And it all kind of happens for you all of my groceries Your new video so I'm just about to go run errands. I had a really productive morning worked out showered I even washed my hair so I just finished doing that because it takes me so long to do my hair my Carrot and treatment if you guys didn't know I got like a carrot and treatment and it's honestly wearing off now And I'm just gonna wait a couple more months I think I'm gonna get it done again in June so that it's fresh for the summer And then I don't need to worry about like doing my hair in the summer Because then I can go swimming and I feel like that's just the best way to do it because if I do it now Then it's gonna wear off a little bit for the summer and I want it to be like super fresh for the summer So I'm just gonna wait it out and get the carrot and treatment down again Because it's honestly like the best thing that I've ever done for my hair But anyways, so I'm just going to go grocery shopping run a couple errands is my fit I'm wearing the Nike's with these jeans that I thrifted and then just this plain white basic t-shirt from H&M And then this person I wear every single day So usually I would start off this vlog in the mirror that we have in our house But as you can see it's not there anymore And the story is actually quite tragic. I'm over it now like it's fine So one morning I come out I was in the bedroom and I wake up And I literally like just walked into the bathroom Walked into the kitchen and I went back in the room and then all of a sudden I hear this huge ginormous Crash and I'm like what was that like don't tell me that was a mirror and I walk out and the mirror literally from this wall just face planted onto the floor and Glass it wasn't everywhere, but it was just like shattered so we couldn't just like pick the mirror up it was Very tragic. Honestly, I have no idea how that happened because my mirror at my house I have like a full-length mirror in my room And I've had the mirror leaned up against the wall for like five years now And I never have hung it up and it stayed like it's never fallen So I thought that by putting the mirror on this wall is like, oh, it's fine Like my mirror at home that I've had on my wall for like five years have never fallen So why would this fall right? I didn't even like expect that and Then below and behold, I don't know what happened. I don't know how it happened, but obviously it wasn't Like seated up correctly. I don't even know but it crashed it fell and Kind of tragic because this is like my favorite Honestly the favorite thing that we have in the house right now just because I would vlog there I would take pictures there. It's just like such an iconic moment right here. So we're gonna buy a new one I'm probably not gonna go today just because since I'm going out alone That's kind of a lot for me to do and I don't even know if that would fit in my car Like it's kind of too heavy for me So I'm gonna wait till I can go with Joel one day and we're gonna get a new one It's just like an IKEA mirror. It's a habit mirror It's $150 which is really tragic that I have to spend that again But it's like not the end of the world the most important part and like to make light out of these situations You just got to tell yourself like everything happens for a reason. Nobody got hurt We cleaned it up safely like it was all fine. So I'm not trying to be mad about it Like yeah, I was a little bit disappointing, but it's not something like that.   It's fine. It's not even tragic like it's honestly just kind of Disappointing okay, I just got to Starbucks and I'm gonna treat myself today I'm gonna get a thinking of getting a brown sugar Oatryk and espresso, but the thing is with that drink is every single time I order it they make a different I don't know how to explain it, but they literally make a different every time and it's not consistently good One day I'll get it and it's like so good and then the next day I'll get it and it's like not as good I think I'm also gonna get one of their breakfast sandwiches because I had a smoothie today had that right after my workout But I didn't have like anything to eat after and usually like I do and I'm kind of hungry right now And I don't want to be hungry going into running these errands or else I know that I'm just gonna buy everything that I see That's like one tip is to never grocery shop while you're hungry or else you will over buy like When I'm hungry and I go grocery shopping, it's not it's not a good mix So they don't have a drive-through here, but I'm literally gonna put the order through on my phone and then just walking to get it Okay, I got the brown sugar Oatryk and espresso and the sandwich I'm thinking I'm just gonna sit here and eat for a bit just so I can not eat and drive because I eat doing that I just got to the grocery store But I just filled up on gas and in the city that I used to live in like when I lived with my parents They would it wasn't like self-serve gas like you would go when you get gas and you would fill it up yourself And I didn't realize that here most of the gas stations are not self-serve They have like someone to do it for you But I have like no idea because I feel that I won gas station here at this whole time and it was Self-serve so you would do it yourself But this gas station that I went to they had a worker there that did it for you and I felt like an idiot because I had no idea So like I went out and I'm like what is he doing like coming up to me and then I like put my card I'm like, uh, and he's just like they're standing and I'm like what the heck is he doing? He's like can you open your gas cap?  Anyway, so we're gonna go grocery shopping now I came to a store that's I think everything is like organic in here so i'm gonna pick up like vegetables And mainly like fruit and stuff it is a little pricier here, but I would spend the extra coin for organic and healthier natural local vegetables and fruits I just feel like that's worth it. I'll bring you guys inside because it's so cute in here actually Okay, so I'm officially finished grocery shopping. I hope I didn't forget anything I'll give you guys a nice grocery haul when we get home It's actually such a beautiful day outside like I didn't even need to wear sweaters like a little bit chilly But the sun kind of heats things up. Which is so exciting I am literally so excited for summer like comment down below if you're excited for summer because I sure am And the summer content you guys it's gonna be on a different level. It's gonna I literally cannot wait as of right now. I don't really have like any plans for the summer But I definitely want to plan a couple of trips. So let me know if you guys have any summer plans Okay, guys, so I just got home And I'm just the parking garage right now, but I was driving and whenever I drive and listen to music I get so motivated. I don't know what it is But like just listening to music Your favorite songs and driving and just like being in a happy mental State appreciating life It's just the best but anyways, I just feel really motivated to turn on the camera right now So I was just like thinking back to when I first started Taking this youtube channel seriously when I first started posting and at that point Like I wasn't really making an income off of it And I had a goal and my goal was like in one year. I want to be self-sufficient. I want to be able to um be financially stable and Be able to be like on my own make my own money And it's like now that I reach that goal I'm looking back at that time when I was working towards this goal And I'm like, holy shit like I kind of miss that like I kind of miss that period of my life And that's why it's so important to appreciate every single stage of life that you're in