So this is the outline of my talk today. First of all an introduction about multi-body simulation next. Yeah, okay some background information. Then I would like to show you some assemblies. So I would fill this talk at least half of it to show you some assemblies so that you get an impression what is in fact possible with this package in the end. This package is not in public already. It will be published maybe in September. And in the end I will give you a short note of future work and some back up. Package name is multi-body symbol which is says multi-body symbolic. So in fact there are two different ways to approach this problem. You can use symbolic equations and you can stick more to the numerical side. Most of the industrial products stick to the numerical side, but we decided to approach it analytically. Our aim is to provide on basis of existing Python packages to provide once in a while a complete multi-body simulation tool. So why is this important for us? I mean you can guess it. We want to be independent from market leaders. Market leaders for example a sim pack or also VL or also Adams costs a whole lot of money. The license and all of these companies are now not they are now yeah, bored by very big companies. So it is not possible to yeah to stick in this development process much easy. Second scripting ability is included. Of course it's in Python, so it's of course included and third educational purposes. So what is multi-body simulation? Multi-body simulation deals with systems which can be described by these equations. These are the Newtonian Euler equations. They are differential equations, so they are well known since several hundred years. What is the problem writing them down and integrating them? Well the problem here is as you will see in my talk this F is not only an expression which you can write down. It happens that most of multi-body simulation assemblies include constraints and constraints are like a ball which runs on a table or sliders or whatsoever. So these constraint forces are in fact the difficult thing in multiple simulations. We look back at the development process of 30 years more or less, not us, but in general, so the yeah, the community and the scientific community is working on this problem since more or less 30 years and you can imagine they have come up a whole tons of papers out of there and yeah, and you cannot expect to climb up within half a year on top, but we are very enthusiastic and we think we can go ahead this way. So use cases of this multi-body simulation is mechanical engineering, ground vehicle dynamics, robotics and biomechanics. Each of these branches are more each of these spreading branches is modern and relevant. So I'm working in ground vehicle dynamics since more or less seven years and I'm doing right and handling simulation for another company right now and I know how, what difficulties are in this in this field. So what package are we using? SimPy, it's more or less the basis of this one. SimPy is these guys who produced SimPy, they were doing a really really really great job and I would like to thank you those people. It's a symbolic algebra package, so it replaces more or less these three products and it's on a very, it's right at the moment, it's on an advanced level, so it's not that you can just do some algebra derivatives or integrals, it's on a high advanced level and it also includes already advanced mechanics. So why do not parcel these together, stick these loose ends together and and produce something with which you can do your multipoly simulation. So fine, we try to do this. Yeah, I would like not to forget these packages which are really really helpful and maybe the core of numerical and scientific, Python programming, NumPy and SimPy and without these it would not happen anything about of these. For linear algebraic solvers, we use NumPy, they're very very very advanced and not forget well tested. So these packages are so well tested that you can trust on this and this is good. There are some ODE solvers in SimPy available. So in the end we need some graphics. Graphics we did with vPyzen, vPyzen is a medium advanced. It is really really nice, but it has some primitives, called primitives, some rods, springs and so on and you can put these together and make out of these your graphics simulation. In fact, you need this to make sure that your assembled equations behave well. So just a visual check of your solution. I mean you cannot just solve your equations and then put some some graphs and then you cannot judge if this is done really nice or really good. You have some visual check up. Now some background theory. I will I will try to make this short. Building blocks of a mechanical system, you have your bodies, everybody has six degrees of freedom, translation rotational, including the time derivatives you end up with 12 degrees of freedom. So each body should lead to, yeah, to 12 lines in your system of ordinary differential equations. If there wouldn't be some possibilities to boil it down somehow. Each of these bodies has mass and moments of inertia in intrinsic. So this is the figure citation. This is not mine. This is also not my figure, so I will cite it. You can boil down. You can boil down the numbers of degrees of freedom by joints. Toins you can think about as two bodies are connected. We are joints like in your skeleton. And in fact, it's technically done more or less the same. Each of these joints can be produced in a technical sense and in the end. But these joints, you reduce the numbers of degrees of freedom. Here we talk about these type of joints, cardinic, axis, revolute. For example, if you think about a tire on a car, it's just revolute, except that, okay, the front tire can also steer, but more or less revolute, so it's a revolute joint. In these equations appears forces and torques, forces and torques accelerates your masses. So forces, most of the time, appear pairwise. So if one body is attracting another, it's the same done for the other body. But you have different types of forces, pairwise forces. So think about sun and earth, for example. The external forces, if you just want to find a system of a mechanical system on earth, you would add the gravitational force, of course, and you wouldn't include the earth as an independent mass, but you just would add your gravitational field as an external force. And the difficult things, the constrained forces. For example, if you have here a surface and a ball is running on the surface, the surface would act a force on the ball to be on this surface. So in multibody simulation, you'll see most many times these kind of drawings, because these kind of drawings show most of the things included. Here, for example, you have a chain of bodies and here are the joints. And you can see, if you switch from Cartesian coordinates to just the angle here, you can reduce it somehow, the number of degrees of freedom. Nobody would write this down in Cartesian coordinates, but in angles. But you know, if the generalized coordinates are minimal, it equals the number of degrees of freedom. But it is not always the case, so you can have more generalized coordinates, so you would have add on top of it some equations, which gives you the constraints. Even the generalized coordinates are not unique. So you can, for example, measure the angle towards the set axis or towards the axis of the previous body. So it is not at all unique, the set of generalized coordinates. One problem, which is really maybe the main or one of the core problems in multibody simulation is this one. So if you have, this is called a constrained loop. If you do not just have your joints, but if you have another constraint in the end, which builds a constrained loop, you can say, okay, these angles here on top, they are somehow connected to each other. They cannot be independent at all. And this is called constrained loop, and this constrained loop produces another equation, most of the time an algebraic equation. And this algebraic equation, you can take care of in several possibilities to solve these kind of problems. Most of the time, there are differential algebraic equation methods, but they are very costly, and in Python, maybe too slow. So we propose here a solution according to Lagrange one with additional drawback force. For linearization, you can always put this algebraic equation into your set of equations. Here, this is the set of methods we can use to generate our equations of motions. In this package, they produce here already Keynes method, which is also called Dallon-Bear's principle of virtual work. And Lagrange method number two, emittance equations is another possibility, but not used here. Okay, so I will show you what, how it is used.  A marker is always a coordinate system in the language of multi-body simulation. There are methods provided to add bodies, markers, so extra coordinate systems, external forces, extra constraints, and for example, reflective walls. ODE solver is connected, more or less automatically. A 3D graphical backend is connected automatically. So each body signs up in the graphical backend and appears somehow as you want it to be appeared. I will show you examples later on. Some physical quantities are provided, like energy, forces, velocity, and so on.  And this is the advantage. New and interesting. So what did we put into this work? We would like to have a completeness of joints and tools. And the Jacobian is calculated for linearization analysis, so this is on top. A nice feature, very nice feature. The linearization tool, which is already in Sympi, is kind of completed. You can detect automatically independent and dependent coordinates and so on. Constraints loop are more or less kind of solved here. External models and parameters can be included. This is a very important point here, the external models, which I will show you in one example. We have also some B splines, which can be used if you don't have an analytical expression for your force. You can also include some kind of B splines for having a representative of your force function. So sometimes measurements don't give you analytical expressions. Okay, coding style, set up the system. Here, this is your multi-body simulation world.  