Let us start our today's lecture on this video course of Geotechnical Earthquake Engineering. Let us look at the slide here. On this video course of Geotechnical Earthquake Engineering for NPTEL, we are going through this module 4 on strong ground motion. Let us do a quick recap what we have learnt in our previous lecture, like we have learnt about what are the amplitude parameters of an earthquake, like it can be acceleration, velocity and displacement record with respect to time, then how to define the peak value of the acceleration we have seen that PHA peak horizontal acceleration and it can have two orthogonal components in north-south direction and east-west direction and the maximum resultant value of the PHA we can take by taking the vector sum of those two orthogonal PHA values. And Trifunik and Bredi in 1975, they have proposed for the design what is the value of PHA with respect to the relationship with the modified Markhali's intensity scale MMI scale and generally the PVA is not that important earlier people used to think about as proposed by Newmark and Hall in 1982, but in recent days people say it is better to estimate PVA also that is peak vertical acceleration and in absence of the data of PVA as per suggestion by Newmark and Hall 1982, PVA can be considered as two-third of the value of that PHA for the design purpose. And peak acceleration data with frequency content and duration is more important, because we have seen that it is not necessary that only that PHA value will be more important, it is also necessary how much is the frequency content and how much is the duration of an earthquake. Then we have seen that relationship between PHA versus MMI and PVA versus MMI. So, this is for the vertical, this is for the horizontal as proposed by Trifunik and Bredi in 1975 corresponding to various modified Markhali intensity scale. So, if you know the MMI value of a particular earthquake at a site using this relationship you can get your value of PHA or PVA which can be further used for the design. Then we talked about the value of PHV that is peak horizontal velocity and we have mentioned that PHV is a better estimation that PHA because of capturing the intermediate frequency also very well, but whereas the peak displacement or peak horizontal displacement and peak vertical displacement though they are associated with the low frequency content, but because of the filtering error that is after filtering out the noises etcetera it will be very difficult to get a reliable results in terms of your peak displacement values. So, that is why in most of our earthquake engineering design either we use PHA that is peak horizontal acceleration or PHV peak vertical acceleration. Then we talked about various other amplitude parameters like sustained maximum acceleration we have seen it can be a three cycle sustained or five cycle sustained depending on your requirement that is how much that highest value of acceleration is continuing through how many numbers of cycles. Then we have seen for the design what is known as effective design acceleration and as per the proposal by Kennedy in 1980 that EDA can be considered as 1.25 times of that three cycle sustained maximum acceleration of PHA and Benjamin and associates proposed that if you filter out all the higher frequencies that is above 9 hertz frequency if you filter out all accelerations then whatever acceleration spectra or acceleration response you get with respect to time that acceleration time history whatever PHA value is gives directly you can use that as your design or effective design acceleration. Then to provide the frequency content parameter we have seen either using Fourier spectra or by power spectra or by response spectra we can find out how much frequency content exist in a particular earthquake motion Fourier spectra is nothing but it is an assumed Fourier series of a randomly behaved earthquake motion that we express in the form of a Fourier series through this periodic function and this value is given as the amplitude and this value is given as the phase angle of whether if you consider it is an acceleration or displacement accordingly this value will correspond to that value of amplitude and phase. We have seen what is known as Fourier amplitude spectra which is nothing but a plot of that amplitude versus frequency and also we have seen Fourier phase spectra which is nothing but a plot of phase versus frequency this is a typical plot of Fourier amplitude spectra Fourier amplitude in log scale in y axis and frequency in the log scale in the x axis there we have found what is the definition of the corner frequency and the cutoff frequency that is the minimum value of the frequency at which that maximum amplitude or maximum value of that Fourier displacement or acceleration whatever you take as a response that will start and cutoff frequency is up to that maximum frequency with up to which it will continue. Then we have seen another mathematical expression of this earthquake motion through power spectra the advantage of this we have discussed that it can consider the random process through using this power spectrum density function like this. Then we have discussed the most widely used frequency content parameter through the response spectra as we have mentioned response spectra can be a acceleration response spectra or displacement response spectra or velocity response spectra that we have seen for various rocky site and soil site acceleration velocity and displacement response spectra how this response spectra is obtained through the single degree of freedom mass spring dashpot model by applying an particular input motion corresponding to a particular exciting frequency and the damping ratio. So, we will derive it today in this lecture. Also we have discussed about the duration in the duration we have seen it is nothing but the time required to release the entire strain energy during an earthquake process whereas the relative duration is nothing but it is the time between that 5 percent to 95 percent release of the energy. And for engineering design we have seen another important duration parameter is nothing but bracketed duration which considers the time duration where earthquake acceleration is more than that minimum value or threshold value of acceleration which causes damage to structure which is 0.05 g. So, that is the time or duration which is known as the bracketed duration with this we had completed our previous lecture. Now, we will continue our today's lecture with the derivation of the response spectra. So, let us go back this is the typical picture of a response spectra how to arrive at the response spectra this is because this is the maximum used frequency content parameter in the earthquake engineering. Let us take a simple mass spring dashpot single degree of freedom model which we have already discussed in our previous video course on soil dynamics. But for clarity let us complete it once again over here. Let us say this is a single degree of freedom system as we know is DOF system with mass m and spring constant k. And U t is nothing but that single degree of freedom which defines it position at any instant of time and P t is nothing but the externally applied dynamic load on the system. Suppose if we have the variation of this P t with respect to time. So, how this P t varies with respect to time let us say it varies like this. Let us take a very simple example first then we can idealize it to a generalized case. Say this is the dynamic load which is acting on the system that is from time 0 to time t d. It is a constant force which is acting on the system is P naught after t d there is no force acting on the system. What does it mean from time 0 to t d it is a forced vibration and beyond time t d it is a free vibration case. So, that is the simple problem which already we have discussed in soil dynamics. So, let us see the solution of it for that we should have the initial conditions be known because that is the basic information should be known to us. Let us say U that is displacement at t equals to 0 say it is 0 and U dot at t equals to 0 that is the velocity at time t equals to 0. Let us say that is also 0 that is I am considering a system which is starting from absolute stationary condition with 0 displacement and 0 velocity at the initial starting of the dynamic time t. Now, as we have already identified it is having two phases of vibration one is forced vibration case up to time t d and then the free vibration case beyond time t d. Let us see how the variation is occurring. So, let us consider for different portion that is for forced