even though if it's not like the greatest and even if you're Right now you're working towards a goal that you want to achieve Make sure to take those moments in even if you it's hard to see the light at the end of the tunnel Make sure to still appreciate every single step of your journey and Every single step that you take just appreciate it and soak in the moment and don't rush anything Like there's no point of rushing anything and trying to get to the finish line so fast because Everything is going to happen in due time and everything is going to happen and unfold exactly the way that it's supposed to Looking back now when I was in that moment I want it to be so bad in the moment that I Am now like in this time where now I'm financially stable and everything And back then I wanted to be in this position so so so bad as much as I did Soak up and I knew that I was going to miss that part of my journey Like I miss it to be honest, and it's just crazy how just over a year ago I was Wanting and striving to be in the position that I am today And now I'm here and I have new and higher goals And also it's like the goals never stop like once you reach a goal You're going to set new goals for yourself and you're going to want to be at the next stage of your life So it really never stops And that's why it's just so important to not rush things and just just like take a step back Enjoy the moment be present and just let life Happen because if you're not present in these moments and you're rushing them to get through them just until you reach that um goal that you want to achieve you're going to regret not Being present and not appreciating the moments that you were in and you're going to look back and miss them Obviously like I'm so thankful for I am right now But when looking back at that it kind of makes me nostalgic and it's just crazy how life happens so fast Like it was over a year and a half ago and at that time it like felt like such a dream And deep down I knew I was going to get there like I did know but it also felt like a dream a big dream of mine You know and it's just crazy that I'm here now And it just doesn't feel as big As an accomplishment than it did when I was in that position A year and a half ago because it all unfolded so slowly if that makes sense Not saying like obviously I'm so thankful like I'm literally living my dream life and like I couldn't be happier But the message that I'm just trying to get across is to soak in your journey Everybody's journey is going to look different if you're 20 if you're 25 if you're 30 And you think that you're falling behind in your life because you're comparing to somebody who's your age And they're at a completely different step than you there's no reason to compare yourself to them And put yourself down because they're at a higher place Your journey is unique and no matter how old you are it doesn't matter It doesn't matter if somebody your age has your dream job Like that doesn't take away from your journey and your life your life is going to unfold Exactly how it's supposed to and when it's supposed to unfold and that's kind of the magic of life Is that everybody has their own Journeys everybody is here for a different purpose and a different reason And that's what kind of makes the world work. It's just so important to never feel behind And to always just be present in any step of your journey that you're in if you feel like you're in a really Bad place right now and you can't wait to jump to the next part of your journey Just take a step back be present and realize that like one day you're gonna Maybe want to be back in that moment and you're you might miss it Every single step of your journey is going to lead you to the next part of your journey And it all kind of happens for you everything happens to get you to the next part of your journey so right now if you feel like you're at the bottom and Because you're trying to accomplish this huge huge huge goal And you don't like that you're at the bottom and you haven't accomplished it yet I would really really reconsider those Feelings of not wanting to be in that position Because trust me trust me on this one. You're gonna want to you're gonna miss those moments of building this goal And working towards the goal not about the destination. It's about the journey that quote literally just popped in my head It's such a cheesy quote, but it's so true Okay, here is an overview haul of my groceries So I really try to minimize how much plastic I was using because I definitely want to be more conscious of that So I didn't put any of the fruits or vegetables that weren't already in plastic bags in any plastic So we're trying to do our part and be more sustainable So I got two heads of broccoli and then I got Some fruit here just to stock up my fruit bowl because I just love having fruit as a snack They got an asian pear two mangoes two plums two pears Got a box of strawberries cucumber got some green beans to cook up for dinner. I love green beans So I've never tried this before but this is the califa oat Um coffee creamer and it's in hazelnut and I love this brand But I've never actually seen this creamer so I had to pick it up to try it And then I also got a big bottle of kombucha because this is the best deal This was like nine dollars And if you were to buy the smaller bottles, they're like five dollars each So this is actually a really good deal I got some lemons because I want to start doing lemon water in the morning I got pierogies just for a quick dinner chicken thighs I got some chicken cordon blues and then I got some cod There's actually tea on these peppers So I saw this tiktok of this doctor and she's like a dermatologist And she said that yellow bell peppers are one of the best foods that you can eat to have good skin Because apparently they have so much vitamin C in them and that just really helps your skin So that inspired me to buy some peppers because I honestly love eating peppers with ranch. It's so good So that's a nice snack I can have then I got two avocados just to have with like toast or something in the morning I got Fox choice to have with a meat for dinner bananas and yeah, that's a little overview haul Okay, this is the current state of my fridge I just actually turned it off because I'm gonna be keeping it open for a bit because I want to clean it out But I just kind of want to wipe the shelves down and reorganize everything so that when I put this in It's all nice and organized for the week. So that's what I'm gonna do right now Okay, so here's the after of the fridge. I just wiped everything down So it feels a lot more clean and put together and then I just organized everything We got like the vegetables in these two drawers here And then we got just like random stuff organized up here And yeah, it just feels so much more better and clean. Okay. So while I was doing the fridge and stuff and putting everything away I was actually listening to money affirmations and affirmations isn't something that I've ever really like done or dived into I just like write one every morning But I've never actually like just listened to a youtube video with affirmations before So I forget who I saw do this, but basically they were just like listening to affirmations Oh, I think it was Maya Pham, but I literally love her youtube videos so much I recently just got into watching her and I love her videos so much But anyways, so I think it was her that actually got me onto this so basically When you're doing something instead of like listening to a podcast or music or whatever put in your headphones and Search up money affirmations like beauty affirmations like any type of affirmations and just listen to them And you might think that it's stupid But basically what it does is it plants