Assembling and solving is just this one. Here, you have maybe some constant, like the gravitational constant. You give it a number. You produce equations of motion and integrate them. Post-processing is calculation of linear analysis, linearization, so stability analysis. You prepare and animate your result. Okay, if you would like to be a developer once in a time or if you would like to work with SimPy once in a time, you should be aware of these three things. I mean you should be aware of many things, but these three, especially, never use SimPy for numerics. Do not try to use, for example, to use SimPy to solve for eigenvectors. It will never happen. It will never be as fast as NumPy. So find the right step between SimPy to NumPy. Okay, so I got the sign for 10 minutes right now, so I will hurry a little bit up. LambdaPy is one of the core functions of SimPy. I mean if you have an algebraic expression, what can you do with it in a computer? You would like to use it as a function and to use it as a function, you use this word which is called LambdaPy. You LambdaPy expressions into Python functions. This is maybe the most impressive invention here, not our from SimPy. And ODE solvers don't use your own, so even if it looks like fun to produce one, it is not never as good as those which are around. Use those. We use LS ODE solver. This is also called for sundials. Maybe if you are interested in these topics, you know that sundials is an open-source solver which is out there, but not connected to Python. At the moment, it is connected, but it stopped kind of at Python 2.6 also. So I would like to connect this and use this sundial solvers, which is really good in my opinion. Okay, I will show you examples. And for these examples, not only the pictures, but also the results, so the movies. Okay, this is bad because now it appears here on my screen and not on the screen. I wanted it to be appeared. So this is what comes out more or less. This is a crank slide. Something called crank slide. And this is a simple example for a constrained loop. Here, this goes round and round. And this goes linear. So this is rotating linear. You see we put in also some forces. And here, an extra constrained force. So this, if we don't put this constrained force here, it would be just a pendulum. So I will skip some of these because I have 12 and this is too much. Maybe this one. Yeah, some spring and it's a reflective wall here at this position. There's a reflective wall. It's interesting because it's not so fluent, but I don't know why because it's in the middle of two screens maybe. Yeah. So this is a reflective wall example. I will show you this one. This is a simple car. And this is non-trivial. I mean, maybe you can see this, that assembling these equations takes around 60 seconds. Let's take a look at the assembly here. So these equations, they just come up by this mechanism. And this mechanism, as I told you, is quite easy. So we just add bodies, markers, special forces, and so on. And in the end, here, this is the steering, more or less. And in the end, here, this is the starting vector. So you need starting vectors. And in the end, we just call here canify and then these equations are assembled. And now, it's around 60 seconds assembling equations of motion. And why is this non-trivial? Because it is not only the mechanics, which you can see here. It's also kind of an external model. It's a tire model which we plugged in. And the tire model gives you, I mean, if you think about tires, I know, yeah, if you think about tires, it's a non-trivial external model. And I'm working in ground vehicle dynamics. So it matters a lot to plug in to your system non-trivial external models. And the nice thing here is that it is possible to do this. Now it's integrating. We have around 27 degrees of freedom, in fact, all together. No, 28. So it's okay. It's fast. It's not real time at the moment, but it's fast. So it's not bad. I mean, if you would like to make it real time, you would have to export it in a C or Fortran code. Then it would be real time, but at this level it is not. But it's okay. Hope so. Somehow it's a little bit slower. I don't know why, because maybe it's some resources here out. Yeah. I can tell you this. We used here a Pacheco model. Pacheco, maybe one of some of you may know this. Pacheco is a professor. He's working on tire models. And he's really, really famous in this area of research. And tires, they are quite interesting to model, because it's rubber. And rubber is always difficult. So, for example, if you think about rolling, rolling tires or so, you sometimes include a no slip, a no slip constraint. But the tires, this would never work, because tires produce the longitudinal and vertical force only with slip. So you have to include slip in your calculation. So now, here on top of this, we have calculated, in the end, the eigenvalues of the Jacobian. So you can see this. And now I will go into the animation. In this step, all of these degrees of freedom has to be prepared in Cartesian coordinates, that it works. So now here, let's go. This is our car model. It looks simple, but it's okay. And it is, in fact, more or less fixed on zero, so that it... This is a sign steering. It's a simple maneuver, sign steering. But it's nice that it's working well. You can see it's breaking in the end here on top. I can show you just this. We have also some outputs calculated for the tires, special values for the tires, and put these into these graphs. Okay. So I would skip the examples and go to some future work. This is not so easy. We thought about making this assembly as equations that are very complex objects. This is non-trivial. The assemblies are not. They are quite complex objects. So ZODB, which I really like, but it's based on serialization. And very complex objects cannot be serialized this way. And I would like to do this to make it persistent, because to skip the assembly, which may take a little bit of time. So graphics always, some improvements to be done, model validation. And just in time, compilation is another nice idea to speed up. Post-processing with pandas, maybe you know this package. Okay. So future work. Complete the basics until September and full vehicle simulation. So to end up with a nice full vehicle simulation, better than that one I showed to you October until December 2015. And thank you for your attention. And I would like to invite you to ask questions. Thank you very much. You talked about transitioning from SMPI to NMPI to do numerical computations. Is there an automated path from SMPI to NMPI, perhaps? At the moment, I'm not aware that they are closely connected. And this is a kind of a pitfall. I think you have to, yeah, except for this lamdify you need sometimes, if you plug your numbers in, just convert your SMPI matrices to NMPI matrices one by one. This is how I did it, and this works fine. Thanks. Okay. Thank you very much.


Hello Psych2Goers, we just want to take the time to thank you for all your kind support. We are a team of dedicated, passionate, and hardworking individuals who come together every day with one goal in mind. We want to make psychology come alive for you. We are self-funded and recently launched our Patreon. If you enjoy the work we do and find it meaningful, please stick around until the end of the video for information on how to get more involved with us and all the cool rewards you can get from us. Falling in love isn't always exhilarating the way we imagine it. Sometimes it has a way of creeping up on us when we least expect it. Are you together with a special girl? Here definitely head over heels about her, but how do you know she feels the same way about you? Here are six clear signs she's in love with you. 1. She loves your humor.  One thing you should never compromise in a relationship is your sense of humor. The person you're with should essentially be your best friend. You can laugh with over just about anything.  To learn about how women fall in love, check out our video, 5 ways women fall in love. 2. She is willing to face her fears with you. When you meet the right person, they challenge you by helping you confront your fears together. If you find that your partner is being more open-minded after you've encouraged her to try the things she was once afraid of, then you must have made a lasting impression on her. Years are hard to work through, but love has a way of conquering them. 3. You've inspired her to become a better person. Think back to the first day you met her. Has she grown since that time? Maybe she's more responsible now, a little wiser and able to bounce back from bad days quicker. If you've been giving her advice and helping her through the bad times, perhaps your words and actions finally made a way into her heart. You can see that she's become a better person, not because she was pressured to change, but because you saw the potential in her. 4. She becomes more open-minded about trying the things you like. When we're young, we usually fantasize about falling in love with someone who listens to the same music as us and has the same hobbies. But sometimes, the person we fall in love with ends up breaking those rules and makes us question our expectations. For example, you may enjoy playing video games, but your partner might not know the first thing about them. If you find that she's willing to play around with you, then it shows that she wants to understand you better, even if she's bad at it. What counts is her effort towards bonding with you. 5. She doesn't want to go to sleep mad at you. It's normal and expected for any regular couple to fight, but if your partner wants to resolve problems before you go to sleep, then it means that she cares about working things out with you. Sometimes when we hit rock bottom, we can become obstinate and refuse to listen to the other person, but if she refuses to hold a grudge against you and wants to communicate better, then it shows that your relationship is more important to her than her pride. 6.  It's normal to have insecurities, but when you're in the initial stage of dating, you may not always be your true self, hearing that the other person won't fully accept you. Vulnerability, however, is the ultimate test to love. If your partner can be her natural self in front of you, then that's a clear sign she's in love with you. When the two of you can disagree openly about things and see the worst of each other, but know that you still care for one another, that's when you truly have won her heart. Do you agree with these signs? Please share your thoughts with us below. Also, don't forget to subscribe for more content from Psych2Go, and check out our Patreon. We started it because we want to go into a bigger platform that reaches more people who are in need of help. With your contribution, you can receive our PSI pendant, t-shirt, issues of our magazine, and many more membership benefits. Your funding will help us produce quality script writing, voiceovers, and animation that makes our content both entertaining and educational. We want to make sure our community members get the best, and only the best. Thanks for watching. I just want to give a personal thank you video for you guys for always supporting Psych2Go and making this all possible for us. Our vision is to make psychology as accessible as possible so that it promotes self-awareness and it helps you guys grow. However, we want to make more content for you guys. And we'd love your support in buying one of these bracelets from our partner, Introvert Palace. Check out the bracelet. It's pretty cool, and it even includes Pluto. The link to purchase will all be in the description below, and I hope you guys have an amazing day. Bye.


