Welcome back, we are into the final leg of our course, only a few lectures remain now. What we have done in our last lecture is that we described all the real numbers which are expressed by a continued fraction which is ultimately periodic. We actually proved this very interesting result that these are nothing but quadratic irrationals. What are quadratic irrationals? Quadratic irrationals are these numbers which are solutions to ax square plus bx plus c equal to 0 or which are also called the zeros of this degree 2 polynomial. Here we have that abc are allowed to be any integers but there is a small condition that b square minus 4 ac has to be a natural number. This is because we want all these roots the zeros to be real numbers and further we also demand that this b square minus 4 ac b not a square because we are looking at the numbers which are irrational, the numbers which are not rational numbers. We have also noted that all these numbers can be written in the form x plus y root m where x and y are rational but y is non-zero because we are looking at the numbers which are not the rational numbers. If y is 0 then any such number equals x which will then be a rational number. So, we are looking at all these type of numbers and we proved that they are nothing but the ultimately periodic continued fractions where ultimately periodic is defined in this slide. It means that after a stage the partial quotients keep repeating periodically.  So, the next ones keep repeating. So, this finite sequence of partial quotients is the sequence that keeps coming there periodically. This is what we mean by saying that it is an ultimately periodic continued fraction. So, there is this word ultimately that is because the periodicity has started after some stage. If you remember we did the continued fraction expansion for root 2 in the last lecture and we noticed that it was 1 comma 2222. So, the first integer a0 the first partial quotient that we had obtained was 1. So, we leave the a0 but from a1 onwards we had periodicity and that period was 1. So, every integer that you obtain after that every partial quotient was just equal to a1 which was 2. So, we had 1 22222. So, there the period the m is 1 and your capital N is also 1. The 0th one is not part of that periodically repeating state of partial quotients that is what we had. But it may happen sometimes that your periodicity starts on the nose. If you look at 1 plus root 2 remember root 2 was 1 comma 2 bar the 2 was getting repeated. Therefore, if you add 1 to root 2 now the integral part of 1 plus root 2 is going to be 2 and then you have 2222. So, you are you have the periodicity right from the word go you are you have the periodicity on the nose and then these are somewhat special periodic these are somewhat special periodic continued fractions and one may wonder whether you can describe these also in some certain way are these of some special form and indeed that is true. These are what are called purely periodic continued fraction expansions and there is this very nice result that a real theta has a purely periodic continued fraction expansion if and only if there are 2 conditions condition 1 says that your number has to be bigger than 1. So, the number theta has to be bigger than 1 if the theta has to have a purely periodic continued fraction expansion it should be bigger than 1 and minus 1 less than theta prime less than 0 where theta prime is the conjugate of theta. So, let us understand this result first we are saying that we have this theta whose continued fraction expansion is purely periodic that means it is starting from the word go from a 0 we have the periodicity. So, a 0 has to be equal to one of the a n's appearing later and therefore a 0 has to be a positive number a 0 cannot be negative and a 0 cannot be 0. So, a 0 has to be 1 or more. So, this condition that theta has to be bigger than 1 that is very easy to see the second condition is that the conjugate now what is a conjugate we have that our theta if it has a purely periodic continued fraction expansion it has an ultimately periodic continued fraction expansion it just happens that the periodicity starts from the word go. So, this theta satisfies the condition in the previous result and therefore this theta has to be a quadratic irrational at least that much we have beyond quadratic rational this theorem does not make sense. So, theta has to be a quadratic irrational therefore the theta should satisfy a degree to polynomial. So, if theta satisfies say a x square plus b x plus c equal to 0 then we have x minus theta into x minus theta prime equal to this a x square plus b x plus c for some theta prime. This is easy to see and I will not do this in this course. So, we can actually factorize this degree to polynomial over reals where one root is of course theta because theta does satisfy this when you put x equal to theta you are going to get 0. So, one root is theta and then there is one more root theta prime this theta prime is called the conjugate to the theta that we started with. So, if your theta has the form a plus b root d then theta prime is of the form a minus b root d. So, if you know how your theta is written in the form a plus b root d then computing this theta prime is not difficult. But the condition now says that your theta is bigger than 1 and then this theta prime has to be negative number but it cannot be a very large negative number it should be between 0 and minus 1 and it should not be equal to any of these two it is an irrational number. So, of course it will not be equal to any of these two so it should be between minus 1 and 0 this is the condition. So, the condition is that the quadratic irrational that you start with if it is bigger than 1 and it is conjugate theta prime is between minus 1 and 0 then the theta has a continued fraction expansion which is purely periodic and similarly in the converse would say that if you have a purely periodic continued fraction expansion for your theta then theta should satisfy these two conditions. We are not going to prove this theorem in this course but we will use it we would like to see that there are some certain real numbers which have purely periodic continued fraction expansions and whenever we want to have that we need to only check that these two conditions are satisfied. So, we give some examples of such real numbers the numbers root d plus integral part of root d and 1 upon root d minus integral part of root d these are some examples of such real numbers. So, in fact if your theta is root d plus integral part root d then of course theta has to be bigger than 1 here d is not a negative number we are looking at real numbers so we are looking at a plus b root d where d is positive. So, d is of course real therefore this is the when we talk about square root d note that square root actually may mean positive or negative for instance square root of 4 is the number 2 and also the number minus 2. So, let me just take a minute to explain this symbol for you whenever we have a symbol I may have told you initially that the number p by q that is an expression to write some certain number and that expression means that it is particular number which when multiplied by q gives you the number p. So, p by q is that number where when you multiplied by q you get p. So, 1 by 2 is one particular point one particular dot on the real line which lies exactly half way from 0 to 1 and we call that 1 by 2 we are giving the name 1 by 2 to this number because this number has the property that when you multiply that number by 2 you are going to get the answer to be 1. Now ideally whenever we want to write a number in this way there should be a unique number it should not happen that there are if you use some certain way to write denote a number but some another number is also possibly expressed in the same way we would like to try and avoid such situations because if there are such multiple possible numbers which