a seed in your subconscious and the more you listen to it the more you The more it'll grow and the more that you'll believe that it's true Because your subconscious is so so so powerful and there's so many limiting beliefs that are held within it That we don't really realize every single day listening to affirmations It helps kind of rewrite your subconscious So I really want to try this So I've been listening to this money affirmations video for this is my second day doing it now And I want to try to do it just like every single day And see what happens because I've been I was reading the comments of the videos and I was like, oh my god like this works So it's kind of really interesting and I'm going to try it I'll update you guys on it But it's just something that I want to Start incorporating into my everyday routine because you can literally listen to it Whenever like before you go to bed while you're showering Doing chores like doing whatever try it out I will link the video that I listened to down below actually listen to it twice while I was doing the cleaning Yeah, it's something you knew that I want to try out and I totally believe that like repetition Even if you don't believe it at first, it's gonna make you Believe it through your subconscious and then it's actually gonna play out into reality So it's just such a cool concept and I don't know why I've never really like done it before But I'm excited and if you guys want to start this with me We should do it together because that would be really fun.  It doesn't have to be money I'm just doing money for fun because I do I feel like I have a lot of limiting beliefs about money So hopefully that can help reverse them like in my subconscious. So yeah, I will update you guys on how that goes But that's what I was listening to Okay, so here is my dinner. I got the cordon bleu with bok choy. I honestly love making bok choy It's so easy to make I just put it in a pound with oil and then put salt on it And it's so good and then I just have it with rice and kombucha in a wine glass you guys It hits different like it really does. So 10 out of 10 would suggest This is my little dinner for tonight


The Avan River here just outside of 2J meandering its way all the way to Perth. The last thing our teams have been doing though is meandering through these stages. Just about to complete their final runs here in 2J. We can catch up with them in service before we head to the Shiret chittering this afternoon. The guys worked all night on the car, had it all done, tested it last night. All good. This morning we'll go to start it at Park Firmay and there's lights up on the dash codes so we have a chat to the guys I said yeah no problems we'll just clear it and it should be good. We pull up at Gidja Gannup, computer won't talk to the car so took about 45 minutes and it did talk to the car and it cleared the codes and it's been perfect ever since so but unfortunately we've missed the stage. Graham Finesh me doing a fabulous job mate and someone said your world was turning around on you in one of the last couple of stages there. Yeah I got a bit light-headed and felt I had a bit of a spin but yeah we improved on the second run through Coon-De-Wes. Double-annu times are going really well. Yeah well that's something to do with Ray and Tracy navigating a lot of full faith in the notes you know really and it's I suppose unsung heroes you never really talk about them much but full faith in what she says and we do write good notes, had a couple of years together now even the gravel and it's sort of working together. Chris Bure is only about two or three years ago you're a target rookie and now inside the top 10 and doing really really well again mate. Yeah doing really well happy with the co-driver and the calls we're getting and yeah the cars is handling beautifully so very happy.


I'm particularly interested in innovation, pushing out the boundaries of possibilities and potentially what we are going to be seeing in the future. I certainly want to see a lot more when it comes to women being involved and I'm really interested in what are the projects that you've seen where the use of crypto currency or blockchain has really pushed out the boundaries and inspired you, what has been the most inspired project that you have actually seen yourself that you think could actually help inspire people to think beyond what we are actually witnessing now? That's a tough question. I think a lot of the things I see are boring and quite disappointing. Yet another ICO, yet another person trying to reinvent the existing system only now plus blockchain. It's like, let's build a plan. I'm betting with blockchain. Let's do an investment fund with blockchain. Let's build a transportation company with blockchain. A gaming company with blockchain. It's like, you don't need blockchain for most of those things. Why? That's boring. One of the most inspiring stories I have is from a woman called, and I'm going to probably mispronounce her name, Faresti Farouq. She is a woman from Afghanistan who is running a program called Code to Inspire. It is a program that teaches teenage girls in Afghanistan how to write software, which is something that they can do in the privacy of their own home with a cheap laptop without anybody knowing what they're actually doing, and then how to sell software programming services and earn cryptocurrency that they control in a country where it is illegal for women to own property. That is inspirational. There's a couple of charities that are doing interesting work in Bitcoin and other cryptocurrencies. One of them is called BitGib Foundation. It's a woman-owned organization which is a non-profit registered charity. They've got a program called GivTrack. What they're doing is they're using the radical transparency of the blockchain in order to give donors the opportunity to watch their donation on the blockchain all the way down to purchasing the bricks that go into the well for the water well project in Kenya. They're basically taking a problem that is fairly big in the charitable world, which is accountability for donors' money. In many charities less than 50% of the money donated actually goes to the charitable causes. A lot of it goes up at administrative costs, etc. Here you can watch your donation and see which part of it ends up, and track it all the way down to the charitable project, so GivTrack. I think that's a really interesting project. There's a number of others like that. They're few and far between at the moment. Most people are trying to make money as fast as they can and get rich. But every now and then I meet some really inspiring, humble individuals who are doing some really fascinating work. Thank you for asking that question. Can I just add another question then? What would you like to see? I think the most important project that people could be working on right now, there's a couple of companies working on it, is to address the issue of international remittances. Remittances is when immigrants, migrant, itinerant workers send money to their home countries while working abroad, often working as illegal or undocumented labourers, farm workers in other countries, including of course the United States, the United Kingdom, the Northern Europe. But also in Southeast Asia, there's a lot of migrant workers in the United Arab Emirates, in Kuwait, in Saudi for example. Sending money home is a $550 billion business here. That $175 billion goes to fees and profits for two or three companies, Western Union, MoneyGram, Wells Fargo and a few others. This is basically taking a significant chunk of money from the world's poorest people. Ironically enough, $175 billion happens to be the total sum of foreign financial aid by all governments in the