vibration phase that means t any time should be less than or equals to that t d because force is acting till the time t d. So, any time if we consider between this range that is nothing but a forced vibration phase. So, what is the solution of this one if we refer to our former course on this soil dynamics we will see that U of t with U s t U s t is nothing but static value of the displacement can be expressed as 1 minus cosine omega n t for a constant force like p naught is acting on the system. So, that was the solution already we have derived in our soil dynamics video course. If you have gone through that you can easily understand I am not again repeating that portion I am trying to derive beyond that what is the response spectra. So, if you are having any doubt you can refer to that course and clarify by yourself. In this case omega n is the natural frequency of the system which is nothing but root over k by m which is nothing but once again 2 pi by t n t n is the natural time period. So, if I express it in terms of t n it will look like 1 minus cosine of 2 pi t by t n and this is valid as I said for a time which is between 0 to t d. So, this is one set of solution as we already know about it. So, now let us see what will be the response in the free vibration phase. So, in the second phase that is for free vibration phase that means the time exceeds that value of that t d.  What is the equation of motion? You have basic equation of motion m u double dot plus k u equals to 0 from our chosen model. Now, u of t the solution of that t equals to can be written as u at t equals to t d times cosine of omega n t minus t d that is the initial displacement for this case of free vibration. What is the initial displacement for this free vibration? That is the last point of the previous phase or forward vibration phase at t equals to t d is the nothing but the starting point of your free vibration plus the velocity u dot at t equals to t d by omega n times sin of omega n t minus t d. That is the solution as we know for any free vibration phase that initial displacement times cosine of omega n t plus initial velocity by omega n sin of omega n t. In this case t is nothing but beyond that time t d. So, that is why t has been replaced by t minus t d and the initial time has been taken as where that t equals to t d condition was existing. So, at t equals to t d it is the starting time for the free vibration that is the reason as I have already mentioned starting time for free vibration phase. Now, with this what we can rewrite this as a solution let us see over here. So, next we can write that u at t equals to t d will be equals to u of s t 1 minus cosine 2 pi t d by t n times sin of omega n minus sin this is the solution we can write from the forced vibration phase because that was the solution we have seen u of t by u of s t equals to 1 minus cosine 2 pi t by t n. So, I have just placed t equals to t d over there. So, that is the initial condition and initial velocity u dot should be for this second phase of free vibration can be u of s t if I differentiate this omega n sin of omega n t d fine. Therefore, what we can write u of t by u of s t static can be written as the initial value is 1 minus cosine 2 pi t d by t n times cosine of omega n t minus t d. I am writing now the complete solution that u of t for the second phase that is the free vibration phase. I have taken this u s t out in the denominator that is why we can write it like this class sin of omega n t d by t d times sin of omega n t minus t d because omega n was in the denominator. So, it gets cancelled. So, remaining portion is this one I have already taken this out. So, this is the simplified form am I right therefore, if I further simplify it what we I can write it u of t by this u of s t can be written as this is the initial value. This is the trigonometric function as you can see the variation we can simplify it and rewrite is as 2 of sin pi t d by t n times sin of 2 pi times t by t n minus half of t d by t n. So, this complete solution for the second phase is valid for which time. So, this is valid for t greater than equals to t d am I right. So, what we can see in this case that the if you look at the value or the function of that u t by u s t it is a function of this t d by t n ratio that is why I have expressed it in this form t by t n ratio and t d by t n ratio is it clear what I am trying to say. Let me express it in a more simplistic way. Therefore, my final output says that u of t by u of s t that is the dynamic displacement with respect to the static displacement is a function of what parameters that t d by t n ratio and that t by t n ratio. So, that means any dynamic response or dynamic displacement is dependent on not the individual values of this duration up to which the earth is acting or the dynamic load is acting nor it is dependent on the individual value of the total duration or the individual value of the natural time period of the system. But it is dependent on the ratio of this that is how long the dynamic load was acting over the natural period and how long the total time you are considering what does it mean. Suppose earthquake duration was for say 20 seconds and I am interested that after 1 hour of earthquake what is the damage on my structure then this function tells us clearly that in that case in the solution you have to put t d as your 20 seconds but t has to be 1 hour that is 3600 second clear. So, it is clear that the damage we are considering for any structure whether substructure or superstructure anything it is not only a function of your earthquake duration it is a function of your at time where you are interested to but not that individual value it is a related to a ratio of that natural time period of the system. Clear? That is the reason if you look if you have understood this solution clearly this automatically tells us that it is not necessarily that all the earthquake damages are going to occur during the earthquake or soon after the earthquake it may happen that your structural damage or any damage as such due to the earthquake in the soil also may occur after a large time has spent after the stopping of the earthquake also. So that is what I wanted to show through this solution what it says it says that dynamic displacement or the response is not only a function of that ratio of duration of earthquake to the natural period but it is also a dependent parameter on at what time you are interested to know the behavior of your structure. So, we have to be careful about both these two parameters this as well as this ratio. So, once knowing that let us find out what is the maximum response then we can probably be able to appreciate it maximum response of the structure subjected to this case. So, in the forced vibration phase that is the first phase forced vibration phase if we look at at t equals to t n by 2 that means if our time is equals to t n by 2 then what will be the value of that u t by u s t maximum value maximum amplitude of that will be equals to 2 am I right that is if you put it in this solution I will show you once again that is what was my solution for this case if I bring it here yes this was the solution if you look at here within the forced vibration phase so I am talking about within forced vibration phase. So, obvious reason is my t has to be within t d now what I have chosen this t value I have chosen as t n by 2 that is the ratio I have taken as t by t n ratio I have taken as half 0.5 right. So, if it is so if you put that value what it is becoming it is becoming minus of cos pi so plus 1 so 1 plus 1 2 that is the possible maximum value of this solution right. So, that is why I have said it gives us the maximum value of this u t by u s t max is 2 at this point. Now, if your value of this t d is greater than this t n by 2 then what happens then we have to see two solutions what are those we will look at here. So, let us see mention this as a response let us identify this as a response u t by u s t that is with respect to static so if I want to show the response r d let us say response which is nothing but u t by u of s t I am defining it can be expressed by two solutions 1 minus cosine of 2 pi t d by t n and 2 these are the maximum values this is applicable when your t d by t n ratio is less than equals to half and this is applicable when t d by t n ratio is greater than equals to half am I right. So, that is what we said just now that maximum response is very much dependent on this ratio as you can see if this ratio is less than equals to half then your maximum response will be computed like this based on whatever