can be written in the same way then it leads to confusion. So, if you talk about root of d then ideally it is the number whose square equals d that is what we mean by root d but there are two such numbers whenever your d is not 0 and let us say we are taking positive because we do not want to go into the realm of complex numbers whenever you take d to be positive let us say if your d is 4 then square root of 4 can be 2 and it can also be minus 2 because both plus and minus 2 have the property that their squares will give you 4. So, when you mean when you write square root of 4 you should actually tell what you mean by this and I am sorry for not having explained this earlier but luckily I realized it now and so I would like to emphasize here that whenever we put a root we always mean the positive number. Note again that d is positive so we are within the real numbers and therefore it is clear what is a positive root and what is a negative root. We do not talk about positivity and negativity when we have the d to be imaginary because that would lead to further complications let us not go into that. So, now our root d is positive by convention this is bigger than 0 and of course we have the integral part of root d since root d is bigger than 0 and if your d happens to be a non-square that would mean that anyway d is an integer and so root d will be 1 or bigger therefore the integral part is also 1 or bigger. So, both these quantities would certainly add up and give you that you have something which is bigger than 0 in fact you have something which is bigger than 1. So, this number theta which is root d plus integral part of root d that is bigger than 1. So, we are done with this now we consider theta prime. So, I told you that if your theta is of the form a plus b root d then the prime the conjugate is a minus b root d. So, here the conjugate would be integral part of root d which is simply an integer minus root d. Now, integral part of any number is less than or equal to that number and if you add 1 to the integral part then you would have gone beyond the number. So, when you remove the integral part from any number what you get is the fractional part and we have noticed that the fractional part can be 0 or it can be something which is less than 1. Here we are taking the negative of the fractional part because we are taking the integral part and remove the number from that root d is our number and we are looking at integral part of root d minus root d. So, here we get some number which is negative of the fractional part. So, it is going to be between minus 1 and 0 and being an irrational number it is not going to be equal to any of these 2. So, we have that your theta prime is negative and it lands between minus 1 to 0. So, the number theta equal to root d plus integral part of root d satisfies both these definitions. So, it has to be a purely periodic continued fraction expansion. We will remember this and we are going to use this that root d plus integral part of root d is always a purely periodic continued fraction expansion. So, we are done with these quadratic rationals and expressing them as continued fractions for the time being. Now, what we are going to do is to consider a little bit of very basic algebraic number theory. This is something that we are going to use in solving the Brahma Gupta equations. So, what we do here is the following we take a square free d square free means that there is no square which divides d earlier we were looking at non square d. So, for instance 8 is a non square d because 8 is not square of any natural number. But 8 is not square free because 4 divides 8. So, when we are writing the corresponding this is called q root d. When we are writing this q root d we will consider only the square free d. The reason being that if I have x plus y root 8 then this can also be written as x plus 2 y root 2. So, the number of elements which are in q root 8 the elements which are in q root 8 are contained in the elements which are in q root 2. And of course, we are allowing rational coefficients x and y are rational. So, if you have a plus b root 2 this is a plus b by 2 root 8. So, we have that this is also contained in q root 8. So, these are the same sets we have defined a set q root d by this way. So, this is our definition it is of the form x plus y root d where x and y are rational numbers.  So, we will stick with this particular convention that our d is always a square free d. What can we do with this set?  So, this set q root d is actually closed with respect to addition if you take addition of any two such numbers in the set then the sum is again in the set. So, q root d is closed under addition there is the 0 which can be written as 0 plus 0 root d. Therefore, this q root d has the additive identity and it also has the additive inverse x plus y root d plus minus x plus minus y root d is going to give you 0 plus 0 root d. So, q root d is a group with respect to addition. You also have the multiplication defined on it. We can write x 1 plus y 1 root d into x 2 plus y 2 root d as we have x 1 x 2 plus y 1 y 2 d plus now the coefficient for root d that is x 1 y 2 plus x 2 y 1 root d because x i are rationals y i are rationals we see that these two numbers are rationals. So, the set is closed under multiplication also you have rational coefficients and you are taking the sum and product and you again have rational coefficients. There is the element 1 which is 1 plus 0 root d. So, you have that there is multiplicative identity. We of course, have the associativity for both addition and multiplication. So, to check whether we have group structure the question that we should ask is whether we can divide by every such x plus y root d and remain in x plus y root d. This is something which is very important. In the very first few lectures we have talked about divisibility in natural numbers and the important thing for us was that whenever you divide a natural by another natural we do not want to go outside the natural numbers we wanted to be in the same set. So, here also we are asking whether we have one particular element of q root d. Another such element and let us assume that the element that we are dividing by is non-zero because we know that we are not going to divide by 0 in and then if you divide by 0 you will not remain in this set you will get something called infinity let us not go into that. Let us remain in our finite world. So, we are dividing by a non-zero number and the question is can you divide by a non-zero number and that is true you can actually divide by a non-zero number and you can you will remain in the set q root d. This is something that we have already seen when we have computed the continued fraction expansion for root 2, root 3 and so on. There were instances when we had 1 by root 3 minus 1 for instance and we needed to multiply both sides by root 3 plus 1, root 3 plus 1 and we obtained some rational combination of 1 and root 3. So, this is indeed true that you can divide by a non-zero element in q root d. So, the set is first of all equipped with addition and multiplication and with respect to addition it is a group with respect to multiplication all the non-zero numbers form a group. There is another way to see this we have this norm map defined on q root d. What does the norm map do? Note that this is nothing but x plus y root d into x minus y root d. If you take the product x plus y root d into x minus y root d we get x square minus d y square which is what we have and the coefficient of root d happens to be x into minus y plus y into x. So, it is xy minus xy and that becomes 0. So, we have that this norm is always a rational number x square minus d y square and if you have x and y non-zero x y is not 0. If you have that the product is non-zero then norm of x plus y root d is also not 0. This is because if you have any rationales giving you zero solution for x square minus d y square that would mean that d is of the form x square by y square and we have taken d to be an integer which is not a square. In fact, we have taken d to be square free. It is not a square and it is not even divisible by any square other than one of course. So, this d cannot be square of some integer it also cannot be square of any rational number. I told you in some of the last lectures that this is going to use the fundamental theorem of arithmetic that if you have a non-square then its square root is not a rational number. So, you are not going to get solutions to x square minus d y square equal to 0 where one of the x and y is non-zero. Of course, if you have y to be 0 you get x square equal to 0 and so x is 0. If x is 0 you get d y square equal to 0 and then y is 0. So, if any one of them is 0 other is also 0 and you have no solutions when none of them is 0 that would mean that the norm x plus y root d is 0 would imply that x is 0 and y is 0 and in fact turning it in the other way if you have that if any of them is non-zero your norm cannot be 0.  