world donated each year. So, the same amount that governments are spending to support poor people around the world by giving it at the top and none of it gets to the bottom. The money transfer companies are taking from the bottom. So, instead of trying to fix foreign aid, how about letting those people keep their own money? If we can do remittances with cryptocurrencies, which will involve breaking a lot of laws because, you know, no licenses. You have someone here who takes, ring it, buys a cryptocurrency, and then the cryptocurrency gets transmitted to another country, and then that in that other country gets converted to cash and given to the recipient. And you've basically got a system of remittances that is informal and in some cases legal. But what it does is it injects $175 billion directly into the pockets of the poorest people on earth. Not only that, the recipients of remittances are 85% women. The World Bank has estimated that for every $1 that they get, it generates $2.5 of economic activity, primarily in education, healthcare, sanitation, and security, food security, most importantly. So, this is an area where these cryptocurrencies could actually deliver enormous benefits to some of the poorest people in the world. They don't even need to know that they're using cryptocurrencies. In fact, some of the best applications out there just hide that. The cryptocurrency is just a pipe that's being used to convert the money and send it across the borders, which is the hardest part. The fees can be less than 1%, significantly under the country of Western Union. And there's one small downside. If this plan is successful, Western Union, who invented wire transfers in 1996, did you know that? They invented wire transfers in 1996, 1896. Not 1996. Unfortunately, they're going to go out of business. And at least on this side, not a single tear will be shed. So, yeah, that inspires me.


The primary purpose of an equipment management system is to provide the right equipment at the right time and place at the lowest possible cost. Other purposes include minimizing equipment ownership costs, reducing downtime, and increasing utilization. An equipment management system provides tangible benefits in terms of expanded cash in the operating budget, reduced ownership costs, and more efficient execution of the work program. Reduced ownership costs accrue through better planning of fleet sizes by extending the useful life of equipment through better maintenance by increasing equipment availability and by replacing equipment at the end of its economic life. Reduced operating costs occur because of proper sizing of equipment for job requirements and better purchasing practices for parts, tires, fuel, and other supplies. Reduced maintenance and repair costs occur through establishing more effective preventive maintenance programs and tailoring equipment specifications to job requirements. The potential for reducing costs through improved management is estimated at 5 to 15 percent. The illustration here shows the specific potential for cost savings by type. An equipment management system helps to meet your objectives by providing guidance and information in the following areas, optimization of fleet size and mix to meet user needs economically, replacement of equipment at the most economical point in its life cycle, improvement of internal management policies for more productive operations, and monitoring actual performance in relation to plans. To be effective, the system must address the following stages. Authorize, purchase, deploy, use, maintain, and replace. Four subsystems are involved. Inventory planning and control, equipment maintenance, parts and supplies management, and financial management. The inventory, planning, and control subsystem contains tools that assist the equipment manager with the following functions. Inventory, fleet planning and authorization, equipment purchasing and replacement. The equipment maintenance subsystem has four components. The first is the preventive maintenance program. It establishes preventive maintenance service levels, schedules, workloads, manpower, and equipment requirements. It also includes methods for program evaluation, quality control, and safety inspections. The second component is shop operations. It includes techniques for improving the daily management of the shops, such as work orders, job standards, job prioritization, job scheduling procedures, performance criteria, and evaluation of in-house versus commercial repair costs. The third component is personnel. It combines the preventive maintenance and repair workload so mechanic staffing can be projected. It also develops staffing guidelines for non-mechanic personnel. It projects needed skill requirements and training for mechanics. It evaluates work shift requirements and develops an operator and mechanic certification program. The fourth component is facilities. This element identifies required physical facilities for the shops by adopting standard shop layouts, identifying requirements for work bays and support facilities, evaluating the effectiveness of portable facilities, and establishing standard shop tool and equipment requirements. The parts and supplies subsystem involves five components. The first component is stock numbering and classification. It develops a parts numbering scheme. Second is stock selection and stock levels. This component establishes the most economic stock levels by evaluating in-house stock versus local purchasing. Third is inventory control. It includes procedures to ensure effective control of parts at stock locations. Fourth is inventory management. It includes procedures for automatic ordering, evaluation, and monitoring of stock. And fifth is fuel and oil management. This component provides effective fuel and oil inventory management. The last subsystem, financial management, involves three components. Cost accounting, which identifies and distributes all costs related to equipment. Budgeting, which establishes budgets for all operating entities. And rental rates, which ensure effective control of an equipment revolving fund by defining cost elements of ownership, developing a rental rate structure to capture total cost by equipment class, and establishing billing procedures. An effective equipment management system requires the input of a wide range of personnel. Development representatives must be fully committed to providing the necessary backing and resources for the development and implementation of the system. The fleet manager plays a key role in any organization implementing the system, but will normally be too busy with other duties to serve as project manager for the system. But the fleet manager will have a key role in overseeing the efforts of the project manager. The fleet manager will have primary responsibility for the operation and management of the system when it is completed. The maintenance manager must provide the equipment manager with accurate and timely forecasts of equipment needs. The director of public works seeks approval for the project from the governing body, approves the appointment of a project manager for development of the system, and oversees the utilization of resources. The parts manager needs to initially establish usage levels of parts and supplies as well as reorder parts and safety stock levels. After the system is operational, this person will have to carefully monitor the parts and supplies management function. The project manager manages an in-house development team or an outside consulting team. The accountant will be responsible for providing current and historical data on equipment ownership costs such as depreciation, insurance, and operating maintenance costs. After the system is implemented, this data will have