value of cos you are getting that will be coming. But if this ratio this ratio is more than or equals to 0.5 in that case always your maximum response will be two times that is the dynamic response will be two times of your static clear. Now, let us see in the another phase that is the free vibration phase. So, for second phase that is for free vibration phase what is the maximum value of this u t. So, if I write down that u t of max that will be nothing but your amplitude whatever you are getting at t equals to t d that square plus that u dot t equals to t d by omega n that one square am I right are you satisfied with this expression let us look at here. So, as I said the solution of this will be in the form of for free vibration phase I brought it this here u of t is expressed as initial displacement times cosine of omega n t plus initial velocity by omega n times sin of this. So, what can be the maximum value of this u t obviously it will be root over this amplitude square plus this amplitude square right. So, that is why u initial square plus this velocity by omega n this square that will give us the maximum value of this entire solution is not it. So, u of t maximum that is why I said can be written as this. Now, if I simplified. So, u of t this max u of t max can be written as on simplification by putting the known expression 2 of u s t times mod of sin pi t d by t n. Where from I got it let us look at the solution of this then we will able to understand. Yes here was the solution if you remember this one if you see this was the solution for free vibration phase at the end right. So, what is the maximum value of this solution this portion this amplitude remaining is sin. So, if sin is 1 then it will be maximum am I right. So, if it is maximum. So, 2 times u s t sin of pi t d by t n that is what I have written over here and it can be amplitude either minus or plus. So, with this absolute response will be let me write it down once again. Therefore, the absolute maximum response that is r d what we are expressing that can be written as 2 times of that sin pi t d by t n this is for the free vibration phase. Therefore, if I write it in a combined form I can write it as 2 times mod sin pi t d by t n 2 solutions. So, this is the solutions actually this is one case another case is 2 when this case is valid when this t d by t n ratio is less than equals to half and this condition when t d by t n ratio is greater than equals to half is it clear see this is the complete solution what is the maximum value of this again when this sin parameter is 1 am I right that will give us that value of 2 maximum value when it will occur that will occur when this ratio t d by t n is more than equals to half. Otherwise, if it is less than equals to half it has to be 2 times of whatever the sin value gives us. So, this is the response in free vibration zone and in the forced vibration zone if you look at this was the maximum response. So, everywhere it is a function of that t d by t n and that t by n concept will come to you only when you are interested about a particular time when you want to study the effect on your structure as I said after 1 hour after 30 minutes after 10 minutes like that. So, that is the reason if you see over here here I have not considered the damping portion, but if you consider the damping portion if you remember my soil dynamics lectures the typical value of this plot the response spectra which we show that t n and say s a by g it can be acceleration response spectra it can be displacement response spectra it can be velocity response spectra this looks like this for a particular value of your damping ratio say 5 percent damping or something like that for a particular damping ratio this behavior we can obtain and if I want to plot this u t max by s for our case how it should look like let us see. So, I am now plotting this value of u r d versus t d by t n. So, this is the variation of t d by t n with respect to r d r d as I have defined. So, u t by u s t maximum of that I am plotting. So, as I said over there it is 0. So, this is 1. So, this is 2 this is 0 let us say this is half this is 1 then this is 2 then this is 3 like that. So, at half if I draw over here the variation will be something like. So, maximum response it occurs at the t d by t n ratio of this one when it is subjected to a that constant force type vibration for a finite time period, but if it is a random similar process has to be used to get the solution and get this response like this. So, that similar procedure we adopt for the earthquake random motions also which probably you have to solve using the Duhamel's integral process which I have discussed thoroughly in the soil dynamics course for any kind of motion, but everything finally will be a function of this how long it is occurring that earthquake motion with respect to the natural time period and at what point of time you are interested to find out the value or response. So, another parameter I want to highlight over here. Let us look at here like it is called the pseudo value of acceleration response spectra and pseudo velocity response spectra and pseudo displacement how it is defined. Let us say this is a typical structure of height h which is subjected to this force F s t over here. I have a base shear here B naught t let us say and a moment resisting moment let us say M naught t. For this structure and let us denote that U naught as the maximum value of that U of t the function with whatever it is subjected to any kind of dynamic load that F s t is nothing but a spring force acting on the structure with k as the spring constant or the stiffness times U of t which if we simplify it further it can be expressed as M omega n square times U of t why because as we know omega n is nothing but root over k by M. So, automatically k is nothing but M omega n square is not it. So, in this case we call it as M times A of t what is then A of t if you look at here A of t is nothing but as per our written expression A of t is omega n square times U of t. So, this A of t is known as pseudo displacement. So, this is pseudo displacement this A of t. So, A of t can be written as omega n square U of t this A of t is called pseudo acceleration pseudo acceleration response spectra.  If you plot this U naught versus this t n that is known as displacement response spectra and if you differentiate it further this U naught with respect to time what you get over here that U naught dot which is nothing but maximum of this U dot t versus that t n that plot will give us velocity response spectra. If you further differentiate it with respect to time U naught double dot is nothing but maximum of this U double dot t versus the plot of T n that gives us the acceleration response spectra. So, for the chosen solution of A of t what we have seen. So, pseudo velocity response spectra can be written as A of t. Can be obtained as let us say v in the unit will be velocity unit semitra per second will be omega n times d or omega n times displacement 2 pi by T n times d and pseudo acceleration response spectra will be A in terms of meter per second square unit that will be omega n square. So, what I have written over here earlier if I correlate you can see over here this is known as pseudo acceleration which is nothing but omega n square natural frequency square times your velocity your displacement profile with respect to time omega n square times U of t. So, that will give you the pseudo acceleration response spectra. So, like that we can draw any response spectra whether it is a pseudo acceleration response spectra or pseudo velocity response spectra or pseudo displacement response spectra. Now, let us come back to our topic now, let us start some more parameters like other spectral parameters what are the others various spectral parameters which generally are used one is called r m s acceleration nothing but root of r m s. Now, let us come back to our topic. Now, let us start some more parameters like other spectral parameters what are the others various spectral parameters which generally are used one is called r m s acceleration nothing but root mean square acceleration. So, this is the parameter that includes the effects of amplitude as well as frequency. So, this acceleration parameter root mean square acceleration it consider the both effect of the amplitude as well as the frequency it is expressed in this form A of r m s equals to root over 1 by t d integrate 0 to t d A of t whole square times d t A of t is nothing but your actual variation of acceleration with respect to time. If you integrate over the time period that t d and