Everybody forced here being 2023 Star Wars six series 20 bucks case number 50 random hit style The type of the hits as we go along or at him at the end to see who he gets what? Look, let's get started Get your spots for tomorrow everybody 10 bucks Tuesday. You got NT NT football on Wednesday and Platinum anniversary. We start ripping on Wednesday Lots of lots of lots of good stuff this week. We off the rich will be off Maddox live on On Wednesday actually so that'll be that'll be interesting guys to check that out, too three streams going Got a fixer auto Fixer Skyler Bible or Bible Even earlier tonight you spell fixer Evan peel auto McKellick a trellis Evan peel got an adi Gallia auto Adi Gallia Angelique Perrin a corn trawler auto 36 out of 50 corn trawler to 50 Demetrius Pistrovsky Lyra or so auto that is Valine Kane is Lyra or so 8d8 auto Matt Berry is 8d8 Grandma of Tarkin auto blue numbered 8 of 50 grandma of Tarkin 8 of 50 Sefton Vanik auto 19 of 25 Sefton Vanik 19 of 25 is Joseph Alton next up is a beta trawler auto Scratch on the Mac there beta trawler Ryan Watson Jar Jar would be good Governor Arundh price on the auto. It's Mary Elizabeth Maclin Governor Arundh price There's a five of five Cozzuto ziono five of five Cozzuto ziono It's Christopher Sean is Cozzuto ziono five of five on that one nice low number there. We go See some more numbered autos now bar tender bartender auto is Alan Graf all names are made up Greg T0 B1 T0 B1 auto is Jayden Waldman Got a Cursanton auto. It's a lot of new characters Cursanton auto Carrie Jones Cursanton is awesome. I gotta get Cursanton auto Famous Cursanton Got Mayor Mock Shies auto Mayor Mock Shies is John Rosengrant Honda Onaka Fan favorite right there Honda Onaka Jim Cummings on the auto General Draven General Draven auto is Alistair Petrie Petrie It's Hanway on the auto Hanway base auto is Rena Owen Lovey auto. Come on. We need one more numbered auto here. Lovey auto is Lily Cole and a Rio Durant Katie Cartwheels Rio Durant did get some low numbered autos this one at least Alright, let's go ahead and run the random. Good luck everybody. It's five and two or five and three. Excuse me eight times Names first in the hits one two three four five six seven and eight Greg M top and bottom there and then the hits eight times one two three four five six seven and eight Core and trawler down to Mayor Mock Shies Greg with the core and trawler auto Luis with the lovey Greg Taunway Jazzwinder with Lyra Erso Greg with General Draven Andrew ST0B1 Greg with Honda Onaka Chintai got the Adigalia auto Michael G. Evan Peel Jared R. Grand Moff Tarkin auto the 50 KLF with the Sefton Vannik auto the 25 Jason R. Arenda Price Michael G. Rio Durant Felix got the fixer auto Greg with the beta trawler auto David D. 8D8 auto Mark L Kizuto's Iona to five Paul B with chrysanthemum bartender and Greg M with Mayor Mock Shies get the results posted we're on a sapphire now


Hey everybody this is Brian and this is our 9th C++ tutorial. Today we're covering arrays. Now I'm going to cheat and show you the C++.com tutorials. They define an array as a series of elements of the same type placed in contagious memory locations that can be individually referenced by adding an index to a unique identifier. That is a mouthful. What they're really saying is an array is like a line. A line has multiple spots. Let's say there's five people standing in line. The first one is zero. Second one is number one. Now why these are zero based is because they're positions in memory. The zero position is the current and then one, two, three, four. So there's five elements. First one is zero. That's what you need to understand. Their example they use the variable name Billy. I think that's a bad representation because you're sitting here going what in the world are they talking about Billy? So we're going to actually just ignore that tutorial for now. Jump in here and actually write some code. Let's go int line. Let's say this is line at the bank and we've got five positions in that line. And we want to know how much money each person has. So we will say line zero. First person in line. Let's say he has three dollars to his name. Not very not very rich. And then line we'll say the second person. Whoops. See how they get kind of tricky with that zero base. The second person. We'll say he has eight dollars to his name. And then the line third position. We will simply say he has four dollars to his name. And for the second time I'm just going to start copying and pasting here. And we'll say six and two. That is how you assign elements to an array. Notice how it's variable name bracket position in bracket and then equals value. Now it kind of has a different uh different syntax than what you're used to if you've never really worked with arrays before. So let's review. You have a type in this case an integer. You have the variable name line bracket and the number of elements you're going to put in there. That's the total number of elements. Then in bracket and then semicolon. Then when you want to assign these you say variable name bracket position. Remember it's zero based. In bracket equals and then the value. Not to access this. You can just say end L. We'll say person. Whoops if I could spell. We'll say person two has and let's say line two. All sorts of errors today. All right let's compile this and see if this runs. I'm sure enough it runs. Say person two has four. Well what I really should have said is person that position two has four. Let's see if that's true. Two four. Yep so what happens if you try to access an element outside of your array. Notice the upper bound is a four. We're trying to access nine. Let's see what happens here. Well runtime check fail. The variable line is being used without being initialized. You get the same thing as if you try to make a variable before initializing it. Because that doesn't exist. It just does not exist in memory and of course your output is going to display some crazy number. That just happened to be the value that was in memory next to position nine would have been in memory. It gets into a little bit of math that we're not going to cover. You just need to understand how arrays work. Now the same thing happens if you just don't initialize one of these. Let's take this out and set it to three and the exact same error. So if you don't initialize you're going to have a problem. Now it doesn't want to stop. We made it angry. Okay so now you see how arrays work. Now let's just flip back over to the tutorial here. And you can see they're covering pretty much everything that I just explained to you. Now there is a way to initialize an array. Its syntax is you know the variable type, the variable name, how many, and then you have equals and then these squiggly brackets and the values. What that does is it creates the array and then it says this is the first position or zero. This is the second or one and you can see how it correlates here. So that's a very quick way of initializing an array. So let's actually do that. Whoops. And let's just get rid of that. And we're going to say we want the value of the third. Let's run this. Now before I run it can you take a guess what it's going to be? I'm sure some of you are going to go come on, run it already. So we'll run it and person two has four. Well that's misleading because it's actually person three. So zero, one, two, three. That's the third value. Now remember this is zero base so if you want the first one you do a zero. I know that seems a little bit confusing if you've never learned to raise before but I'm going through this very quickly making the assumption that this is not your first programming language and if it is excuse me I implore you go learn another language first it'll be much easier on you. I'm doing this mostly for review so we can get to more advanced things. This is Brian. I hope you found this video educational and entertaining and thank you for watching.


How can we assume the best out of people when they're super attractive? Why do we associate intelligence, leadership skills, kindness, and all these other positive qualities with how a person looks? Well a psychologist actually named Edward Thorndike, he actually coined the term for this cognitive bias we have and he called it the hail effect. He did a whole research study and a paper and the paper was actually titled The Constant Air and Psychological Ratings. It's mouthful. In this study actually Thorndike asked a few commanding officers to rate their subordinate soldiers based on a few qualities and guess what the results were? The higher the physique, the higher the ratings were on leadership skills and obedience and all these other wonderful qualities. And although being attractive means everyone kind of worshiping you sounds amazing, it can actually be a double-edged sword in a way because in a few other studies done people assumed because another person was super attractive, that they were vain, that they were mean, they just weren't a good person overall. And of course this is all dependent on the person creating this hail effect on this other human being. Now although this study was done in the 1920s, the hail effect is still happening now, today in this age. It's even led jurors to be less likely to believe a person who was very attractive could not have committed a crime, again based on their looks. Why an employer may be more likely to hire an attractive person even if their competition has the same set of skills as the other people? Or why we fancy celebrity so much? And although becoming aware of the hail effect is absolutely wonderful, you should always remember the lesson of this video. People are very, very complicated. So don't assume someone's looks reflect exactly who they are as a human being.  Maybe I used to post videos a while back, school, work, got hectic but here I am again, hopefully I can post more. If you want to check out what I've been up to, you can check me out on the Twitter's and the YouTube's Twitter, my personal YouTube channel. I also have an Instagram, a Periscope, Snapchat, all that good stuff here. I don't use them that often but I have them. If you want to add me, they're here. I'll post something here. If you can't click these wonderful annotations then you can definitely click the description box below and I'll have all my wonderful links there. But until next time, I hope you have a wonderful night. Bye.