We have noticed that this is a rational number of course x square minus d y square and it is not 0. So, you can divide by a rational number you can always divide by rational number and b in the set of rational numbers. So, you will divide by this rational to x you will get a rational you will divide by that to y and you get a rational. So, ultimately this number is again in q root b. So, this tells you that you can always divide by a non-zero element of q root d and remain in the set q root d. This is all encoded in this sentence that the set q root d is actually a field. Just like we have seen the notion of a group there is also the notion of a ring and here we have that there is a notion of a field. Whatever it means it just says that the you can divide by non-zero numbers and of course you can add and subtract and multiply by any number and you will remain in the set q root d. Now, we noticed that any number which is here in q root d suppose it is of the form m plus n root d which is here in q root d this satisfies a polynomial a x square plus b x plus c is satisfies means it is a 0 of or a root of this polynomial a x square plus b x plus c where a b c are integers. This a need not always be equal to 1 because you know for instance we have the element 1 by 2 which is there in the rational numbers. So, it is there in q root d also and the polynomial satisfied by 1 by 2 over integers if you want a b c in integers then the only polynomial satisfied by 1 by 2 is 2 x minus 1 you cannot have a polynomial of the form x minus alpha satisfied by 1 by 2 where alpha is also an integer. Similarly, if you have any higher degree polynomial satisfied by 1 by 2 over integers then the leading coefficient the coefficient of the highest possible degree that cannot be 1 this is something which uses slightly advanced mathematics but that was only for an example. So, what we have is that if you have a number in q root d this number a need not always be 1 but we would like to take numbers where this a is also equal to 1 we call such numbers to be algebraic integers. So, these are the elements plus n root d in q root d that satisfy x square plus b x plus c equal to 0 with b and c being integers. So, for instance if you are looking at rational numbers which satisfy such polynomials it will turn out that those are nothing but integers. So, these algebraic integers we are calling them integers, algebraic integers for the reason that when you consider the field of rational numbers the algebraic integers in rational numbers are the ordinary integers that explains the nomenclature. What happens later is that all these elements form a ring you can add such elements you can subtract 0 is there associativity of course holds in the whole complex numbers. So, we will not keep mentioning it again and again. So, the set of algebraic integers is a group under addition you can multiply by 2 algebraic integers and get an algebraic integer of course the element 1 is there but we have problem when we come to division. Of course 1 and 2 these are algebraic integers because these are ordinary integers but you cannot divide 1 by 2 and get an algebraic integer 1 by 2 is not an integer any algebraic integer which is a rational number has to be an integer. So, you cannot divide by them but you can definitely multiply by them and therefore it is an interesting question to determine all the elements by which you can divide within the set of algebraic integers. These elements are called units and we will see a very nice way using continued fractions to describe the set of all units in a given q root d and it will also lead us to what is known as the Brahmagupta equation. So, this is something that we are going to conclude our course with I hope to see that you will stick until then. Thank you very much.


This was narrated by Imam al-Tabarani and it is a sound chain, you know, that Saint Najib Reel came to the Prophet Sallallahu alayhi wa sallam telling him that live as long as you wish, you know, and you are going to die and do whatever you want to do and you are going to be rewarded according to this and love whoever you want to love, you know, and you are going to leave him alone and be sure that the honor of the believer to have night prayer and the, yes, the honor and the high rank of him, you know, not to ask anyone, you know, or be self-sufficient. This is in Arabic, you will die and love whoever you want to love and do whatever you want to do and you are going to be rewarded and the honor of the believer to have night prayer and the high rank of him, you know, this is a pure letter from Allah swt about the meaning of this life. Many of the Muslim unfortunately they don't understand the meaning of this life Do whatever you are going to do, and you are going to be rewarded according to it, you know. By intention, by good intention, you are going to make most of your reward as good one, you know.  This is, there's an improvement of this, yes. There's an improvement when you live according to Allah SWT, when you have your deed, and your intention is going to be according to Allah SWT, when you get the maximum of the time, namely those asgar that may be doubled, you know, and whatever of that. Because we have limited age, we are limited to such an age, you know.  And this was narrated by Imam Malik in his Muwatta that the Prophet, Allah SWT, did observe the previous nations, you know, and did observe his nation, and he found out that they have short, very short of age, and he was given Laylat Al-Qadr Khayrum in Elfi Shahr. That's mean we are lucky to follow the Sayyidina Muhammad ﷺ, and many of our deeds, they are going to be doubled, you know, for one way or another, namely like Laylat Al-Qadr or by asgar, or by merely follow the Prophet ﷺ as illustrated, you know, in some hadith. Then he showed two facts, you know, the honor in this life may differ from one person to another, being a president or so and so or whatever, you know. Here the honor to have night prayer, I'm sorry to tell you, because of the power we kept sleeping, you know, over the night, you know, and we are going to look forward for those people, you know, it's going to be beneficial for us.     Why? Because you are fanatic? No, because when I say Allahu akbar, I'm going to face Allah.  Personally, I don't cry. Why? Because of deficiency in me.  And then what Allah SWT said, That's mean, this is to give us description that we waste in the prayer, and we follow our desire, you know, in this life, and we shouldn't do as such, you know, because this negative, you know, description from Allah SWT to correct our safe, may Allah SWT correct us. May Allah SWT correct us. And may Allah SWT bless Sayyidina Muhammad and his family and companions. Alhamdulillah, my Lord of the worlds, and the end to the righteous. And there are no enemies except the oppressors. And I bear witness that there is no god but Allah alone, there is no partner.