then find out the root mean square this is nothing but the you are taking the mean by dividing it and root you are taking. So, root mean square acceleration you will get by this over the time domain and t d is the duration of the strong motion. And A i is another important spectral parameter which are commonly used for design A i is nothing but full form is areas intensity. This areas intensity is a measure of the total energy at the recording station and is proportional to the sum of the squared acceleration. So, it is defined as areas intensity is pi by 2 g integrate 0 to infinity A of t whole square d t. So, that acceleration response with respect to time whatever you have during an earthquake if you integrate it over 0 to infinity by taking a square of that and then multiplied it by pi by 2 g that estimate the total energy which is measured during a recording station which is known as areas intensity. Another spectral parameter is spectrum intensity spectrum intensity or A i. A i is defined as the integral of the pseudo spectral velocity curve just now I have discussed what is pseudo spectral velocity curve which is known as the velocity response spectrum. So, if you integrate that between that time period that is if you have that plot of the pseudo velocity spectrum versus t n between 0.1 to 2.5 seconds between that whatever you get if you integrate that curve these quantities are motivated by the need to examine the response of structure to ground motion as many structures have fundamental periods between 0.1 to 2.5 seconds that is the reason why the spectrum intensity it is calculated for any structural damping ratio to determine their response or determine their damages is it clear. So, this is the typical range of the fundamental period of any structure of our civil engineering structure it will be within 0.1 second to 2.5 seconds clear. And in the reverse way we can see considering the structural period or fundamental period of a structure if you take the in hards how much it is coming about 1 by 0.1 to 10 hards and this is 1 by 2.5. So, it will be inverse of 2.5 that much hards will be the typical range of the natural or fundamental frequency of the system. So, if your earthquake frequency also comes within that then there you have to take care of the structural damages etcetera that is the reason you have to integrate that velocity pseudo velocity response spectra curve between this time period of 0.1 to 2.5. Another spectral parameter is dominant frequency of ground motion f d what is f d it is defined as the frequency corresponding to the peak value in the amplitude spectrum that is whatever amplitude spectrum you have in that whatever is the frequency which corresponding to its highest value or peak value that will be your dominant frequency. Thus f d indicates the frequency for which the ground motion has the most energy because it is giving you the maximum amplitude. The amplitude spectrum has to be smoothened before determining the f d which is quite obvious as we have already understand we have to smoothen it filtering it etcetera. Other parameters like predominant period what is predominant period or t p period of vibration corresponding to the maximum value of the Fourier amplitude spectrum that is you have to express the amplitude response in terms of Fourier series. So, as we have already seen Fourier amplitude versus the period if you plot it like this the something it will like look like this is for two different ground motion this is for ground motion 1 this is for ground motion 2. Can you see for both of them the predominant period is same t p is same that is where it is occurring the maximum value of the Fourier amplitude. So, this parameter represents the frequency content of the motion the predominant period for two different ground motions with different frequency content can be same making the estimation of frequency content very crude. That means suppose for this one if you plot it in the logarithmic scale whatever is your frequency content and if you plot this in logarithmic scale whatever is the frequency content they are quite different. But, their predominant period where the maximum value occurs is same that is what you have to use the combinations of this various spectral parameters to identify the nature of any earthquake motion not only in terms of maximum amplitude, but also in terms of frequency content. What is bandwidth bandwidth or b w is of the dominant frequency measured where the amplitude falls to 0.707 which is nothing but 1 by root 2 of the amplitude of the dominant frequency again this is based on the smooth amplitude spectrum. Central frequency what is central frequency it is a power spectral density function that p s d what we have already discussed within that can be used to estimate the central frequency of the ground motion. The n th central moment and the central frequency can be estimated like this this lambda n is the n th frequency that can be estimated as 0 to omega n omega to the power n g of omega that is the power spectral density function times d w. So, and that central frequency is defined as this second one spectral moment divided by the 0 h 1 that is lambda 2 by lambda naught root of that will give you the central frequency this is another just estimate of a spectral parameter. So, central frequency is used to calculate the theoretical median peak acceleration using this expression this value of this omega capital omega you can use for that to calculate the u max value in this fashion. And the shape factor it is indicating the dispersion of the power spectral density function that p s d about that central frequency how it varies with respect to that central frequency that delta can be obtained using this expression that is the lambda 1 the first spectral moment square divided by 0 h 1 and the second one. Then it lies between the value of 0 and 1 higher value indicates the larger amount of bandwidth the or higher value of the spectral. Another very important spectral parameter is nothing but v max by m x ratio this is important what is v max v max is the maximum velocity. If you consider the simple harmonic motion is applied to a single degree of freedom system like structure what I have already discussed about the derivation etcetera. And a max is the corresponding maximum amplitude that is from your u t max if you find out the velocity max for a single harmonic motion it will be how much omega times u t right is not it that is if I want to express suppose my u of t is having some expression say u sin of say omega times t. Then u t maximum of that is nothing but u then what is the v max v max is nothing but omega times u mod of that am I right because velocity you can find out by differentiating it with respect to time this displacement and maximum value of that will be this will become cosine omega will come over here.  So, that says in this slide whatever I have discussed just now look at here. So, v max by a max ratio is related to the frequency content of the motion for simple harmonic motion with a period t this v max by a max can be represented as t by 2 pi is not it. If I look at here let us see here.  Now seed and idriss in 1982 proposed average values of that v max by a max for different sites within 50 kilometer of the source that is they have analyze the values of v max by a max between the earthquake epicenter to a point of site of response for different types of site that is rocky site soil site etcetera. And what are the typical values they have mentioned the average values for rock they have mentioned this value of v max by a max ratio. And remember what will be the unit of this it will be the unit of this t that is in second is not it. So, that is why for rocky site they have mentioned the typical value is 0.056 second for stiff soil stiff soil within the 200 feet that is a stiff soil available at relatively shallower depth the value is 0.112 second and deep stiff soil that is the stiff soil is available beyond 200 feet in that case the value of this t by 2 pi or v max by a max ratio is 0.138 second. So, what we can see this value of v max by a max ratio keep on increasing if we go from a stiffer to a softer soil that is what it means. So, this gives us a very good estimation, but remember these are the typical average value the actual value can differ and how this value can be used to estimate for estimation of the magnitude of another location or computation of epicentral distance that we will see through an example problem in the next class. So, with this we have come to the end of today's lecture we will continue further in the next lecture.