Hello and welcome back to the craft box, my name is Brenton today. We are on episode 195 of the Wizard101 Death Walkthrough. Last time if you haven't checked out that video already you should. We finished off part one of Chrysalis, we defeated Ghostdog, we did all the things, and today we are starting part two by speaking to Zoltana. I have taken Zero Zinnia's Council and I believe it is time for you to assail Crescent and cross the Starfall Sea. Wait, what is this? You know these apparitions? Quickly, speak to them and discover what they want. Okay, we're just going to speak to these guys, I'll talk them up. Be at ease, good mantis, young wizard. It is time to throw down more ganth and her dark work. You have restored the Eclipse Tower and in so doing you have delved into shadow. I see now that it was inevitable. For I like wood not and could not teach shadow magic at Ravenwood. I have faith you will not forget our principles. Use these principles to steer yourself between light and shadow. You will need all your wits to take on more ganth. Your next step is to find the Alcazar of Radiant Judgement, a shrine to star magic. Reclaim it in order to deny more ganth its powers. More ganth and her warlords know you are about. So you must expect each league to be hard fought. Be brave and we will be with you. Jambo, young wizard. The restoration of Bastion is a wonderful sight. I'm sure more ganth still burns in anger. Of course, that may not be so good for you, but you will face her challenges with grace and skill as we know.  Take this and use it wisely. What was that? Who knows? Weird. By the spiral spellbinder, you have some powerful spirits in your corner. Travel to Fort Rockius. I've sent Zarrosinia the death song ahead to wait for you. She will guide you down to Crescent Beach. From there, you'll have to find a way to sail Starfall Sea. The ruins of the Alcazar of Radiant Judgement lie somewhere in the waves. The dying starstone you recovered from Ghostog will guide you to the Alcazar, but I do not know how you will survive the storms. Find Zarrosinia and look for a way to cross the Starfall Sea. Okay, I'll be back in just a sec once I am there. Okay, I am back so I just had to go and help one of my friends because they were desperately dying, which is not good. So anyway, I'm back now. We are heading over to the warp portal. Oh my god, we got all of these portals here. Hello. So yeah, let's see what trouble we can get up to now. That dialogue that was quite a lot actually. I'm surprised. What realm am I in? Am I in a good realm? I'm in a full realm. Of course I am. Let's go to Dwarven. That dialogue was like really quite a lot. He said he would give us something. I don't know what that was, but I don't think I got anything. So who knows. But yeah, so it kind of hinted at leaving Ravenwood I would say. Yeah, I'm also using a new pit for a bit. Yeah, yeah. Use them to burn down the barricade. Help me collect some dragon beetle pods from this cabin. Be careful. Dragon beetles. Do they know? Oh my gosh. So this sounds like a mob battle. We are going to remove Prism. I don't think we need it. Not that way. Where are we going? Where are we going? I don't know. Okay. Well, I'll be back once I'm in there. Okay, I am back. That was fun. Yeah, I've just been doing Ghost Devil 1 with Rosalyn, so that's fun. Anyway, we are back here and we are defeating these dragon beetles. What are these things? Oh my gosh. What are these? What the heck? Oh my gosh.  I was quite happy with that one. Also realized that I need to transfer my life mastery because I thought I already did, but I apparently didn't. So yeah, I should probably do that. But anyway, crit. Okay, we're already getting into crits. Geez. So this is the first battle of Part 2, so that's fun. Okay. It shouldn't be too difficult. They have no health at all. I've literally been fighting things with more health than you. Like what the hell? What the heck? What the heck? That's, yeah, that's 50. Well, we're going to hit and see what happens. We can always blade and hit again. So, yeah, that should be good. That should be good. Yeah, I forgot how much of a struggle Ghost Devil 1 was. Like, it took forever. Like, seriously, there were minions there that had 4000 health.  Why do these guys only have 2800 when like people there had like 4000? Like, what the heck? I forgot how easy this is. Like, minions just have no health. It's ridiculous. It's ridiculous. Anyway, stop complaining. Be happy that they have no health. We're going to blade, then we're going to pass, and then we're going to hit again. Hopefully, by then, they will be dead. Fingers crossed. Who knows? Hopefully. What's this? Phoenix? Okay. They love Phoenix, apparently. So that's fun. It doesn't do much, so I'm not worried. Yeah, I'm also, I don't know if I said this before because it's been literally like an hour and a half since I last recorded. No joke. I don't know if I said this, but I'm using a new pet, obviously. Obviously, I am. Slightly better. Yeah, slightly better than Xena. So, RIP Xena. You will be missed, but it has more resist and may cast unicorns, so that's fun. It should be good for a bit of questing. I mean, I've only seen, what is its name? I don't even know what its name is, but I've only seen it cast unicorn twice in about three days because I've been doing a whole bunch of sidequests. So, Abby, I need to change that name.  Terrible. Yes. But anyway, I've only seen it. I've been doing a whole bunch of sidequests. I've finished all the sidequests, the Mushu, and nearly finished them all in Dragon Spire, so I'm pretty, pretty happy with that one. That's actually where you get the Emerald Champion badge from completing all the Mushu sidequests, so yeah. I also realized that there's like no sidequests at all, and like Dragon Spire, there's barely any. It's ridiculous. Like, honestly, where are they sidequests? It's good, but like, what? That's the pod. Thank you. Let's go to talk to Zarazina. I believe she's the one we saved from Forrakius before, so that's cool. Meeting old characters, which is good. I mean, they're literally just the same world, so why not meet old characters? She's over here. Hello. Look at that. That's Crescent Beach down there. It looks so like, painted and fake. Like, it's actually really fake, but that's Crescent Beach. Okay. Here we go. Into Crescent Beach. The beetle pods burn bright. The barricade burns down, leaving little more than a pungent smell. Okay, let's go through. I'm excited. This is quite cool. I've never been here before. Whole new place. Oh my gosh, it definitely looks like a beach. So this is the map. That's quite cool. Yeah, that's quite cool. Gonna have fun with this place, I bet. Not. Crescent Beach, the Shadow Queen's grip is still strong here. Crescent Beach remains in the Shadow Queen's control, perforces train here, and keeps supplies flowing from across the sea. Crossing the storm tossed waters is challenging at best. Many have been lost to the maelstrom or vicious predators. For now, we must focus on reaching the surf. Strike down some sand crawlers to get the password into the Umbra Guard Station. Okay, let's do this. I'm gonna quickly get some health. I probably won't do as much as normal in this episode, so I'm gonna keep these battles in just to flesh it out a bit. Just because I've been trying to record this video for a long time and I've got to get other videos ready. Yeah, because I might have accidentally messed up a recording of the privateer walkthrough that was meant to go up today as I'm recording this for yesterday as you're seeing this. So I need to record another one for that, so that's gonna be fun. But yeah, we're just gonna, yeah, yeah, sorry, kind of got caught away, but it's good to help people. I mean, if people need your help, they obviously need your help, so it's good to help them. We're gonna pass and wait for a sharpen blade. Hopefully we get it next time, that would be great. And then we can wait and hit and hopefully kill. Maybe not, but we'll see. I definitely do a lot of damage. Rah, hello. Haven't seen you for a while, but I can now go and sleep. Have a five hour nap and come back after dinner and it will still be going. Maybe not, but nearly. Okay, here we go, got that. Okay, that's not what I wanted, but that's fine. We're just gonna hit because I prefer using sharpen, so yeah, we can sharpen and then we can hit again. So that's cool. How much is this gonna do? If we crit, we might be able to do a lot of damage, but we don't count on crit. If you haven't seen my gear, what I'm using, you should probably go check that out if you wonder why I don't crit. And also wonder what I'm gonna be getting when I'm level 100, which is coming up soon. Can't wait for that. Yeah, we're level 98 now, which is so close to level 100 that it's ridiculous. Sidequests really do help. Yeah, so we need one million to get to level 99, so that'll be a while. We definitely won't get that this episode, but maybe in a couple. I'm thinking we'll probably be... It won't be too long until we're level 100, which is kind of annoying because then I have to farm the gear again, which I don't mind, except it's like I don't have much time to do that in between when I record, so we'll see what happens. Weekends might be farming the gear, that'll be fun. Weekends and evenings, we'll see what I do. I'll somehow manage to do it. What is that in the... What's that there? What is that? Weird. Is that one of... Is that like a comet tail? Is that one of the reagents? I don't know. It's not sparkly. Oh, Rosalind's offline. That's unfortunate. Okay. It was comet tail. That has a really cool sound. He spoke really quiet, so that was cool. The password is... Sandcrawlers have no imagination. No, they don't. You're correct. Use the password to get us into the Umbra Guard Station. Once inside, we will have to fight. Their commander should have a signet ring. We need that to get through the Umbra Barriers and down to the seashore. Yeah, you're coming with us. Hello. Where are we going? Here, Sandcrawler. Hi.  Like, what the heck? I've kind of changed my deck a bit already from the gear video, which I did a deck setup sort of thing. Yeah, I just added a couple more blades and a couple more feints just so I can do it. You're not one of my sandcrawlers. Who let you in? I don't know how you cleverly learned our password, but it won't do you any good. Yeah, well, he's myth, so that's kind of annoying. I'm sensing some earthquakes in the future. I don't actually know if he can earthquake, but probably wouldn't be surprised. Yes, let's do that. What are we doing? What is his name? Let's see. He can Medusa? Okay, that's cool. Damn, didn't... Bizarre. Let's see if he can earthquake. He can Medusa, so that's fun. He can earthquake as well, so we're screwed. He can also Basilis, so we're completely screwed. Yay. Oh, gosh. First boss of part two, and we're already stunned for two rounds. Isn't that fantastic? I just love this game sometimes. Like, I really do. This game is so great. We go second and we're stunned for two rounds.  