We turn our attention to what's going on in the marketplace, particularly when it comes to security, terrorism, espionage, and sometimes when we're before a court, line on the oaf. Todd Mickelson has this new product called Converis. It's not new to the marketplace, it's been out for about six years. Todd, welcome to this edition of Your Voice, Your Future, and thank you so much for joining us. Thank you for having me. Todd, tell us a little about Converis and how it works with the lie detector, how it may work with COVID-19, and other areas of security as it relates to the world, because it's already being used at other parts of the world and in certain aspects of the federal government here in the United States. Yes, so Converis is a company that produces a next generation lie detector.  I've got to tell you, my HHS correspondent at Amish and I had an opportunity to detect that test, and it was pretty perfect. What's the accuracy in terms of the percentages, Todd? So it is 88 to 90 percent accurate in terms of correctly classifying someone as being honest or deceptive about the topic they were tested on. To put that into perspective with a traditional polygraph, a traditional polygraph ranges between about 78 percent and up to 85 percent accurate. It has a range because with a traditional polygraph, you have a human being that is administering the test and interpreting the results, and with IDetect, the computer administers the test and then uses a computer algorithm to analyze the data that's collected with an eye tracker during the test and scores the results. You also think that IDetect is on the cutting edge for detecting COVID-19, the coronavirus, not only here in the United States, but also for new immigrants coming into the United States. How does that work? Yeah, so an IDetect test can cover really any topic that you can imagine. Prior to COVID-19, and even during COVID-19, it's been used for screening individuals who are going to work in the intelligence community or perhaps law enforcement, where the hiring agency wants to know if these individuals have had issues in the past that would disqualify them for coming to work for the agency. In the case of COVID-19, we have a number of tests that can be used to verify if someone is being truthful about whether or not they have been exposed or whether or not they're coming from a location where there's a hotspot and they could have been exposed. We have a number of governments that are wanting to use it in that situation where someone may be inclined to lie because they know if they're truthful about having been exposed, they may not be granted entrance at that point in time or may have to be quarantined. So talk about the lie detector. What is the turnaround before you get the actual results and also the turnaround for COVID-19? Yeah, so any IDTEC test takes approximately 15 to 30 minutes, depending on the number of topics that you're testing for. During that test, we capture up to a million data points, and that data is analyzed by a computer algorithm in approximately one to two minutes, where a score is generated indicating whether or not the person was deceptive or truthful on the given topics they were tested for. So it's near instantaneous once you finish answering the questions. What are the flaws? So you said 86%. What are the flaws, the 14%, where it's not always accurate? Yeah, so excuse me, the range is 88 to 90%. That means that out of 100 people, if you consider a 90% accuracy, you'll have 10 that it either can't classify or will classify into the wrong categories. So you have a mix of false positives and a mix of false negatives. That's true for any of these technologies where it's trying to analyze from a physiological response whether or not you're being truthful or not. So it's a data point. We don't claim that it's 100%. We have a number of customers that we use IDTEC in conjunction with a separate independent tool such as a polygraph. If you get the same result on the two independent tools, then you have a 99.5% probability or outcome confidence that you got it right. So it's another tool in your tool belt that you can use to help make a decision, but it's not 100%. How does this IDTEC and this other technology that's out there can also assist with social distancing? So the traditional polygraph requires that a number of sensors be attached to the body, a strain gauge that goes across your chest and your abdomen, a pressure cup on your arm, other sensors that get attached to your hand, for example, to detect if you're starting to sweat. Those sensors really require that another individual attach them to the subject, to the examinee. And one of the benefits of IDTEC is it doesn't require those sensors to be attached to your body.  They can click a start button and simply touch a mouse to respond to the questions that are being presented. The mouse can be easily cleaned, excuse me, after the fact. And a test proctor, someone who's just ensuring that the person is following instructions, can actually manage that entire process remotely in a separate room or in a socially distancing compliant way in the same room. Listen, and it's available in most places. Is there a website? Yes, you can go to Converis.com, spelled C-O-N-V-E-R-U-S. How long before you think IDTEC will be in the market, particularly when it comes to COVID-19 and the viruses that seem to be sweeping not only the world, but especially the United States? Well, like I said, we have clients in 45 countries all over the world, including here in the United States that have been using IDTEC during COVID-19 because it can be used in a social distancing compliant way. Some of those organizations are using it for more of our traditional scenarios where they're testing for whether you're lying about your previous activities, whether you have a drug problem, if it's a security clearance, whether you've engaged in activities that would disqualify you from getting that clearance. Some of those governments that do use it for immigration-related situations. So to be able to verify if, for example, your flag is having terrorist ties, whether in fact you do have terrorist ties, and they're just now exploring whether or not it makes sense in certain situations, like I said, to verify if you're coming from a hot spot, if you're not being truthful about where you're coming from. So we have one particular government that is looking at using this because individuals may attempt to enter the United States indirectly through their country.  And so unfortunately, I can't disclose those countries that are doing that, but it's currently in process as we speak. How expensive is the eye detect? So the system itself is a standard computer with a specialized eye-tracking camera. And it sells for approximately $5,000. We charge on a per test basis that is run. And the average cost is in the neighborhood of about $60 for the test itself. Well, listen, I want to congratulate you on your product. We look forward to hear more about it in the future. Thank you so much for joining us for your voice, your future Tahoe. Thank you so much for joining us for this edition of the Armstrong William Show. On behalf of all of us here at WGLA 24-7 in Hollister Holdings, have a blessed day. I'm Armstrong William.