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Yo, my Baby's voice is like, wait a minute, why would he have Baby's voice? Oh yeah, that's right. Parasite! Oh my god! Why is it so easy when it comes to... Oh my god! Why? Why? I'm sorry! Hey, hey, Dotto! Dotto admitted he was good, dude, he was blocking everything! Dotto, all I know is that me and you have our green health. I know, what is the deal with that? What is the deal with that? Why, Dotto! Listen, we got body snatcher versus body snatcher. We got Goku, but it ain't really Goku versus Vegeta, but it ain't really Vegeta. Who's going win? Let's find out. Let's find out. Cause I'm gonna start with the 5-H. Treat myself to a 5-H. I'm so worried. I'm so worried. In case you're watching this and don't know, Baby actually has the ability to call the assist of the characters he beats. So this might be the first raid video where we kill each other. No. No. No.  Hey!  I'm already not liking how this is going. Why? Why? I'm already not liking how his raid's going. Why is he strong? Alright, take care of it. Finish the job. I got your back. I got your back! Look, I'm dropping things. Why are you... You're... Oh my goodness. Oh, why is he going? I would rather die than leave. I would rather die than leave. Okay, if you died you'd be on his team and I don't want that for me. Yeah, alright. For the continuity. No, no, no, no. Brother, you're dead. Is this the content? It's round 2.  Come here, son. Let me show how this is done. Level 3, just for good time's sake. Let's go. Oh, Dotto, Dotto, Dotto. It's Siriax here. Look, I have to interrupt your video just to ask the audience one simple question. How many lives can this video get hit the like button right now? Why is the like button up? Please! I'd appreciate it. Thank you. Oh my... Bro, this guy's building a literal army. Stop! I... Maybe I didn't take this seriously enough. Treat yourself to a win against this army. To him? I got you. I'm gonna wait till Spark. To him? That was a 6. That was definitely the opposite of what it did. I got nervous. Alright, it's fine. As long as we deal with Baby, the threat is significantly lower to us. Beam assist, I got your back. Overhead. Woo! I got that red air, not on my jab. The seriousness I gave the last round is already... Already appearing to be pretty detrimental. I know. I got you. I got you. Don't bring him in. No, no, no. I got you. I got you. I know what needs to be done. Go ahead, Mr. Job. No, no, no, no, no. That's really bad. Oh, no. You're finishing the job.  Yeah, exactly. I need him to run away though, because if he gets caught, I can get him. No, I got you back. Are you saying you don't believe in our team title? Bro. I'm too good at the game. Not that I don't believe in it, but I... There we go. There we go. Now I'm playing. We got to talk in the kitchen after this. What? No. Why are you charging on me? When I tag you in, I'm not trying to tag you in because I want you to... Woo! Oh, my God! Oh, my God! Turn around! Now I'm going to make a team decision. There you go. I'm sparking. I would have asked the team, but okay. No, no, no, no. The team does not... I don't need to consult the team. The team needs to consult me. Let's go! Maybe you could try like using an item or something. Hold on. Oh, I'm sorry. I brought you into sure death. You get in there. Hey! We got some good, all happy little resets. You know what we do after this? We're going to do the forbidden tech. Do you know what the forbidden tech is, kids? This is the forbidden tech right here. They don't block this ever! Let's go. I really wish I had a move that they didn't block. Okay. Vanell is the lowest level of all of them, so we should be... We should be good to go. Bragg rush reads. Why would you... That was so dangerous. Yeah, you know... But just looking like the end. You know what? You know what? I'm going to finish it. Why would you finish it? I'm good at the game! I thought you was ready. I wanted to get a piece. My controller was down. My controller was down? Oh, I'm sorry. Did she not die? You were ready. I just want you to know that I killed two of the three characters. I'm the best. Dotto, are you pondering what I'm pondering? No, I'm not. I'm not. I specifically know what you're pondering. I'm not. Bro, no. We're in the same wavelength. We are in the same wavelength. I'm not. Dotto. It wouldn't even be entertaining. I would just wait. All right, baby. Come here. If you want an assist so bad, you got to steal mine. It's a real situation. Please don't steal mine. Please don't steal mine. I was joking. A harmless little joke. Just a little prank, baby. He's pretty confident. Sit down. Sit down. No, no, I'm not dealing with him right now. I'd rather deal with Krillin Krillin. Come speak to me. Krillin. Come on. Why is he moving? Why is he moving like this? Hey, plot twist. That is Dotto's Krillin. That's Dotto's Krillin right there. I know he was taking over. Hey, I got you. From the possession for me. That's Dotto's Krillin. I got to beat these men to ask for your help. Let's go. Oh, no. Nice. I'm going to grab him now. I'm going to get that combo off that run-up jab. He didn't get my drive. He's dead. Krillin's got. No, not the drop. It's okay. Let's take a level. I'm putting a lot of meter. I feel like you did not need to do that. That was a lot of meter. I hope this kills. I dropped a little bit too many combos. It should kill. Oh, man. Barely. It had like three text left. Barely. This is the baby Vegeta that took over. Why would you hate? This is the baby Vegeta that took over. The Lotus and Dotto. Don't worry. Don't worry. Yeah. Take care of him. You know what? Tag baby. Tag baby. I would not do that. I'd save you for last. You're doing it. There you go. There you go. No. I told you. You know what it is. I told you not to. I'm going through it. Great. Now Dion's on his team and I got to fight him. Get my friend back. Paint him over. Don't call him out. Don't call the. Oh, God. Just come back. Give him back. Give him back. Hey. No. Dion. Don't do this. I'm on his side now. Yeah.  He's gone. Why? Don't worry. Don't worry. We got this. We got this. We got this. We're winning. Look at that. He doesn't play. I'm building no. Call me out there. I want it to bring 18 out. Yeah. Bring 18 out. Oh, no. Please. No. Oh. Oh my goodness. You're not good. You're not good. You may spark. Bring me out there.  He's already committed to the other side. He's fallen to the tuffles. Okay. Okay. Okay. I thought you were going to spark. You didn't spark. Why did you not do that? They are just not. They are not taking any damage, huh? I'm going to go for a run. This is like what? Round four? No. No. No. You got that. You got that. Io 0 for yourself. Come here. Beam assist to help.  Oh, okay. Never call me out again. Thank you. I'm blocked now for bentech. Please. No. Yes.  If you have this, you didn't kill him.  Literally just scare. You're just right. He's magic. Watch out. This is a 2v2. No, no. Watch this 2v2 staring. No. Block that or you're dead. What is he doing? I'll handle this guy. Handle this guy. Handle this guy Using my friend again I'm going through tech now. Oh, that's it. He dead.  You're one of the dead now Let's go there we go We got him back Clutch performer so when it comes down to it, that's when that fourth quarter.  All right. Go. All right. I want to go is I don't want to be in the intro and by now Maybe focus on fighting hey, let's go obviously by now we know what that intro is already aired But ain't gonna be me. I ain't gonna enjoy today. By the way, he's already level 80 and we're on stage five We might be fighting a level 100 baby if we make it That's how it goes. I have a spark you can get anything off of that If trunks kills My beam assist right there Be careful with my life Don't worry, don't worry. We're chillin. We're chillin. Are we chilling? I'm not chillin. We're don't worry.  