Ridiculous. Okay, but now we can hit, so that's good. Or not have Blade. It's already Jews, who I think I am. We can Blade. What does she give us? I always forget what she gives us. Does she give Pierce and Accuracy, so we won't Fizzle. And we don't need Pierce anyway, so that's not the best. I preferred Divim. He gave us a decent amount of Resist and a good amount of damage. Like, a lot of damage, so I preferred that. Hopefully we meet Divim again. That would be great, because he's great. But, um, no, Accuracy and Pierce isn't really good.  I need some Sharpenblades, that would be great. And some Fence as well, that would also be great.  He doesn't have much health, though, compared to his Tickerbosses. Um, 18,000, I think. Yep, 18,000, yeah. Yeah. There we go, there's that. Partway to Faint, okay. That was a Sharpenblade, correct. Yes, we can do this one. Not sure what do we get if we draw. Okay, here, that's not the best, but, um, I mean, I could probably do that. We also now don't have, um, 100% Powerpip because of my pet. We have 98, I think, or 97, which is still a lot, so I'm not worried, but we don't have 100% anymore. I didn't actually realize that we had 100% until we did that, um, video, so that's a bit funny. But we now have a Shadowpip, not that I actually think I forgot to put Shadowpip, so I was like, oh well, it doesn't really matter at this point, um, just because he really cares at the moment. He's not deaf, so it doesn't matter. There's a nice wee faint, number one. There we go, that's good. We don't need two of you at the same time. Hopefully we can get a blade. I think I put one blade in, maybe. One blade in, maybe. One blade in, maybe, yay. Fantastic. Epic. He has an earthquake. As soon as the earthquake, I'm going to be annoyed. This is a six-perp humongous frog, so that's always nice. This is going to do just a tad. Just a tad. Just a tad, yep. Six-perp humongous frog is AP, OPGs. Aren't even English today. I haven't done enough to England today. Um, yeah, I put a fortifier in. Not going to use that now, am I? No. We're going to do this, and then probably going to hurt, maybe. Yeah, we'll see. It depends how he goes with perp-wise and how I go with health-wise, because the sooner I hit, the sooner they die, basically. Yeah, I might have to hit next. I'll definitely hit next. Probably a good idea. We've got one, two, three, four blades, I believe that's four, I think. Got that. I mean, I'm keen. Really keen to do that, but we're going to avenge him just because we can. He's not going to hurt me. What? She's not going to... Nobody's going to hurt me? Yeah. And I would have been fine to faint and then hurt next, but, you know, sometimes you just can't risk it, because it can have earthquakes as well, I believe. So, yeah. Oh, no, he can't. Yeah, he can, if he gets a powerpup. But she never know what could happen. So, yeah, that was a decent amount of blades. This should do a lot. And then the overtime as well. Okay, he's dead by. I really, like, underrate myself. Sometimes I just underrate my power, mainly because I don't actually use avenging all that often, so I don't actually know how much it does. Yeah, we are going to, I mean, do this in day and night. That works. Oh, that's doing so much. Oh, my gosh. That's okay. Okay, avenging is okay. I know that, but like, OP is free. Can you heal, pet? That would be great. No, okay, that's fine. Literally, my pet only heals, like, once in a blue moon.  He could be dead now. Well, that's that done. Will I not? That's what you think we're going to heal up, because we need health disparately, just in case we get pulled into battle, because there's mobs right out here. Hi. Where are we going? Zera's in here. Hi. Okay, so we're going to quickly head through here. I believe there's a couple more defeating collect and stuff coming up, so we're just going to head through, and then we're going to defeat and collect information from them in between episodes, so that will be cool. This is Crescent Beach, basically. I haven't actually been here, so I'm assuming this is the rest of it? We're here for a while. This is so cool. I'm sorry, I've never been here. This is what I'm like when I go to a place for the first time. I just spend a long time, just like, oh my god, this is so cool. That sound effect is so cool. I can't do this, like, oh my gosh. But anyway, thank you for watching. We're going to try that again. Thank you for watching. Remember to leave a like and subscribe, and if you're very subscribed, if you're, oh my gosh, thank you for watching. Remember to leave a like and subscribe, and if you're very subscribed, press the little bell. Oh my god, I swear I can't speak today. Press the little bell so you know exactly when I post another video. And remember, craft outside the box. That was the worst outro I've ever done. I swear, oh my god.


Why didn't the narcissist hoover you?  It's an attempt to see if a prior target of abuse can be lowered into another cycle of abuse. It's an attempt to see if they can get more supply. The narcissist doesn't return because they love you or care for you. They see you as an object that exists to meet their needs. They will come back if they think they can get more attention and emotional reactions. If they think they can get money or a place to live, they're not coming back because they care about you. It's only if they believe there's a benefit or gain for them to do that. Narcissists are self-absorbed and they lack empathy. They only care about their own feelings and needs. They are constantly in survival mode. They are constantly looking for something to fuel them, regardless of how it affects the person they're dealing with. They will often fuel themselves at other people's expense by using them for attention, money or as an emotional tampon. And if you are a good source of supply, they may return to you. But that really depends on how the relationship ended. There are always going to be reasons why the narcissist didn't hover you. If the relationship ended with you questioning or confronting the narcissist, that is one of the main reasons why they didn't hover you. The narcissist does not want to be around someone who is onto them. They do not want to be around someone who knows what they're about. When you're constantly confronting them, it makes their lives very difficult. They can see that you're waking up and that's a sign for the narcissist to get out of there. It's a sign for them to never return because they already know that knowing in a sane state of mind would deal with them. If they knew what they're trying to do, if they knew what they're about, which is why they have this disguise. They don't take off the mask until you're already trapped and when you do try to confront them, they get very angry. They shift the blame onto you and try to make you feel bad for confronting them.  It's designed to take the focus off of them so that they can continue doing what they're doing without being confronted on it. But if you continue confronting them and getting in the way of their agenda, it will pose a problem for them and that is something that they will remember when they leave you. They will remember how you confronted them. They will remember how you kept asking them questions. You made it difficult for them so they will be less likely to return to you. The narcissist is only going to hoover someone if they believe that they are still susceptible to their manipulation. If they believe that they still believe in their false self and the lies and illusions that they try to portray. That is the deciding factor in whether or not they will return to you. They're not going to put themselves in a position where they know that they're going to be rejected. Where they know that they're going to be humiliated. They're not going to put themselves in a position where they know that agenda is going to be more difficult. So if the narcissist doesn't hoover you, you should see it as a good thing. You should take it as a compliment because when the narcissist is looking to hoover someone, they're looking for a fool. They're looking for someone who they can trick and deceive and if they didn't hoover you, that means they don't see you as a fool anymore. That means they know you have woken up and they're not going to want to deal with you anymore. The narcissist only hoovers people who they perceive as being naive. People who they perceive as showing a lack of experience, wisdom and judgment. People who they expect to be easy to take advantage of. They will hoover those people and they will take whatever they can get and then leave on their board. Being a target of a narcissist hoover is not a good thing. It's not something to be proud of.  They see you as someone who is naive and they see you as a doormat. They see you as someone who's going to let them do whatever they want and get away with it. So if the narcissist didn't hoover you, you should take that as a compliment. That is something to be proud of because that means that you have won. That means you are too knowledgeable and wise for them to deal with. They're looking for someone who's just got their hand over the goods with no questions asked. Someone who doesn't really value themselves and they know you're just not that person anymore. They know that you've realized your worth. They know that you deserve better. So why would they come back just to make themselves look like fools just so you can remind them of all of the reasons why you deserve so much more? They'd rather settle with someone for less. Someone who doesn't expect so much from them. Someone who will give them what they need without expecting anything in return. But at some point those people will wake up just like you did and then the narcissist will be forced to find someone else. They can only remain around someone while they are still under their spell and if you have woken up, they can't be around you anymore towards the end of the relationship. The narcissist started devaluing you. They went from seeing you as someone who was perfect to being someone who was completely flawed. They no longer valued or appreciated you. They refused to take responsibility for their actions and shifted the blame onto you. They smeared your name and made everyone believe that you were this horrible person even though that was not true. Even though they were just trying to take everyone's focus off of them. They didn't want to be seen as the problem. So they blamed you and they got everyone else to believe that it was your fault. They made it known that you were the bad guy and you didn't treat them right and they thought that doing this was going to be in their best interest. But by doing that they actually ended up shooting themselves in the foot because now they can't come back to you. They can't hoover you even if they wanted to because they know how that's going to look after everything they said about you.  They made you look like the bad guy and all narcissists really care about is their image of reputation. All they really care about is how they look to other people and for them to consider returning to you. After they smeared your name they would have to choose you over their false self and that's just something no narcissist is going to do. Thank you for watching. I hope this video resonated with you. Please like, comment, share and subscribe. If you would like to donate my PayPal link is in the video description. Coach the Inquiries, you can email me at coach.narxvivert.uk Thank you for watching and I'll talk to you soon.