This study examined very early onset inflammatory bowel disease, the OIBD, in children aged less than six years. The results showed that approximately 30-40% of these children had underlying immunodeficiency states. Additionally, gastroscopy and colonoscopy were performed in all patients, along with basic workup for associated immunodeficiencies and molecular genetics. This article was authored by Huma Arshad Chima, Nadia Waheed, Anjum Saeed, and others.


Alright, so everything's fixed question mark ladies and gentlemen welcome back to the channel. My name is Jack the Buster I should know be I'm watching episode 60 of Dragon Ball Super today and in the last episode We got to see Beerus flex a little bit and it felt good He completely obliterated our universe is our timeline Zamasu to prevent of course everything that happened in Trunks timeline from happening here and he said that everything should Be fixed now in the future that stuff with gods and deities is a lot more cut and dry than stuff with mortals in terms of time So I guess we're gonna find out today whether or not this whole the messy situation with Goku black and Zamasu is cleaned up Or if it's a little bit more complicated than that Which I think it will be because there's no way we get off scot-free without having to take down Goku black But alone the invincible body Zamasu if you knew the channel don't forget to drop a sub and let's hop into it No, no, no, I'm just skeptical Trunks has seen way too many people died for it to be that simple I know he's like coddling him. I'm sure they're cowering. I love we some beer is so much They're by far my favorite addition to the entire Dragon Ball verse from Super Shoot Shouts of Alma. That's my goat. It's time travel. So there's no rush after all well I mean his time is said a bit of dire help if everything isn't big stop So like how is that possible that he's not hungry on earth Trunks, it's really good for your tum-tum Talks to him like he's a five Is that just sliced bread? Yeah, it doesn't look very appetizing that looks like a sin-zoo bean in the middle Close eyes comically popped out of his head. This is such a cozy OST Dude Goku is something else man. I Am going to the future too, I would hope so we need some kind of backup plan if it's not all fixed up But even if there's a tiny yeah We should go there prepared saying where's Vegeta. I'd love the chance to fight Zamasu one more He's invincible. We can't just fight them again with others. Yeah, that's hardly your style Vegeta He seems worried. Yeah quite dire with her against it Oh, I promise you Trunks. I won't forget the beans. It's not just about the Senzu beans Yeah, that's ominous. That's very ominous. Holy then you could come with us too to say I told you so That would be interesting if Beerus went to you may be willing to commit taboos But this God is staying out of doesn't want to get in trouble. He'll never we have to check Oh it got to him. He doesn't want the possibility of it still being affected Are you saying he should have vanished the moment things change that they killed Zamasu? Yeah, then how would you know about black? I mean, he's right. This will be confusing time travel always is. Oh, he actually is like a full-fledged theory time has been split into more than one reality oh Branch off to another's one timeline where he's not a thing because their future will be different. Oh, this is beautiful Everything's still here Exactly like 18 there's nothing that can be done to change his timeline now Does this mean that chunks like understands more about time travel and like timelines and everything than Beerus and wheeze I'd only seen father's face and pictures heard about him in stories So to change this timeline, but his is just permanently yet Affected. That's why I traveled here in the first place to give him a drug to treat that disease and stop him from dying And I'm grateful by the way You're the best. So when you went back to your time, he was alive again, wasn't he? His timeline was already permanently affected I've seen stuff like this in movies It only affects the future of the timeline you've traveled to that's why whenever he doubted Beerus It wasn't like out of a selfish reason He's experienced firsthand that it can't change even if it's if deities are supposedly different the timeline where I live Then there's the one where you're home. Is it so tragic man? That's such a beautiful shot of them hovering there next to each other this mean that could still be a future with somebody actually Mentioned That's why you can't believe Lord Beerus changed your future even if you want to because that's not how you've seen it go I mean, I'll try to be optimistic and believe Beerus outing you is disrespectful. I see that and I'm sorry Even though I need to see for myself. I'm holding out hope that you're right. Yeah It's not like you once fierce to be wrong. Maybe God's effect time in miraculous ways Never got his name. I feel bad. I mean it though. You've given me hope. So thank you for that He's had to have touched some sweet spot in Beerus deep deep in that dark heart I'd like you there, but do we have a backup plan if black and Zamasu are there? You'll never come bother us again. Okay? Okay You have a truck here. Yeah, what do you mean? I won't see you again Dog Goku He lost them we can't just stack up Sinsu beans and bank on that man Oh, and by the way, oh wait, he put them back there, but it made sure I saw that something's gonna happen That's true she should go You don't want to see that future Bulma His drip is back, baby Same the zeno verse flip is okay, but the jacket can't be matched Yeah, are they stuffed in oh my Do you I'm more important than you go cool All right now we either go there and everything's perfectly fine or we go there and it's just the exact same There's no in between. I don't think and maybe Beerus is right. Maybe the future is saved. Oh He's seeing them off And there they go. I like how we send beers yet Don't stop them despite the fact that it is blasphemy to them. Don't you want to see how it turns out?  Oh, it's these beautiful. Oh My who is that? Hey little trunks did all he could he gave him himself a pep talk the one he needed all right Let's find out if the things are all fixed up.  