Go ahead. Treat yourself I'll show you a real comment out. Where's baby at? That's a small comment. I compared to mine Fight for me boys. I'm joining the other side Again, just continue to be careful Trunks he's weak Personally, I'm on team baby right now, so I kind of hope you guys get destroyed Now what's up We tried to wait. I'm you I go cool I'm back out. Feel free to call me when you need me boss now. I'm gonna mash I told you this is where champions are made. This is where I make my mark on the world Let me show you the ball were of these nuts prime. You're on board babies team with me. What are you doing cheering him on? I Let's go I'm the better no matter how old I get these nuts will never be not funny What are you doing? You're on baby's team. Oh, yeah, we can't be cheering. Hey, baby She's not a natural spark. Let's go level three this guy, baby. Come on. Use a dragon ball. Come on I'm like that. I'm like that. This is where champions are made. Yo, is it possible for a raid boss to use Genron? If you want My god Bro, I'm working on it. I just know maybe he's gonna do some wild We're back. We're back. I mean we barely skipped anything you you saw us get We're back right here. Why are health leaking?  It worked out All right, I mean that sounds good, I'll make that I'm dealing with a lot right now. Andrew 18 needs to go. Don't worry. Show me that awesome work SSJ Alright, that is not what I was I was free. I was freestyle. I was freestyle. I can combo Freestyling, but then you didn't rhyme Level one style. Yeah, let's go. I Don't like what you just said there I said you freestyle, but didn't rhyme and then he said style. Yeah, I was thinking about calling about I ignored it I'm a team decision again He's so cool There you go deal with it in a way Yeah, I'm gonna need you to stop using my watch out don't three don't don't level three. Where'd you go? No idea don't use my sis come here Come here Get his assist out of the way and then we can deal with the rest we will be getting the stage over this video No extension I got your back though. I'm not good at using you. I assist. I got your back. Go ahead.  I'm mad. Why did you why did you attack it for no no extension? Oh My go ahead get your links in I Will push in the face. Why? I can't argue guys guys guys guys guys forbidden tech forbidden tech He's built a little differently than the rest going I don't think a level one kills there. There we go. There we go. Now. We're making our way back stage five here We come all right. Let me go ahead and redeem this because guess what I'm Goku black and that's a trunks on the other side Hold on. Okay. Okay. Okay spit and super baby, too. Let's go. What I'm the stolen Goku Okay, and everybody knows in the Mingi Goku little bit stronger than badger that so No, they're more canonically.   I go ahead.  Let's get it Come here. Let me have a word with you.  I'm going to fight. Are you sure you don't want to leave? Let me at least get rid of trunks. All right, I'll get rid of trunks. Yeah. Yeah. Yeah Now I could get rid of baby, too. I just don't really feel like it right now. Yeah I'm just scared for our safety as a team I don't think he's dead from that optimal Dead on my neck. He didn't even he didn't even Go just level one all right now somebody else can come in here You might need another level what I do Get your legs in though.  I'm a genius You're dead No, you just made this fight so much You just made this fight so much harder on us for what for why as you like a goosey assist if he wants to watch the game They're coming back I won't be taken out. I'm a champion after that after that all of my friends might get a little scared, but I have confidence That does not block at all. No Also, I'm just super dash watch this reset reset If you want if you feel ever feel scared just spark. No, it was too late No, now i'm the one that has to say today Classic go-kart stuff. You see that at data over there. Come on Please I thought your saiyans were supposed to be stronger than this. Are you in pain? Then allow me to release you from your suffering


What's good, Josh boros back again with another video. So the rock is back at it again with his shenanigans. He dropped a 10 minute video on his Twitter page since Smackdown is in Dallas, Texas. Tonight we got cowboy rock here, man. And I had to check this out before we do the Smackdown live stream reactions. They're interested to see what the rock has to say on this on this video and what he has to say to Seth and Cody on this episode of Smackdown should be some more peak cinema. Let's see what the rock had to say. I know it's going to be some some shenanigans, man. The rock is in his bag right now, and I'm loving every second of it. This is from his Twitter, a message from the Outlaw People's Champ. When I die, I may not go to heaven. I don't know if they let outlaws in. If they don't, just let me go to Texas. Boys, because Texas is as close as I've been. Smackdown tonight sold out Dallas, Texas. Yeah, man, it's going to be very interesting. It is. This is going to be this is going to be good, man. I'm hoping they continue to progress the story, cook it up some more. I really want to see some real interaction with Cody and Seth and they need to start standing up for themselves because lately they've been getting cooked on these promos, man. Let's check this out. This should be a good one to see what the rock has to say, man. You can feel it. You can feel it in the air. Oh, man. You can feel it in the air here in the state of Texas. Yeah, you can feel it in the air in the great city of Dallas. And you can feel it in the air. Yeah, quiet here. Hours away from the biggest Smackdown. Ever hours away from the biggest Smackdown at the American Airlines Arena here in Dallas, Texas. But we're at right now where the monorun strong just as sure as a rock is covered in chills already here at the Mesquite rodeo arena. The Rocks got his belt buckle on top hand. The Rocks got his cowboy hat on and he's ready to go. The Rock has been here in Dallas, here in Texas. For days waiting for days anticipating for days waiting for a punk and a goof to finally arrive. Cody Rose, Seth Rollins. Oh, no. The Rock and Roman Reigns. Oh, no.  Challenge you to the biggest WrestleMania of all time. The biggest tag match of all time, the Universal Champion, Roman Reigns and the Rock the People's Champion against Cody Rhodes and Seth Rollins on Night One of WrestleMania. You went out on Monday night. You went out on Monday night. You went out on Raw and you both grabbed the microphones. And the crowd was waiting. They were anticipating the world was waiting. What are they going to say? How are they going to come back? What kind of fire are they going to spit? What kind of gospel are they going to drop? And would you both do? What's the thing? What's the thing that? What's the thing we did? Hey, brother, what was that? That's right.  That's what you did.  All angry, talking angry like you're scaring somebody. You ain't scaring anybody. And what the other goof do? The walking clown emoji gets on the microphone. He talks about diarrhea. Is that what you do? Is that how you two goofs respond to the biggest challenge of all time? Oh, no, he's actually legit cooking these niggas. No, bro. Cody and Seth, they need to come with it tonight, bro. They need to come with it and they need to be disrespectful because they didn't cook right now. And then you wait. And then you wait until raw went off the air. USA Network, no more raw. You wait till it's off the air when it's safe. You wait till it's off the air. And what'd you do, Seth Rollins? You grab the microphone. Now, now that Raw's off the air. Oh, I could say some truth. I could say how I really feel.  Oh, I didn't know this. I didn't know he did this. I'm surprised nobody sent me a clip of this. I'm I did not know he had an off air segment, which once again, it kind of defeats the purpose. You should have set this on camera. If this is if this happened, just have them bleep it out. That would have been better.  When it goes off the air, when it's safe, but the Rock tell you something right now, brother. The Rock is a lot of things. He's a lot of things.  It ain't one of them.    Achieved when he's achieved.  Brother, you got another thing coming.  The Rock hates politics. Half the country wants a rock to run for president.   It's because he's the opposite. It's because he tells the truth. It's because the Rock says it like it is. The Rock says what the people need to hear. The Rock says what the people want to hear. That's why. And Seth Rollins, Cody Rhodes. Oh, no. Do you think that the Rock has become the most followed American man in the world? Let the Rock say it again because it sounds like gospel because it is.    