The Beltrami County fairgrounds were bustling with excitement and anticipation as a 2018 fair got underway today. All morning and afternoon vendors and exhibitors were busy setting up and entering their projects and animals in the fair. Employees of Gopher State Midway were also hard at work setting up rides and games for the big opening night. This year's fair is one of the largest in recent years and is said to provide infotainment for kids of all ages. We have a good strong livestock display and surveys show that the number one reason people come to the fair is for uh to see the animals. You know kids nowadays don't have exposure to farm animals like they did when I was a kid.  So uh our big theme in the kids farm here this year is where does your food come from? If you happen to be out at the Beltrami County Fair be sure to stop by our Lakeland PBS building. A booth I should say we don't have our own building yet. We're located next to the fire tower on the northwest side of the commercial exhibits building. We do have treats and free giveaways for the kids and giveaways for you as well and about we'll give you information about six PBS channels that Lakeland provides for you. This is also your opportunity to win a pair of tickets or upcoming Celtic Thunder Concert. A fair booth is also an excellent way to get in on our crews with the news giveaway which will have a little more information coming up on tonight. Stop by and sign up before we give that cruise away in the next couple of weeks. Our Lakeland staff will be out there. I'll be there Saturday noon to four and we look forward to meeting you all. The Beltrami County Fair runs daily through Sunday. If you enjoyed this segment of Lakeland news please consider making a tax-deductible contribution to Lakeland PBS.


So, here's what we know about the harmonic oscillator so far. We know there's equally spaced energy levels starting with the ground energy level that has an energy of 1.5H nu, where nu is the fundamental vibrational frequency. We can calculate that if we know the spring constant and the reduced mass of the molecule. And the spacing between each one of these levels, regardless of whether it's the first pair, the second pair, the third pair, each of these energy levels is separated by the same gap, h times this vibrational frequency, or if we prefer k Boltzmann's constant times the vibrational temperature, where we have defined the vibrational temperature as h nu divided by k. So, we've also seen that for a typical diatomic molecule, this vibrational temperature is somewhere in the vicinity of roughly 1000 Kelvin or so. Depends on the individual molecule. Every molecule has a different mass, reduced mass. Spring constant, but it's somewhere in the vicinity of a few thousand Kelvin, typically. That raises the question, how big are these energy gaps? Of course, they're h times nu, but what is that frequency? With what frequency of light would we need to excite a transition from the state up to this state? Or, equivalently, so if that gap in energy is equal to h times nu, we would like to know what is that nu? Equivalently, if we'd rather have it in units of wave numbers, what would the wave number of the light be? Or perhaps we want to know what is the wavelength of light needed to excite that transition? And that'll tell us whether we should shine visible light, ultraviolet light, infrared light on the molecule to excite these vibrational transitions. So, as an example, let's again take carbon monoxide, where we know, we've seen previously, that the vibrational frequency is 6.5 times 10 to the 13th hertz. 6.5 times 10 to the 13th per second, number of oscillations per second. And then if we want to know, let's do the wave number first. So if the frequency is c times the wave number, then the wave number is the frequency divided by the speed of light. So that's relatively straightforward arithmetic. Speed of light is 3 times 10 to the 8th meters per second. Although, looking ahead, we typically want to talk about wave numbers not in units of 1 over meters, but 1 over centimeters. So I'm going to list the speed of light in units of centimeters per second. Light travels 3 times 10 to the 8th meters in a second, or 3 times 10 to the 10th, 100 times as many centimeters in every second. So if I do that math, this frequency divided by the speed of light, I can almost do that in my head. But to a few more sig figs, the units 1 over seconds cancels top and bottom. I'm left with 1 over centimeters. I'll write that as centimeters to the negative 1. And we find that the light needed to excite a transition from this state to this state or from the state to this state between any adjacent pair of states has a wave number of 2160 inverse centimeters. So if you think back to or remember the discussion about the different portions of the electromagnetic spectrum, that falls squarely in the middle of the infrared portion of the spectrum. So this is infrared light of this wave number needed to excite this particular vibrational transition for carbon monoxide. In terms of wavelength, the wavelength of light needed, so hc times new tilde is equal to hc times 1 over lambda. So the wave number and the wavelength are reciprocals of one another. So if I already know new tilde, I can just take 1 over that quantity to find the wavelength. So that's 1 over 2160 inverse centimeters, which works out to be in those units, 4.6 times 10 to the minus 4. If I invert 1 over centimeters, I get regular centimeters. So 4.6 times 10 to the minus 4 centimeters is the wavelength of light. If I find some photons with wavelength 4.6 times 10 to the minus 4 centimeters, that's the right energy of wavelength of light to excite these transitions. Now it's probably more convenient to convert that away from centimeters. If I divide by 100 to convert centimeters to meters, that many centimeters is 100 fold fewer meters. So 4.6 times 10 to the minus 6 meters, or we can convert that to using SI prefixes 4.6 micrometers. So the wavelength of light needed to make this transition is 4.6 micrometers. And again, that wavelength is in the region of the electromagnetic spectrum, electromagnetic spectrum that we call the infrared portion of the spectrum. So both that number and that number tell us that, in fact, the light we need is infrared light. So that's maybe something you know already from other chemistry courses, like analytical chemistry or organic chemistry. Very often infrared spectroscopy is what we use to identify specific molecules. And that's because carbon monoxide with its particular spring constant, its particular reduced mass has a very individual specific frequency of light required to excite these transitions. So if molecules absorb this frequency of light, that's a good clue that there might be carbon monoxide in our sample. And likewise for other organic molecules, each bond of which has its own spring constant and its own reduced mass, I suppose I should point out that it's not just diatomic molecules. So we've, let me draw a carbon monoxide vertically. So here's my carbon monoxide molecule, sorry, double bonded carbon monoxide molecule with a spring constant reduced mass that we can use to tell us this number for the frequency. Let's suppose we have another molecule with a carbon oxygen bond, a molecule like let's say acetone. So there might be the four carbon monoxide. We can calculate that reduced mass using the mass of the carbon, the mass of the oxygen. Let me go ahead and put the triple bond back there. That reduced mass, if we know the mass of carbon is 12, the mass of oxygen is 16, we can calculate that reduced mass. We could do something very similar for acetone. And then if we're talking about that CO bond stretch, the reduced mass that we need would end up using the, so that's the bond between the oxygen and this carbon CH3 2 unit. So the mass of this unit, the mass of this unit could give us the reduced mass for this quantity and that, that's a different number than it is for carbon monoxide. But it's not terribly different, it's in the same ballpark. So it's still going to be a frequency of infrared radiation, but it's going to be a different frequency of infrared radiation. So every individual molecule has its own signature, its own absorption energies in the infrared spectrum. So that's why we use infrared spectroscopy as sort of a fingerprint to identify specific molecules. So the other thing that this may, other reason you may know infrared spectroscopy is used to excite vibrational transitions is because the way we experience infrared light, infrared is not in the visible portion of the spectrum, it's off the red end of the spectrum. If you have any previous experience with infrared light outside of a chemistry lab, it might be, for example, in a fast food restaurant using a warming lamp, lights that don't give off very much light but are very good at heating the food underneath them, those lights give off infrared radiation. So we think of infrared radiation very often as simply heat. And the reason that's true is because the infrared photons that are coming out of an infrared light source excite these vibrational transitions, cause molecules to vibrate with more energy than they were previously. As those bonds vibrate, they cause lots of collisions within the material and then that heat turns into energy that's stored in other portions of the molecule so that infrared energy gets converted first to vibrational energy and then to other forms of energy within the molecule. So that's how infrared energy is used to heat molecules up. So we know how to predict now what types of light, what colors of infrared light to use to excite these vibrational transitions if we know the fundamental vibrational frequency for molecules that behave like harmonic oscillators. The next question is to ask which of these transitions are actually allowable and so we'll talk about the selection rules for harmonic oscillators next.