Here we go. They're still destroyed building right there Everything's still flattened all the matters if zamasu and black are like alive Or does it matter that everything's still obliterated? I guess because it hasn't been undone No Well, I don't know something's still gonna happen to them. He still could be right. I think Well, I guess biris said that would have reversed everything so everything would have been fine from the moment black came Or that zamasu came to earth Oh, they are perfectly fine. They are here. Wait, so biris was completely wrong. That's gonna I mean, I wonder what his explanation for that would be then whenever he finds out mom Can you be in charge of this? You bet. Does none of this make sense now? He was so he was banking on the fact that it would change things. Is everyone okay? My snot. Oh wait, what she was trying to help some people fleeing from black. Oh, no Is this the foreshadowing I was talking about? Is she dying? Oh, surely she doesn't oh, wait, they have a senzu bean Just give her one goku quick. Yeah senzu bean. Oh, yeah Oh my god. Oh, I thought you lost them already. Oh, I would have lost it Wait, what it Oh, I guess because she she can't chew it So he was like a like baby bird. I was like, what was that? You've never kissed someone. No, of course not.  Yeah, so what you're looking good I mean, she has to be fine rise to senzu bean. It's like all purpose medicine She wakes up to see trunks in all of them.  I I can't man goku is just different In perfect timing. Yeah, that means we only have four senzu beans left. They only brought five Hi, ideal smiel. So grown up. It's great to meet you mom. She said you're so young That energy do you sense it? Well black and zamasu knew. Yeah when they got here So I guys like actually, what's the plan? Surely we came up with something. I wish biris had come now So we could see that he was wrong. I'm sure we'll find a way. He's so optimistic I love that if they literally have all right, they're perfectly fine like nothing has changed here seemingly How will it be different? Oh my god, Vegeta, what are you doing?  I mean, maybe they'll develop rose over the course of this fight So this earth can have a future. Well, that's not very sane of you And we know you're quite the detective And made this fake copy here wrong goku. Wait, this is actually goku. No There's no way like goku's actual body down to the last battle scar Oh, I took the time ring and found the super dragon ball and put his mind in goku I switched bodies with you goku. Oh my gosh. It's actually goku's body So that means you took over my body. Wait, so what who is this zamasu? Then I killed you Okay, by your own fist That's kind of dark. That's it. There's a new outro. Oh my god that episode felt so short Okay, so biris I literally could not have been more wrong Nothing has changed in the future. It is still obliterated. Nobody's alive and goku and zamasu are completely fine So There's as many answers as we've gotten over the course of the last five or six episodes It still brings up a even bigger one this episode of why biris was so wrong He was so obscenely gung-ho about the fact that that that this cleared everything up killing that zamasu And maybe it was just his ego getting in the way that he wouldn't consider any other possibilities But why was he that wrong? Maybe I'm looking too into that as well And maybe it is just his ego, but I'm gonna keep that as sort of like a point in the back of my head as well I'm not sure if I should but now we know that that's actually goku's body It's not any fake and that's why he's kind of been talking about how he's like getting used to the body and whatnot Or getting used to being a saiyan because he literally just took over it But man, I don't feel any better now than I did when the first time we came here and fought them Because I know how powerful they are and again literally invincible body. What are you to do? Yeah, you have what would they say four senzu beans now left great You could take four Insano hits use those and then what you don't have any power I mean, and I know the whole thing is like saiyans pushing getting pushed to their limits is like the goal And that's how they become stronger But and you'd be pushed so far to destroy that which is invincible We'll just have to find out if you need a channel Don't forget to drop a sub this has been episode 60 of my dragon ball super watch through and I catch you guys in the Next one is base


Hello there, everyone, and welcome. This is Melissa Armel with Stocks, Wishing and Reviewing, AEO. This is a gap down that was a follow-through from yesterday's sell-off, which actually was an earnings that gapped up and fell, which was not something that I would have done yesterday whatsoever at all and did not do. But today was good, and I wish I would have seen this earlier, quite frankly, but we did end up getting this late. I'll go over it. High of the day was 1839. Low of the day was 1717. This probably still is lower, even perhaps another day down. If you feel so inclined, but let's take a look at it. So again, this fell out of the gate, and usually I have a couple of things I'm watching in the morning. The things that I watched this morning weren't amazing, but this, I wish I had on my list right out of the gate, and I did, but luckily I saw it early enough. Early enough, here's the sell-off, boom, and then this did continue to sell off a little bit more. Broke the low of 1721, went down to 1717. Just thinking 17 didn't get there. But anyways, this, we ended up getting and got the drop. Some people got out. Some people held it, and you also could have taken more in here. I'm going to go back, and you could have tried to maximize your profit a little bit more in here, and here's the drop then into where it ended up being in the low. So this is pretty much done for the day here at 330, but this, I still believe at some point this gets to 17, whether it's tomorrow or not, I don't know, could get down tomorrow. It's hard to believe anyone would buy this here. I mean, honestly, this is so weak. If you look at the market right now, and you look at this market, it's green today, excuse me, an A-yo fell. So I don't know who would come in here and buy this at this point tomorrow, no matter what the market does, but either way, it was a nice day trade today. Again, wouldn't have touched this yesterday, but today it was a good one. So we'll see what we get tomorrow. It'll be interesting. There are a few earnings out tonight and tomorrow morning. We'll take a look tomorrow's Friday, slow week here for the market with the way that the holiday was. We're just getting into the groove here with June, but we will see what tomorrow brings last day of the week. A lot of data out tomorrow morning. Anyways, if you have any questions that you're interested in the Golden Gap course, it's this weekend, June classes this weekend, 8th and 9th, 9-to-5 Eastern time, cost of class is $59.99. Email me at Melissa at thestockswish.com if you want more information.