Because the Rock tells it like it is. Because the Rock is and will forever be the people's champion. And you know what that means? That means that the Rock will say what the people want to hear. That means the Rock will do what the people want them to do because the Rock is the one who says the things that they want to say. The Rock is the one who says the things that the people wish they could say that the people wish they could say. Against the system and against goofs like you, but they can't. That's OK because the Rock can. The Rock does. So you see, my friends, Seth. You're walking clown emoji.   You wait until broadcast can't do anything to you. So speaking of broadcast, last week, everyone complaining on on on Friday night SmackDown, what's going on? My TV is blacked out during certain times of the Rock's promo. What's happening in certain pockets across the country? Well, here's what happened. Standards and practices, baby. Standards and practices. They get nervous now when the Rock has a live microphone in his hand and the world is watching. They got nervous when the Rock went to Phoenix and the Rock dropped the gospel. Phoenix, Arizona, the number one city in the country for cocaine and Matthews. Unlike how he's spending this, he's spending this like he's above all of it. That's good. If y'all I like what he's doing, because I think the reports came out that it was more so involved with, you know, what the crowd was saying, what some signs they saw or whatever. But he's spending this like because they're afraid of what I'll say. And because I'm above all of this, I can say what I want. So they they're they're afraid. So that's why they were doing that. I like he's spending what we may know into what fits his narrative, what fits his story that he's trying to tell. I like what they're doing here. I like that. And the Rock caught them all. You cackless, loving, crack heads. And they booed. Oh, they hated it, but they loved it because the Rock said the truth. Every woman in the arena, you want to go one on one with the rock. The sexist man alive. The women cheered and the Rock said, settle down. Your crack had Karen's settled down. Your meth had Mary's. You're not ready for the rock and you know it. They loved it. They hated it. They cheered. They booed standards and practices, though. They push the button. They push the button because they want to control the rock. Just like they push the buttons like they want to control the people. But you can't control the rock. You can't control the people. And the Rock is the people's champion.   That's why the Rock is the people's champion. So standards and practices. You can get scared all you want. You can have your finger on the button. There ain't nobody means nobody that will tell it like it is more than the Rock, the people's champion.  Yeah. Tonight in Dallas, Texas, that walking clown emoji. Seth Rollins, you get ready. And tonight, Cody Rhodes, you get ready to because you've got to come to Dallas where the Rock has been waiting, where the Rock has been waiting, you come to Dallas and you give us your answer, whether you're going to go two on two with the Rock and Roman Reigns at WrestleMania and put on the biggest WrestleMania of all time. So Seth Rollins, your walking clown show.   His name. Farrow. Hey, hey, Farrow. Hey, Farrow. Don't call that dog, Farrow. Call him shithead. That's what you should call him. Catching residual smoke, Cody. There needs to be no more talking, bro. No more talking. No more. He's talk. Why? Your dog is catching residual smokes. Your only response needs to be a slap to the Rock's face. What do we do? Seth Rollins, Cody Rhodes, shithead and all the Cody crybabies out there and standards and practices. You listen to the Rock right now when the Rock has that microphone live as a people's champion. The Rock will and will always and forever tell it like it is.  Standards and practices.  Rection.  I've never heard anyone use that term like that.  Oh, my God. You come to Texas, boy. The Rock is waiting for you. Cody, the Rock and Roman were waiting for you. Seth, what are you going to do? You're going to come and cackle. You're going to come and cackle and dance. You're going to dance again for everybody. Is that what you're going to do?  You guys. Oh, my God. You come to Dallas, Texas, where the Rock is waiting, where Roman reigns. We are waiting when I die. I may not go to heaven. I don't know. They let out laws and oh, my God. They don't just let me go to Texas. Texas is as close as I've been. If you smell. Oh, my God, bro. What the Rock? Cody Rhodes, one more message for you, boy. Now and forever. Hi, bro. Hey, man.  No talking. We accept your challenge, Patrick, to the face. Start fighting, bro. Sticking disrespect at your dog twice and it got even worse this time out down there. Oh, God.  It's the direction you get.  I'm done. This is fantastic. Fantastic, bro. Comment down below. Let me know your favorite part of this video. I'm done, bro. I'm done. I'll catch you next time.


The study estimates the prevalence of psoriatic lesions in the genital area among patients with psoriasis, finding that a substantial proportion of patients experience genital lesions at some time during the course of psoriasis. This article was authored by Kim A. P. Muiz, Alison Potts Bleakman, Peter C. M. van de Kerkhoff and others.


Hello and welcome to today's episode of the International Daily Roundup brought to you by People's Dispatch, where we bring you major stories from around the world. Let's take a look at some of the headlines. Wetzewet and activists warn of another police raid, Israeli forces kill Palestinian men during another raid, U.K. jury acquits constant four anti-racism protesters, and rural childcare workers go on strike in India. In our first story, we go to the province of British Columbia and Canada. The U.S. water protectors of the Wetzewet and Territory have warned of another militarized raid. In order to avoid further arrests, they have announced a retreat from the Coyote Camp protest site. The Wetzewet and protest have been resisting the coastal gas link or CGL pipeline on the land for years. The area in question covers over 22,000 square kilometers of traditional unseeded territory. Since 2019, the Royal Canadian Mounted Police or the RCMP has carried out three invasions into the territory. Over 70 people including hereditary chiefs, activists and journalists have been arrested. Meanwhile, CGL has refused to abide by a 2020 eviction order issued by Wetzewet and hereditary chiefs. In September 2021, indigenous activists set up the Coyote Camp to block a key pipeline drill site. In November, they shut down a forest service road to enforce the eviction order against CGL. However, RCMP forces attacked Camp Coyote and arrested 30 people including traditional leaders. To justify this, Wetzewet and activists reoccupied the protest site and blockade on December 19. However, on January 3, the Grimton Checkpoint stated that they had received reports of the RCMP making its way to the territory. The activists announced on Thursday that they had carried out a strategic retreat to avoid arrest and violence. However, the Wetzewet and water and land defenders have said that they will continue their struggle through other means. In our next story, Israeli forces killed 21-year-old Palestinian man during a raid in the occupied West Bank on January 6. Bakir Hashash was shot at the entrance of the Balata Refugee Camp near Nablus. The Wafa news agency reported that Israeli forces had opened fire on Palestinians in the area. Hashash was shot and later died of his injuries in the hospital. Israeli forces repeatedly carried out violent pre-dawn raids in the West Bank, including in areas under the Palestinian Authority. Palestinians resisting the occupation's actions are met with disproportionate and deadly violence. A Batsalem report found that Israel's lethal, wanted and unlawful open fire policy killed 313 Palestinians in 2021. 