Hi everyone, Joe for jaspyscasebreaks.com here coming at you with jaspys the diamond dozen Baseball break a product a repack product curated by us Just for you the collector big. Thanks to this group right here for making it happen Thanks to the people who bought their spots straight up congrats again to the people who won spots in that capstone filler all 30 teams are in Let's roll it. Let's randomize names and teams one and a three four times each one two three and four After four we got Greg down to Dan Then one and a three four times for the teams one two three and four After four we got the halos down to the rays All right, here's how the randomizer shakes out for you Greg You got the angels Nicole with the Giants Ken with the diamond bags Josh with the Cardinals James with the Marlins Ivan with the Rockies Ed with the Astros Jordan. You got my Dodgers Matthew with the Braves Ed with the Tigers James with the Red Sox Daniel with the Reds Jordan with the White Sox Logan with the Mariners Josh with the Yankees Jim with the Rangers Logan with the Royals Matthew with the Orioles last spot mojo Daniel with the Brew Crew Jeremy with the Phillies Ken with the A's Tristan Blue Jays and Cubs James with the Nats Matthew with the Guardians Jared with the Pirate Zach with the Mets James with the Padres Devin with the Twins and Daniel with the Tampa Bay Rays So let's sort by Team and feel free to trade trade window is open. Remember trade at your own risk Keep an eye on some of the break previous breaks Next breaks also loaded up Jasper's case race comm now before I pause the video for the trade window Let's go here. Let's generate a number. So if you watch the break we did last night. We did case 8 So those are the case numbers remaining. So let's generate a number Number four, we have not done four. So that's the case. We're gonna do There it is diamond doesn't case number four All right, so now we're gonna go ahead and pause the video when we come back We're gonna see if there's any trades and then we'll have the break stick around. We'll see on the other side All right. Welcome back ladies and gentlemen. No deals were done. There was a lot of trade chatter But in the end no deals were done Here in the diamond doesn't to Thanks everyone for making this happen appreciate it and remember doing case four So we got those cases remaining And maybe we can run another one back tonight All right, there it is. Jasper's the diamond doesn't let's see what we got here Good luck. Good luck. Good luck. Some nice stuff in here. There's some graded cards in here I'm gonna do the non graded cards first. I'll feel around for those All right. Good luck everybody. Here we go. We're gonna lead off with Chris Bryant Rookie Chris Bryant Rookie silhouette relic and on-card autograph 11 out of 49 Nice that's gonna go to Tristan with the Cubs Next up is nice Louise Robert Like that fireworks pattern right there. That's 38 out of 99 Nice one for the South Siders. That's for Jordan back-to-back Chicago That's a graded card on here's a non graded. It's Nice Gretz prospect. Allie Della Cruz one of one of their top prospects Daniel with the red legs. All right We have a one-of-one Esteban Floriel clutch Nike swoosh relic and autograph Nice immaculate baseball hit for the Yankees. That's gonna go to Josh. Yo, it's Josh All aboard the Big Hit Express Are the rest of these graded? The rest of these are great and there's something else inside here interesting. All right and check all that out We got a PSA 10 Juan Soto from Gypsy Queen. Looks like a font swap variation as well Still national edition here that goes to James Then we've got Ezekiel Tovar PSA 10 for the Rockies that's gonna go to Ivan tried to trade couldn't trade mojo and we have We got a Barry Bonds You don't see a lot of Barry Bonds autographs Nice 2002 Fleer showcase Barry Bonds PSA 8 Game-worn Jersey authentic autograph That's 301 out of 400. Is that like 400 bucks? Wow Giants Nicole And we've got beam a team Derek Jeter 30 out of 40 PSA 10 from 2022 Stadium Club another Yankee for Josh then We got a hammer and Hank Aaron from transcendent PSA 10 love seeing the tens 21 out of 95 And the last slab is 2020 tops complete set your dawn Alvarez blue. It's his rookie card PSA 10 and that's gonna be for Houston That's for ed P Now there's two extra cards in here. What is this Marlins get $500 in break credit? Look at that. That's James with the Marlins I'll email that break credit to you. It'll arrive to you as a break credit code Gift card code it never expires and you don't have to use all of it at once Congrats, and we got another one here Pirates getting $500 in break credit. Wow that goes to Jared Pollard with the Pittsburgh Pirates We'll email you that code. It's a gift card code could be a could be in your spam folder double-check that Congrats You don't use all that at once it retains the code the balance for you never expires There you go gang, I'm Joe for jazby's case race calm and that was the jazby's diamond dozen Next cases in the store check it out, and I'll see you next time for the next one. Bye. Bye


The first piece that she wanted me to read is called When I Take Off My Mask, and this is by a ninth grader from June Jordan School for Equity. When I take off my mask, you'd think I'd feel free. Free to act how I want with no insecurities. But I've tried. Tried to slowly rip off this mask. But I've realized in this world, I can't. I can't afford to get hurt once more. Especially not by the people I love and adore. That's why I wear this mask. I'm afraid they'll ask why. Why I chose to stay silent and hide. All I can say is, I'm sorry, I didn't mean to lie. So that was When I Take Off My Mask.


Hello and welcome to the session. Let us discuss the following question today. For which value of k will the following pair of linear equations have no solution? We have 3x plus y is equal to 1 and 2k minus 1x plus k minus 1y is equal to 2k plus 1. Now let us write the solution. Given equations are 3x plus y is equal to 1 and 2k minus 1x plus k minus 1y is equal to 2k plus 1. Comparing the equations with a1x plus b1y plus c1 is equal to 0 and a2x plus b2y plus c2 is equal to 0. We get a1 is equal to 3, a2 is equal to 2k minus 1, b1 is equal to 1, b2 is equal to k minus 1, c1 is equal to 1 and c2 is equal to 2k plus 1. Now we get a1 by a2 is equal to 3 by 2k minus 1, b1 by b2 is equal to 1 by k minus 1, c1 by c2 is equal to 1 by 2k plus 1. Now the given system of equations has no solution if a1 by a2 is equal to b1 by b2 is not equal to c1 by c2. Therefore 3 by 2k minus 1 is equal to 1 by k minus 1 is not equal to 1 by 2k plus 1.  Now, here for k is equal to 2 we have 1 by k minus 1 is not equal to 1 by 2 k plus 1. Hence, the given system of equation will have no solution if k is equal to 2. So, the required value of k is 2. I hope you understood the question by and have a nice day.