to be monitored to refine initial guidelines and optimize the agency's system strategy. There are a number of considerations and pitfalls that will influence the success of the system. The first is commitment and support by government officials. The development and implementation of the system requires a substantial investment of time and resources. It is not simply buying new software computer systems. Fundamental changes will need to be made in the way that equipment operations are planned, scheduled, performed, reported, and controlled. Training of staff will be required. Outside consultant assistance may be required. To obtain funding for the system, the governing body must be informed of the objectives, benefits, operational characteristics, and cost of the undertaking. Citing the successful experience of other agencies with such a system is often helpful. The second consideration is sound planning and scheduling. A work plan and schedule for system development must be adopted. Resource requirements must be estimated. Staff responsibilities must be clearly assigned. And a project manager must be appointed. Another consideration to avoid is excessive development efforts. There is no point seeking refinement beyond the realm of practical application. Attempts to define excessive numbers of activities to cover every conceivable item, or conducting time and motion studies, are generally unnecessary. Once the system is implemented, changes can be made as necessary. Also consider the human element. There is always resistance to change. The best way to overcome it is to keep employees informed of the objectives and benefits of the system, and to involve them during system development. It is particularly useful to involve them in development of standards and optimal work methods. You should also consider coordination with other functions. The best planned systems may not be successful unless efforts are coordinated with other activities of the agency. This is especially true if several different units in the same agency use such equipment. Unless each of the units puts forth an effort to define the equipment needs well in advance of planned use, and to coordinate work schedules, there will always be conflicts in equipment availability. You also need to consider automation for the system. Considering the price of computers today, most agencies can afford an automated system using a PC-based system. Automation will require suitable software and hardware, and training will also be required for all personnel involved. Proper data collection is necessary. This will require the selection of people who have the capability and training necessary for accurate and consistent data collection. Also, don't forget to involve the staff and listing the support of employees at all levels in the development process makes for greater acceptance of end results. In this program, we have covered the basics of an equipment management system, including inventory control, fleet planning, purchasing and replacement, maintenance, parts and supplies management, financial management and management information for timely decision making. Each element of the equipment management system will be discussed in more detail in the five following videotapes on equipment management. For more information on this or other IRF videotapes, write to the International Road Federation or call the numbers on your screen.


security forces and their boat patrol. Our area of responsibility is all of the waterways that's surrounding the Air Force Base all the way out to the Chesapeake Bay. A good rule of thumb for us is if the Coast Guard and the Navy don't need us all the way out there then we're not gonna go out there. So our job is to make sure that everyone's maintaining their distance from the shoreline. That's all the way down to our weapons facilities, down to the Kingtree Bridge and out all towards the Chesapeake Bay. We also assist the Coast Guard in rescues if there's any type of boating incident or accident outside. We help them in the surrounding waters going. So out of all the Air Force Bases, only four of them have a Marine Patrol. Most of them are down in Florida. Most of our coastline here at Langley Air Force Base is water so we are one of the exceptions up here on the northeast coast. Nobody thinks of boats when they think of the Air Force. Usually they think the Navy or the Coast Guard. So when I joined the Air Force I didn't think I was gonna be flying planes but I definitely didn't think I could be driving a boat around day to day. So for security forces members, obviously the first criteria is you need to be a security forces member and you'd be stationed here at Langley Air Force Base.  You'll train with the NASBOLA instructors who are all retired Coast Guard or Navy instructors. We'll train you on everything that there is to know about the boat all the way from the maintenance of the boat to the operation of the boat and then you'll go to the in-class portion where you'll learn everything about navigation, tying lines and tying knots and then we'll get you out here and we'll do a final practical exam. You'll go and you'll do everything that the instructors ask you to do docking to search and rescue to regular boat operation. I enjoy it. It's really nice to get to see the shores of Langley Air Force Base from a little bit of a different perspective than everybody else. Not a lot of people know that the Air Force has boat patrols so it's really cool to get out on the water and interact with people who didn't know you existed.


Regenerative energy, there is a lot of work in the direction of use of biomass and I personally do hate when energy is made from food. It's a no-go in a world where a few hundred million people don't have enough food to eat, we can't convert corn or grain into energy, a little bit of energy, because it's totally inefficient on top of that. So the bioenergy that is up to the standards with life cycle assessment from all aspects that would be wood. And with usage of wood, one specific type of wood utilization stands out and that is the wood gas technology. And it can be used small scale and we work on this together with York Fingers. He has developed wood gas stoves in West Africa, a lot in Burkina Faso, also I've worked with him in Senegal and so these are metal stoves and the big advantage is you can carry them so you ignite them when they burn nicely, they are very clean, you put them inside the house if you like and can take it out again when it has done its purpose. The downside is that the metal building is pretty difficult so it's not so easy to find people who can do that. That's why it's also good to know about the loam stove, a wood gas stove that was developed by Marius Birig and it's the NOAA stove and this is Stefan Hügel from our university and we have done a workshop with Marius and we did cooking on the stove, it works very well and it's something that we also want to bring into Ethiopia and into Aba Minch where we are working at the moment because it's a very cost efficient way of cooking and the way Marius does it, he has done the calculations based on real experience and the family can cook with wood, convert the wood to charcoal while cooking and then sell the charcoal at a higher price as the wood has cost so they can actually earn money with cooking and that's pretty cool isn't it. Normally it's a big burden for poor families the cooking material and so that makes a little bit of an extra income and the stove is also relatively low cost and of course we also want the charcoal as part of terrapita sanitation that we can use at least parts of the charcoal to make the crumbly stuff to put into the compost for building humus that is long lasting even in hot and tropical areas.