A total solar eclipse is an incredibly moving experience. In the continental U.S. there's going to be an amazing event on August 21st, 2017. A total eclipse of the sun. Well a total solar eclipse is this incredible phenomenon that happens because of the sun being 400 times bigger than the moon, but also 400 times farther away. Suppose this tennis ball is the sun and the ping-pong ball is the moon, and I'm a person on earth looking at the two. If the moon is a bit too far away in its elliptical orbit, then it doesn't quite block the sun, and if it's too close, then it blocks not only the bright disc of the sun, but the inner corona as well. But if I line them up so that the ratio of distances is 2 to 1, that's the same as the ratio of sizes, and then they look the same size in the sky.  Nowhere else in the solar system is that the case. So if aliens were to visit our solar system, I claim they should visit earth at the time and location of a total solar eclipse, and they would leave very happy. The Space Sciences Lab, together with Google and a number of institutions, has decided to document the eclipse over the hour and a half that the shadow crosses the continental US. We've got about 1,000 serious photographers taking good quality images of the sun, and anyone else who wants to contribute can do so as well. By having many images of the corona over the course of an hour and a half, we'll be able to examine the changing structure of the corona, and that's important because the satellites orbiting earth right now can't monitor changes in the inner corona for technical reasons, but from the ground we can. Scientists want to understand the structure of the corona better because it tells us about the inner workings of the sun. There are solar flares and coronal mass ejections that then interact with earth's magnetic field and can cause power blackouts. So the better we understand the sun, the more we will be able to respond to and indeed even predict these tremendous outbursts from the sun's surface. And that's something that citizen scientists will actually be able to help out with.  So this is a real opportunity for tens of millions of Americans and others throughout the world to see the total solar eclipse.


Hello, everyone. Often you end up in situations where you want to deploy your applications and you want those applications to run on specific nodes or specific parts of infrastructure. Or maybe you have your application made up of multiple components. And for example, you may want your front end to run on specific infrastructure, your database to run on some other part of the infrastructure. So you want your application components to run on different parts. So let's talk about how we can do that in OpenShift and how you want to run your application components on different nodes. In my OpenShift environment, I have a set of nodes. If you look at the nodes, I did some labeling. There is one node which is an infrastructure node and I labeled it as infra. But there are four nodes that I want to use to deploy my applications. And if you look at the labels, there are two nodes that have categorized as region equal to secondary and region equal to primary. So node one and node two are in the secondary region. Node three and node four are in the primary region. Now these labels, regions, and zones are just the names that we use because they come as set up by default. But you can choose to use whatever names you want. And the policies that based on which the scheduler makes a decision on where to deploy your application component depends on these labels. Now as a first example, let's look at how the OpenShift behaves by default and how we can configure the default behavior for the scheduler to make a selection of where to place your applications. So for that, in the OpenShift's master configuration file, you can set up a default node selector. And in my case, I set it as region equal to primary, which makes sure that if I don't provide any values on, or if I don't provide any configuration while deploying my application on where to place my application parts, those application parts will land up in region equal to primary. So the OpenShift administrator in my case has set up the default node selector in the configuration file as region equal to primary. If I don't provide any other selection, my application parts will land on the nodes that are labeled as region equal to primary. Let's verify that by deploying an application. I'll create a new project. And I'll deploy an application with a simple app. I'm just deploying whatever is the default. Let's see where it lands up. It takes a moment to build and deploy. The application is now running. A new pod is up. The pod is on node three, which is in the region primary. So by default, the pod land up on one of the nodes, which is node three, which is in the region primary. Let us try to scale up. I'll scale to two parts. Now, if you look at where the second pod is getting spun up, the second pod is on node four. So again, node three and node four are both in the region primary. If I scale up further, all the parts that get added will be either on node three or node four. So let me go to a different view. So these are all pods. Every pod is either on node four or node four, node three, node three, node four, node three. So they're all landing up in region which is labeled as primary. Now I'll clean up this project and we'll see how we can change this project configuration in such a way that any pods that are created in this project will land up in region secondary instead of primary. In order to do that, the OpenShift administrator needs to edit the project configuration to add a node selector to the namespace. So as an administrator, I got into the namespace for the new project and I'm adding a new annotation and the node selector here says region equal to secondary which means that any pods created in this project will end up in this region. Now let's go back and create the same application and see what happens. The application is getting built and it will get deployed. The app is now running and it is on node one. Node one is in the secondary region. Now if I again scale up, all the pods are either on node one or node two, node two, node one, node one. So everything lands in the secondary region. If I try to add another application component, let's say I had a MySQL database here, I have a second application component that's starting up and even this part is on node one which means it is in the same secondary region. So now we have the default as region primary and we have forced the namespace with an annotation of where we said node selector region equal to secondary and all the pods in spite of the default being region equal to primary, they are landing upon in the secondary region on one of these nodes, right? Now note that the default node selector configuration for OpenShift as well as the node selector configuration for individual projects is done by the OpenShift administrator. The administrator defines where pods created for any project should land. Now let us say you want the administrator to give you freedom to choose between primary and secondary as and as a developer you wanna choose where you want your application components to land up between these regions, right? How do we do that? That's the next use case. So as an administrator, we'll go and edit that namespace. As an administrator, I'm editing this namespace to have a node selector value as blank, empty string. Note that I am not deleting this node selector configuration. If I delete it, the default would apply. I don't want to delete it but I want the users of this project to be able to deploy the application to any region they want. So