So now that we understand symmetry operations and the symmetry elements of a molecule, we're almost ready to understand the statement, which we'll really consider in the next video actually. The statement that the symmetry elements of a molecule form a group. But before we can understand what that statement really means, we need to understand what is the thing I just called a group in the mathematical sense. This general idea of group theory is the mathematics of these objects called groups. And it turns out a group, you're somewhat familiar with them by experience already, even if you've not heard that name before. A group consists of two things, it consists of a set of elements, so a set like you're familiar with from introductory math classes, and an operation that tells you how to combine two elements of that set. So to help make this a little more concrete and understandable, we'll use some examples. The main example we'll use to understand the properties of a group is the integers. So I'll let the integers 0, 1, 2, 3, and so on, and also the negative values, negative 1, negative 2, and so on. So that full set of integers is the set that we'll be thinking of, the operation with which we'll combine those integers. We can combine the integers in various ways, we can add them, subtract them, divide them. So the operation we'll consider is addition. So as we talk about the properties of a group, we'll use adding of integers to understand what those properties mean. So not everything is a group, a group is a set in an operation that has the following four properties. So there's four of them. The first one is that the operation needs to be associative in the same sense that in elementary school when you learned about the associative law and the commutative law and the distributive law, associativity means the same thing here. Whatever my operation is, so again, maybe my operation is addition or multiplication or some other operation. If I have some element of a set and I want to combine it with another element of the set, I don't want to write plus or times here because these are not rules specific to adding or multiplying. For my operation, I'm just going to use a circle. So a circled with b, a added or multiplied or whatever with b, a combined with this operation with b. If I do a and b and then combine it with c, combine the result with c, that's going to work out to be the same as a combined with the result of b and c. So that's the associative property like you're used to. As our example over here, it's certainly true that if I just take some of these integers, if I take 1 plus 2 and add that to 3, that's going to be the same as if I take 1 plus the result of 2 plus 3. You're certainly used to addition being associative. You use that almost every time you do any arithmetic or algebra. It doesn't matter in what order you add these numbers together, you get the same result. So addition is associative. Addition of integers in particular is also associative. So that property is satisfied by addition. The second property that a group needs to have is there has to be an identity element in the set somewhere. So what that means is that if I take an element from the set, one of these numbers, for example, there must be some element, the identity element, that I can combine it with and get back the same number as I started with. So the identity is a particular element of the set that no matter what element I combine with it, I get back the same element I started with. So the identity element in addition is 0. If I take 2 plus 0, I get back 2. If I take 3 plus 0, I get back 3 and so on. So no matter what element of the set, if I add 0 to it, I get back the same element I started with, so 0 is the identity. A key point about the identity is there's only allowed to be one identity element. The same identity element, 0, has to be the element that you add to any element to get back itself. The third, and in some ways the most interesting property, the most characteristic property of this groups, is that the set needs to be closed under the operation. That one might begin to sound a little bit unfamiliar, but what that means is if I take any element from my set, I combine it with any other element from the set, I'm going to get a result. That result needs to be in the set. So in other words, what closed means is the set is closed under this operation. If I perform an operation between two elements, the results of that lands back in the set. It doesn't ever land outside of the set. I don't get a new element when I perform an operation between these elements of the set. So A operating with B must be in the set. That's what it means for the set to be closed under our operation. For the case of adding integers, that again is clearly true. If I take 1 plus 2, I get 3, and that's already in the set. No matter how big the integers I take, if I take 100 plus a million, I get 1,100, that's also an integer. So I can't find two integers that I can add together and I won't get an integer. So that set is closed under addition. And then the last of the four properties that we need to consider is that every element of the set needs to have an inverse. So watch carefully the difference between the identity and the inverse because it's easy to get these confused. There's one identity element that works when you combine it with any element. Inverse says, if there's an element of the set, there must be some inverse that I can combine it with. I'll write that as A inverse. And when I combine A with its inverse, what I get back is the identity. So if this is one of the elements in the set, this also must be in the set. But every element is allowed to have its own unique identity if it wants to. So how does that work for addition? Let's say I take the number five. What is the inverse of five? What number do I combine? Do I add to five to get back the identity? Identity was zero. So if I add five and negative five, I get back the identity. I get back zero. If I combine four with negative four, then I get back zero. But notice that the inverse of five is negative five. The inverse of four is negative four. Every element of the set is allowed to have its own individual inverse. There doesn't have to be a single inverse, like there does for the identity. So those are the four properties. If you have a set, you have an operation for how to combine elements of the set. And the set under the operation has these four properties. Then we say that that set and that operation form a group. So our example has shown us by validating each of these four properties that the integers under the operation of addition do form a mathematical group. So integers form a group under addition is the way we would phrase that. One important thing to notice is that a group is not just a set and involves both the set and the operation. So it's not correct for me to say the integers form a group, for example. I would have to say the integers form a group under addition. If I were to choose a different operation, let's say I were to take integers as my set and multiplication as my operation. Multiplication. So I can ask integers under the operation of multiplication does that or does it not form a group? Well, we would have to go through and check each of these properties. Starting, it might intuitively seem like they form a group. Multiplication is associative, it doesn't matter what order I multiply numbers in. There is an identity, what number can you multiply an integer by to get back the same number? That number is one. So the multiplicative identity is one. One is a number that's in the set. So there is an identity, multiplication is associative. Is the set closed? Can I take any two integers and multiply them together and get something that's not an integer? Nope, I can't. Any product of two integers is going to be another integer. So far so good. The set is closed under multiplication. But it turns out there's not an inverse. If I ask, what do I need to multiply five by to get the multiplicative inverse? What do I need to multiply five by to get one? I need to multiply it by one-fifth. The multiplicative inverse of five is one-fifth. But one-fifth is not an integer, that's not in the set. So because many elements of the integers, their inverse is not in the set of integers. It doesn't obey this fourth condition. So multiplication of integers does not form a group. So that illustrates this point that you can't say whether the integers are or are not a group. They are a group under addition, they're not a group under multiplication. A couple of other features to point out about groups. Many of the groups we can think of using ordinary mathematics are infinite sets like the integers. There's an infinite number of integers. And that seems reasonable because every time I combine two integers, I might get something larger. So I keep having to make the set larger when I combine the integers to make larger ones. But it turns out there are groups that are not infinitely large. So just as one final example, and we won't work through it in detail. But the numbers on a clock under the arithmetic of clock arithmetic form a group. So the numbers 1 through 12, 1 o'clock, 2 o'clock, 3 o'clock, up to 12 o'clock. And then adding those times together form a group, even though there's only 12 of them. So for example, that set is closed because if it's 10 o'clock now and I want to know what time it is four hours from now, it won't be 14 o'clock. If you're using a 12 hour clock, it'll be 2 o'clock. So once you go off the top of the 12 o'clock list, you circle back around to 1 o'clock, 2 o'clock. So that would be an example of a group with only a finite number of elements, only 12 hours on the clock that is closed. You can think about it hard enough to decide that it's also associative. There is an identity, there's also inverses. So there are finite groups and in fact, the elements of a group don't even have to be numbers like they are on a clock or in the integers. It's possible to have a group composed of elements that are not numbers at all. And in fact, that's what we'll do when we talk about molecules. The symmetry elements of those molecules are not numbers, but they happen to form a group when we combine them in the right way. So that's what we'll talk about next.


I think one of the biggest challenges at a large university is this sense of isolation between the disciplines, between the units and being a saddle specialist that gets to work trans-disciplinarily has given me the opportunity to just realize that they're constructed barriers. All of a saddle specialist, as I experienced it, is to sort of work as a part of a team and then we are paired up with faculty members across different disciplines and faculties to work on a project that they're interested in, in the scholarship of teaching and learning. The role as a saddle specialist really is very dynamic. I am in the faculty of education, but I have training in other social sciences, in particular political science, and I never really would have had the opportunity to engage in science faculty on issues of dealing with chemistry and physics type questions or land and food systems questions. The ability to get to collaborate with faculty members from across disciplines has been truly unique and really special as a saddle specialist. The saddle team is very diverse and what is great about it I think is that we have some specialists who come from a quantitative background, some specialists who come from a qualitative background, and then others who are really great at moving in between those worlds and do mixed methods. This kind of community and connection here is exceptional and it's more than just working in a lab. It is this wonderfully diverse team, it's wonderfully supportive and friendly team. As a PhD student, I end up just doing an awful lot of work on my own, on particular projects and things and having a community of practice as it were in this is really helpful and it's it's motivating too because you know other people who are doing other things and you want to share. So in terms of social support, this has been a godsend. It's way too easy to be stuck with research in a purely limited academic sense and not understanding the full implications. So I think that this has given me incredibly valuable real world experience in terms of research.