Time for sports news. FIFA on Monday find Nigeria's HF 150,000, which is 63.9 million Naira following valent data code at the Moschuda Biola National Stadium in Abuja on March the 29th. And this was after the country's failure to qualify for the 2022 World Cup in Qatar. FIFA also ordered the country to play their next international match behind closed doors. FIFA however gave room for appeal. Hundreds of fans encroached the pitch destroying the technical area and pelting the VIP section of the stadium after Nigeria played out a 1-1 draw against Ghana. According to FIFA, Nigeria's finds were a result of failure to implement order and security at matches. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


Yo, this is Charles the French. We are going back on tour in August and September 2019.  We'll start with Vietnam, August 16th in Hanoi, and August 17th in Ho Chi Minh City. Then after Vietnam, we will head to India, starting with Kolkata, followed by Gorgon, which is 10 minutes away from New Delhi. Then we will head to Mumbai, which is pretty close from Bombay, I heard. And we will finish the Indian tour date with Chennai. On September 7th, we will be going to Nepal. Kathmandu, we're coming, so see you there. And finally, we will finish the second tour in Bangladesh. Daka, see you on September 21st. For more information and tickets, click on the link in the description. Please read the website carefully, because for some cities you can buy the tickets online, but for other cities, you have to email the producers. Looking forward to see you on tour? Love you.


In choosing the healthiest foods, you may notice that everywhere you look, everyone seems to have a different top 10 list of the most antioxidant-rich foods, with probably dozens of competing commercial products swearing theirs is the best of the best. Some are probably just making stuff up, but genuine competing estimates arise from people citing old data, where they only test a few dozen foods or a few hundred, but other disparities arise from different labs using different tests. There are four in common usage, ORAC, TEEK, TRAP, and FRAP. USDA likes ORAC, these researchers used FRAP, in part because it's one of the quickest methods, which is important if you're doing 3,000 foods. Each has their pros and cons, but the problem with all of them is that they're just measuring how good a particular food is at altering a chemical oxidation reaction in a test tube. It's not done in a biological system, but for the first time ever, scientists at Cornell took 27 vegetables and measured their cellular antioxidant activity, their ability to quench free radicals within cells, by testing various vegetables on cultures of human liver cells. Sure, some phytonutrient may be a great antioxidant outside the cell, but what if it can't get inside the cell? That's where we need it. If you do the standard ORAC test, this is what you find. Spinach at the top, cucumber at the bottom. No surprise, dark green leafy leads the pack. But again, this is a chemical assay measuring how these foods slow down some oxidation reaction in a test tube, a reaction that actually doesn't even occur in nature. But hey, look, it's the best we had until now. And he guesses as to who was able to unseat spinach? Here's the cellular antioxidant activity. Cucumber's still at the bottom, but now, beating everyone else, beats. Number one, spinach isn't even in the top 10 anymore. All the cruciferous moved ahead, you know, Brussels sprouts, broccoli, cabbage, cauliflower. And hey, look, between the beets and the red bell pepper, looks like the greens got beat out by the reds.


Welcome back, we proved the quadratic reciprocity law, all the three parts of the law and then we solved some examples, we saw some applications of the quadratic reciprocity law, so here they are. So, we computed whether 2020 the current year is a square modulo prime, so for example 31 and then we also saw that we could find all odd primes P such that 3 is a quadratic residue modulo P that means the Legendre symbol 3 by P is 1, we found all such primes P this was given by some certain congruence relations, so there were some arithmetic progressions and all the primes appearing in those arithmetic progressions gave us that 3 is the square modulo P and there were some arithmetic progressions such that we had that the primes appearing in those arithmetic progressions had the property that 3 is not a square modulo P. So, we will now do a similar example for 5, we want to compute all odd primes P such that 5 is a square modulo P, this is the problem that we now want to think about that find all odd primes here we are looking at odd primes because we know that if P is 2 then every odd number is congruent to 1 modulo 2 and then of course every odd number is going to be a square modulo 2, so we have to look at only odd primes to make the actual computation. So, we are interested in we compute this Legendre symbol 5 by P but 5 is congruent to 1 modulo 4, so the third law of quadratic reciprocity will tell you that you can switch the places of P and 5 without changing the sign. So, this is equal to P by 5 this Legendre symbol but this is very easy to compute because now we have to go modulo 5 and there are 4 numbers 1, 2, 3, 4 and we need to see which of them are squares modulo 5. So, this is 1 or minus 1 depending on whether P is congruent to plus or minus 1 modulo 5 and the second case is where P is congruent to 2 or minus 2 modulo 5. So, this actually turned out to be a simpler problem because we are now able to answer this question.  So, for instance 31 is a prime such that P by 31 the Legendre symbol 5 by 31 is 1, 5 is a square modulo 31 indeed 6 square is 36 which is 5 modulo 31 whereas 37 is the prime which is congruent to 2 mod 5 and therefore 37 will not have the property that 5 is a square modulo 37. This is same as saying that 37 is not a prime square modulo 5 and then we know how to compute the answer. So, we can find all odd primes P with the property that 5 is a square modulo P. So, we have computed the odd primes P where 3 is a square we have computed the odd primes P such that 5 is a square using these things we can compute all primes P with the property that 30 is a square. So, this is our next problem find all primes P with the property that 30 is a quadratic residue modulo P. Here I am keeping odd in the bracket because the prime P where 30 is a square modulo P we should have that P comma 30 the GCD is 1 and therefore clearly P equal to 2 will not come. So, it is not necessary now to say that we are