate here coming from Ireland is It's kind of like there. It feels like there's only really two seasons You've got a big long hot summer that stretches all the way to September even early October before there's like a real noticeable cooling in the temperatures and it starts around this time of year They're recording this video But it's sunny and during that time. There's just like no rain essentially every day is sunny So it means that you can't sort of banter about the weather forecast Which is one of the most popular pursuits in Ireland But if you're into sunny weather hot weather Whether to go to the beach lots and lots and lots of sunshine in Israel Number eight and this is actually I would consider a big one that if I was reordering this list if I had a little more energy today I might have put this like towards the top health care system in Israel There is really really top-class health care in Israel that's affordable and Israel sort of makes it available to all its citizens I've done a couple of separate videos on how health care works in Israel just a real basic stuff But you know, everyone it has to be a member of one of four Kupot rolim that's a health fund And that gives you like your basics that gives you your doctor visits your specialist visits medications at very very discounted rates. I talked about that also in a video and It's just affordable to get like conditions treated. I don't mind sharing a bit about my personal medical history I have a depression and the Antidepressants I take every day. Trentalex are super affordable compared to what they are in the US And I'm currently in the process of attempting to get my blood blood pressure down So I was able to do a test yesterday 24 hour blood pressure thing and that was like basically free as well So, you know, no one's going to move to Israel because of the health care I don't think and Hopefully people don't have health problems that requiring health care, but eventually probably most of us will And I really have very limited criticisms or just almost all almost exclusively positive things To say about the quality accessibility and affordability of health care in israel Okay, getting towards the end reason number nine It's easy and cheap to travel to europe people wouldn't think about israel as a really sort of a great travel Destination travel base. I mean definitely a travel destination, but it's actually a great Base for traveling into europe and this is a reason that's going to maybe appeal more to Any americans who watch this video of them folks from other countries, but Traditionally, it was expensive like everything to fly to and from israel Then israel and the eu concluded something called the open skies agreement in which basically reciprocal israeli Israeli airlines get to fly to european destinations and the european destiny airlines start flying to israel breaking the monopoly of Airlines like ll. What have you and what that has the change that that has brought to the travel market here has been really really Quite significant. You have now ryan air operating in israel easy jet Whiz air I've gone plane spotting a couple of times here sitting at the edge of the You know the airport and recording on my little camera here take off the landings And it was just extraordinary all the airlines are here. There's like I haven't heard a half of these There's like air air dubai or dubai hops since israel signed the agreement the abraham accord. There's been there's been a huge Surgeon traffic between those two countries So lots and lots of flights going back and forth to dubai these days and speaking of ireland ll actually just recently started the first ever Direct flight to ireland from israel that is scheduled There was one that only ran in the summer and that's going on a few times per week now It's a five-hour flight So if you want to get to to ireland you can now do so on a direct flight with ll from israel And I think it runs something like three times a week Okay, the final reason because so far we've talked about kind of very much lifestyle stuff I want to talk a little bit maybe about professional things as well. Um, great country. This is the last list I actually I'm using sort of a low budget teleprompter here. I've got a Piece of paper taped to my tripod and it says great country to launch tech careers So speaking of professional stuff for a moment israel is known as a startup nation because there are so many startups here Now it's true that recently in the last year There's kind of been murmurs of a slowdown in what we call in israel high tech Which really means that whole world of startups But it's still a pretty vibrant scene now. It doesn't mean that you don't have to be a Coding prodigy to work at one of these companies. There's obviously lots of jobs within these companies like sales marketing or personally work in marketing communications or Right now I work for a nonprofit but before that I really worked for tech companies So that's a big employer in israel and definitely, you know, if you want to reskill or upskill or whatever There's boot camps what they call boot camps now throughout israel There where you'll do an abbreviated course in, you know, whatever you want to sort of Whatever field you want to do whether it's ux design product design Content writing probably doesn't require a course, but that's also, you know If you really enter writing that's a decent way to enter the world of high tech and maybe move on to other More lucrative positions within the company. Okay. I need to go 10 to my barbecue now on yoma at smoot These were my on the 75th birthday of israel. These are my 10 reasons I love living in israel 10 things. I think are super positive about the country. Yes, there are negatives spoiler alert for the Counter video to this is the cost of living is absurd. It's way too expensive to live here But let's talk today about the good things and those are my 10 reasons Hope this video has been informative interesting. Give me your thoughts if you live in israel What are your top 10? List or just anything really that you love about living here And of course as I always say at the end of my videos if you do want to get more videos From my good self about life in israel and jerusalem Hit the subscribe button. Thanks for watching guys