I'm just making it blank. Now back as a developer, I'll go back and delete all the contents of this project. Now let's add an application component. Again, I'll deploy my SQL database. Since we don't have any restriction now, it can land either on nodes within primary region or secondary region. So it could be anywhere, right? So the pod is now up. Let's see where it is. The pod is coming up and it would come up on node two. And node two is in the secondary region, right? In spite of the default region being primary, since the node selector is empty, the default did not get applied and the pod landed up in node in the region secondary. It is from the developer's point of view, right? How do I force this mySQL pod to land in the primary region? There are a couple of ways to handle that. Let's look at the deployment configurations. So the first way, we'll edit the deployment configuration for mySQL. I open the deployment configuration for mySQL and go to the spec under the template. This template represents how the pod's template is going to look like. And under this template, where you see spec, we'll add the node selector here. So our pod landed up on secondary, so we will force it to go to primary and I just made this change. Now, if I look at oscget pods, once I made this change, a new deployment would have started immediately, right? It's a deploy is running now. And you can see that the old pod went away and a new mySQL pod is getting deployed. Earlier one was OHTR, the new pod, it's mySQL2j71kd, right? This is the new pod that's coming up. So let's see where this new pod will land up, j71kd mySQL2, right? And this pod is on node four and node four is in the region primary, right? So just by changing the deployment configuration and adding a node selector in the deployment configuration, we moved the pod that was running, that landed up in the secondary region to the primary region and making the reverse change will again move the pod from primary region to secondary region. So it can land on any of these nodes, but you can force a region in the pod by changing the deployment configuration. So as a developer, this is the third way of doing it. You have control on where you want your pods to land up. Now the next example, another scenario, right? I have multiple application components in my application. Maybe I have, I want my database to land up on a different set of nodes. I want my application logic components to run on a different set of nodes. Let's say you want to divide it that way and you want your regions where your database runs to be separate from the region where your application logic turns, let's say, whatever your needs are, right? If you want to do it that way, what else are the possibilities? I mean, do I have to do it each individual component by changing the deployment configuration for each component separately? Or is there a way I can apply all these node selectors across different components in my architecture? Like in OpenShift, we have templates, right? So can I make this kind of a change in a template? And the answer is yes. So let's look at an example of same kind of a change in a template. I clean up the project again. So we will copy an existing template and edit it. So let's look at what templates we have. I'm interested in a template that has multiple components. So let's pick up this one, cake, PHP, MySQL example. Now we will get hold of this template. I'm searching for all the templates in the OpenShift project. Remember, all the templates are stored in the OpenShift project and I'm trying to find that specific template of my interest. The name starts with cake, PHP. So I'm looking at this cake, PHP, MySQL example. This has both PHP and MySQL. It deploys two components. So we'll pick up this template. I want to get this output of this template as a JSON file. And let me save that file. So now I have my template copied in, copied locally into this file. Let me open this file in an editor. And so we are looking for this template and this template has a spec that it deploys two different kinds of containers. One is a PHP and the other is MySQL. I'll add node selectors. We want to deploy the PHP part of the application in the secondary region. Again, I'm looking for the template for the database and for the database part, I want my database to be deployed in the primary region. I also want to change the metadata of my template so that I give it a different name and I'll also make another change to, I'll be using this template in my local project. So I'm also changing the namespace to deploy this template into the new project namespace. So I made totally four changes to this template. One, I changed the name of the template. I changed the namespace in which this template is going to be used. I have made a change to the deployment configuration part of the PHP part to get deployed into the secondary region. And I made a change to the deployment configuration part of the MySQL part to deploy into the, and then I will create a template in my project. So all I'm saying here is process this JSON file which has the specifications for the template which will end up creating this template in my project. So this template is now created. So if I say under this project, it shows the new template that I just added. Now let's go back to the project and this is the template that we just added. We'll use this template to deploy our application and this template deploys a PHP component as well as a MySQL. Just go ahead and say create. It's trying to deploy both the components. The MySQL is already deployed. Let's see where this part is running. This part is being spun up on node three. It's running on node three now. Node three is in the primary region. That's where we wanted our MySQL to get deployed. And we wanted the PHP part to be deployed in the second region, which is one of the node one and node two. The PHP application is being built. It'll take a couple of minutes for it to get deployed and the PHP part is now running in on node two, which is in the secondary region. This is an example of how you can change the templates to add node selectors so that when you have a bigger configuration, you can direct the individual application component parts, the parts of the application to go to different regions if you wanted to, right? Or different set of nodes if you wanted. To summarize, we discussed different ways of deploying the applications to the nodes of our choice. First, we covered how the default works for the entire environment. The administrator would set up a default node selector in the project configuration of the master config file, which will make sure that any project that gets created gets into that default node selector that is defined here if no other values are used by the user. Second, we talked about how you can define those, the node selectors at the project level, where any components that are within that project would go into whatever labels are given in the node selector. Third, we talked about leaving the node selectors at the project level open, but providing node selectors in the deployment configurations of the individual application components that are within the project so that you are directing those particular components to go to specific nodes. Fourth, we also talked about complex situations where you have a bunch of components getting deployed together using a template where you can go and edit the deployment configurations within the template so that when the individual components gets spun up, they go into the specific regions of your choice. So different ways to solve the problem. And each one has its own value. So use whatever makes sense for your situation. Thanks a lot for watching this video.