only looking at odd primes we are looking at primes where 30 is a square mod P and then of course such primes will be odd. So, we are interested in computing this Legendre symbol but Legendre symbol is multiplicative. So, we have that this is 2 by P into 15 by P which gives us 3 by P and 5 by P then all these will give rise to some certain conditions some congruence relations and we have to put them together to get the correct answer. So, this is equal to 1 when P is congruent 2 plus or minus 1 modulo 8 this is 1 when P is congruent 2 plus or minus 1 modulo 12 if you remember from the last lecture and this is something that we have just now computed. So, these are the computations and of course there are the remaining computations which will tell you that these signs are minus 1. So, let me put them in a different color. So, this is when plus or minus 3 modulo 8 this is when plus or minus 5 modulo 12 and this is when plus or minus 2 modulo 5. Now, to compute when this Legendre symbol is equal to 1 we need to find we will have to compute this product and so this product has to be 1. So, this product of 3 integers will be 1 when 2 of them are equal to 1 and the third one is also 1 2 of them are minus 1 the third one is 1 and so there are there is one possibility when all are 1 and there are 3 possibilities depending on the first 2 having negative signs the last 2 having negative signs and the first and the third having negative signs. So, we will get 4 such cases where the number is going to be 1 the Legendre symbol 30 by P is going to be 1 and there will be 4 cases when the Legendre symbol is equal to minus 1. So, these are the cases that we need to compute but these are also the cases modulo a certain congruence modulo a certain number and that number is going to be the LCM of the moduli of these congruences. So, we see that for 2 the modulus is 8 for 3 the modulus is 12. So, the LCM of 12 and 8 is 24. So, to combine these 2 we have to go modulo 24 and then the final congruence is modulo 5. So, ultimately we will get a congruence relation modulo 120. So, the answer will be in terms of congruences 120. I said that there are 4 cases but actually there are more cases. Here when we looked at each of these I considered each of these to be a single case but each of these are 2 cases each. So, we are going to get more cases and what I am going to do is to leave all these computations to you and this will also be part of our assignments for this week. So, this is the final calculation. So, the final calculation is left as an exercise. I have done the most important part in my opinion. So, this is how Legendre symbol can be very useful and it tells you when a number is a square or not modulo a given prime. Now, there are some generalizations of Legendre symbol and the most important generalization is this symbol called the Jacobi symbol. So, what does the Jacobi symbol do? How does it differ from the Legendre symbol? It differs in the following way. This is defined for a general modulus. The Legendre symbol was a by p where the denominator was necessarily a prime. Here we have that the denominator need not be a prime. It is a natural number. So, not negative yet but it is a natural number. So, it is a positive integer. This is what we have. So, we take a and n to be natural numbers. Then we define the Jacobi symbol a by n by this formula that this Jacobi symbol is product of the corresponding Legendre symbols. So, we are looking at a by n. The a is fixed. It is the same a that you have in all these numerators of the Legendre symbols but there is a change instead of n we have p1, p2, pk and then there are these powers alpha 1 up to alpha k which are given by the prime factors the decomposition of n into its prime factors. So, when I have a by n we will take the decomposition of n in terms of primes.  So, this is the way we define the Jacobi symbol. This is now defined for any modulus any general modulus as long as the modulus is a natural number and of course, I can change now the a to be from natural numbers to integers not 0 but to a general integer. Now, we note here that the a by p because I am taking a by n and then I am looking at a by p for all these p's it is possible that some prime p may divide the integer a and by our definition of Legendre symbol if you remember Legendre symbol had values 1 or minus 1 whenever a was co-prime to p but whenever a was divisible by p modulo p a is 0 and then we define the Legendre symbol to be 0. So, now whenever I am looking at a by n as product of these a by p's with various powers it is possible that the some Legendre symbol in the factorization may give you 0. So, even though a is not 0 modulo n you may get the Jacobi symbol a by n to be 0 when it is not 0 it can be 1 or minus 1 because the numbers on the right hand side of the decomposition are all 1 or minus 1. So, this is our next observation that the value of a Jacobi symbol can be 0, 1 or minus 1. So, of course, whenever a comma n the GCD is not equal to 1 the Jacobi symbol is going to give you 0 because 0 because there is a prime p dividing both a and n and whenever you look at the Legendre value of that a modulo that p you are going to get 0 in the factorization. So, the Jacobi symbol a by n is going to be 0 whenever a comma n the GCD is equal to 1 then all factors on the right hand side are going to be 1 or minus 1 because then a comma p is going to be 1 for every p dividing n and then of course the Legendre symbol values are 1 or minus 1. So, in that case we have the Jacobi symbol value to be 1 or minus 1. So, this is the generalization whenever we generalize a concept to a bigger set instead of a smaller set it is likely that some nice properties of the earlier concept may not hold that is because now you are taking more and more elements where you are applying the concept. So, it is likely that some of the nice properties that were true earlier now do not hold. So, one of the property is the following which I am going to now explain.  So, whenever a is a square modulo n the value of the Jacobi symbol is equal to 1 it can also be 0 whenever the GCD of a and n is bigger than 1. So, these values can be 0 or 1 and so equivalently when you have that a comma n is minus 1. So, you have that a and n are co-prime and the Jacobi symbol value is minus 1 then a has to be a non-square modulo n because we saw earlier that whenever a is a square modulo n all the Legendre values are equal to 1 you are raising them to some powers but all the values are 1 so the product is going to give you 1. So, whenever a is a square modulo n the Jacobi symbol value is equal to 1 and what we say in mathematical terms the contra positive of this statement says that whenever the Jacobi symbol value is minus 1 then a is not a square modulo n. This is some property which is true for Legendre symbol also. However, for Legendre symbol you have an if and only if statement. In fact, we define Legendre symbol with the very motivation of determining the square modulo a prime p. So, we started with square modulo p we defined the Legendre symbol we defined its generalization called the Jacobi symbol and now we are asking whether these squares behave well with respect to the Jacobi symbol value. So, whenever a is a square modulo n Jacobi symbol value is equal to 1 if the Jacobi symbol value is minus 1 this is not a square. However, it is quite likely that you may have a non-square modulo n and the Jacobi symbol value may still be equal to 1. So, we may not have an equivalent formulation. This does not imply the Jacobi value being equal to 1 need not imply that a is a square modulo n an example can be constructed in a very simple way. What may go wrong is the following thing. You may have a number a and some number n. Suppose n is product of two primes say p and q. Then a by n the Jacobi symbol is product of a by p with the product a with the Legendre symbol a by q. Now, it is possible that both a by p and a by q are minus 1. So, a is not a square modulo p a is not a square modulo q. So, both the Legendre values are minus 1 but their product is equal to 1 and therefore, the Jacobi symbol value a by n will be equal to 1. However, a will not be a square modulo n because it is not even a square modulo the divisor p of n. How do we get construct a counter example? This is a good way to construct a counter example. This is a thinking which will help us in constructing the counter example. So, a simplest let us take odd primes. So, the simplest odd prime is 3. 2 is not a square modulo 3. So, the Legendre symbol 2 by 3 is minus 1. The next prime after 3 is 5. Luckily, 2 is not a square modulo 5 as well. So, we have 2 by 3 equal to minus 1, 2 by 5 is also minus 1 and therefore, 2 by 15 is going to give you plus 1 but 2 is not a square modulo 15. In fact, we can compute all the squares modulo 15. So, let me call this set again by q 15 although we had used this notation q only for quadratic residues modulo a prime. Let me call it again for this non prime modulus.  So, we get the same number of elements repeatedly. Now, we observe that the phi 15, the number of elements which are non-zero modulo 15, this is phi 3 into phi 5. So, this is 4 into 2 that is 8 and here we are getting 2 squares in this set. So, there are 6 non-squares and there are 2 squares. So, once again what we had earlier that if you have, if you are looking at the set of squares modulo p then q p had exactly half the number of elements as there were the numbers of co-prime to p the phi p. This is not true when we are looking at a non-prime modulus. So, this is a way we can construct this example quite easily and there are however other things which are satisfied by Jacobi symbol which are also satisfied by the Legendre symbol namely that the Jacobi symbol is multiplicative. We know that the Legendre symbol is multiplicative when you had a b by p this was equal to a by p into b by p. So, there was a multiplicativity of the Legendre symbol. However, the Jacobi symbol is multiplicative not just in a, but also in n. So, not just in the numerator, but also in the denominator. What I mean by this is the following thing that a b by n is a by n b by n clearly, but you also have that a by m n is a by m into a by n. So, this will tell you for instance that the Jacobi symbol is equal to 1 unless it is 0 whenever a or n is a square. Whenever a is a square if you have a to be b square, then a by n is b by n whole square and so when depending on whether b by n is 0 or non-zero you get that the value of a by n is 0 or 1. Similarly, if your n is m square then a by n is a by m whole square and once again the value of a by n will be 1 or 0 depending on whether a by m is non-zero or 0. So, the multiplicativity does hold which will help us in computing the values of the Jacobi symbol. There are some more properties which are true for Jacobi symbol and which were true for Legendre symbol namely that the reciprocity laws are true in some form. So, of course we cannot expect it to be true in the full generality, but it is true in some form and the form is as follows that for minus 1 remember once we defined a by n to be a by p1 power alpha 1 a by p2 power alpha 2 dot dot dot a by pk power alpha k I said that we will now extend the values of the Jacobi symbol to the possibilities where a can be any integer positive negative or 0. So, indeed we can ask for minus 1 and for minus 1 we do have this property that for minus 1 we do get the Jacobi symbol minus 1 by n is equal to minus 1 to the power n minus 1 by 2. There will be no question of minus 1 upon n being 0 because no n is going to have a non-trivial GCD with minus 1. So, this is an equation which is always true. This is true whenever n is odd. So, the Jacobi symbol 2 by n is minus 1 to the power n square minus 1 upon 8. This is always true whenever n is odd and finally we have this a more general reciprocity law. So, instead of just having m and n to be primes we have whenever m and n are odd numbers we have that this equality always holds. The proofs of these results are not as difficult as they were in the Lajandra's symbol case. In fact, the Lajandra's symbol case will come and help you here. You have to notice some certain things. For instance, when you go to this particular number you need to notice that this holds whenever it holds for every prime factor of n and so on. So, these are some small things which you need to observe and then you have the full proof. So, these can therefore be proved using the properties of the Lajandra's symbol. We will not mention proofs of these facts but these reciprocity laws do hold. However, I would like to caution you that this equality which is here for minus 1, this need not be true in general. We had the Euler criterion for Lajandra's symbol which was a by p congruent to p minus 1 by 2 modulo p and that helped us computing the Lajandra's symbol in a nicer way. This need not be true in general. We will talk about this and some other interesting things regarding Jacobi's symbol in the next lecture and then in the next lecture we will also begin our next theme. So, see you soon in the next lecture. Thank you very much.