77 of these killings took place in the occupied territories. Beyond the near total immunity already given to its forces, Israel has now revised its open fire rules. Israeli forces in the West Bank can now shoot Palestinians for allegedly throwing rocks at civilian cars. Civilians refers to illegal Israeli settlers who are often themselves armed and carry out violent attacks. The rules reportedly apply to Palestinians who are fleeing or not holding rocks when shot. The measure is a violation of international law. Israel has already been condemned for using an indiscriminate shoot-to-kill policy. The revised open rules will work to codify this. Riot's groups have outlined cases where a person was shot despite being quote unquote neutralized or even unconscious. In our next story, we go to the UK where four anti-racism protesters have been cleared of criminal charges. Ryan Graham Milo Pondsford, Jake Scrooge in Sage Willoughby had been charged in relation to a Black Lives Matter protest. On 7 June 2020, the four took part in tearing down the statue of a 17th century slave trader, Edward Colston. The statue was then thrown into the river Avon near the Bristol Harbour. The action was part of the worldwide uprising against the racist police murder of George Floyd. The trial of the Bristol protesters who came to be known as the Colston Ford began in December 2021. While they did not deny their role in tearing down the statue, they rejected the criminal damage charge. They defended their actions arguing that the statue was so offensive that it constituted a hate crime or an indecent display. Historian David Olisoga gave expert testimony on Edward Colston during the trial. Under Colston, the Royal African Company is estimated to have abducted and enslaved nearly 85,000 African people. Despite this history, his name was displayed on roads and public schools in Bristol. Following a nine-day trial, the Colston Ford were found not guilty by his jury at the Crown Court on January 5th. And for our final story, we look at the ongoing strike by tens of thousands of rural childcare workers in India. Women across 26,000 childcare centres of Anganwadi's in the state of Haryana have been protesting for nearly a month. They are demanding better wages and recognition as government workers. Anganwadi workers play a key role in implementing nutrition and care-related policies with the grassroots. They have also been under front lines with the pandemic, often without adequate safety measures. Despite this, these workers are classified as volunteers, which denies them adequate wages and benefits. Following major protests, a cabinet committee approved a small increment for Anganwadi workers and helpers in 2018. Striking unions have stated that the Haryana government has refused to implement a measure. Anganwadi workers are currently only earning between $80 to $160 a month. Around 20,000 women held a major demonstration in the city of Karnal on January 5th. The day also marks the third round of talks between the union and the state. As reported by NewsClay, the government refused to budge on the 2018 increment. Meanwhile, it has offered dearness allowance alongside other incentives. Anganwadi workers have declared that this strike will continue until the demands are met. The unions have also announced a jail bureau or voluntary arrest agitation for January 12th. And that's all for today's episode. We'll be back tomorrow with more news from around the world. Until then, keep watching People's Dispatch.


Studies suggest that excessive animal protein consumption poses a risk of kidney stone formation, likely due to the acid load provided by the high content of sulfur-containing amino acids in animal protein. As I explored in my video on preventing kidney stones with diet, but what about treating kidney stones? Most stones are calcium oxalate, formed like rock candy when the urine becomes super saturated. So doctors just assumed, if they're made out of calcium, we just have to tell people to reduce their calcium intake. So that was like the dietary gospel for kidney stone sufferers until this study was published in the New England Journal of Medicine, pitting the two diets against one another— low calcium versus low animal protein and salt, and it was the restriction of animal protein and salt that provided greater protection. Cutting the risk of having another kidney stone within five years in half. What about cutting down on oxalates, which are concentrated in certain vegetables? A recent study found that there was no increased risk of stone formation with higher vegetable intake. In fact, greater dietary intake of whole plant foods, fruits, and vegetables were each associated with a reduced risk independent of other known risk factors for kidney stones, meaning one may get additional benefits bulking up on plant foods in addition to just restricting animal foods. The reasons a reduction in animal protein helps is not only because it reduces the reduction of acids within the body, a reduction of animal protein should also limit the excretion of urate, uric acid crystals that can act as a seed to form calcium stones, or it can create entire stones themselves. Uric acid stones are the second most common kidney stones after calcium. There's two ways to reduce uric acid levels in the urine, a reduction in animal protein ingestion or drugs. And removing all meat can remove 93% of uric acid crystallization risk. Here's the risk of crystals forming eating the standard Western diet for five days and then switching to a vegetarian diet leads to a 93% drop in risk within days. To minimize uric acid crystallization, the goal is to get the urine pH up to ideally as high as 6.8, so a number of alkalinalizing chemicals have been developed. We can naturally alkalize our urine up to the recommended 6.8 using purely dietary means, namely by removing all meat, which takes someone eating the standard Western diet up from an acid 5.95 right up to the target of 6.8 eating a vegetarian diet. You can inexpensively test your own diet with a little bathroom chemistry, for not all plant foods are alkalinalizing and not all animal foods are equally acidifying. A so-called lake score was developed, a load of acid to kidney score, which takes into account both the acid load of foods and their typical serving sizes, and can be used to help people modify their diet for the prevention of both uric acid and calcium kidney stones and other diseases. This is what they found. The single most acid-producing food was fish, like tuna. Then pork, then poultry, then cheese, though milk and other dairy only rates down here. Then comes beef. Now eggs are actually more acidic than beef, more acid-forming, but people tend to eat less eggs at a sitting, so they come in here. Some grains can be a little acid-forming, such as bread, rice, but not pasta, interestingly. Beans are significantly alkaline-forming, but not as much as fruits and vegetables are the most alkaline-forming of all foods. Through dietary changes alone, we may be able to dissolve uric acid stones away completely, cure them. Now you see it, now you don't. No drugs, no surgery, just telling them to drink more water and modify their diet, such as restricting the intake of animal protein, and the kidney stone was gone. To summarize, here are the five types of kidney stones, and the most important things we can do diet-wise is to drink 10 to 12 cups of water a day, and reduce animal protein, reduce salt, eat more vegetables, and more vegetarian.


Good evening. First, I want to say thank you to all of the advocates who are here tonight who have worked so hard over the last year in particular, but I know even longer than that on behalf of immigrants to our nation and the last year on behalf of the women and children coming from the Northern Triangle countries of Central America. About two months ago now, I brought in a delegation of seven members of Congress to visit with many of the advocates we met at St. Mary's Law School at the University Center actually, and also to visit the facilities at Carnes and Dilly. And I wanted them first to come here to San Antonio because this has been the epicenter for advocacy. This has been the backbone of support for those women and children and the epicenter of the push to get them released from the detention centers. So I want to answer the questions. I may take them out of order, but first, I continue to support closing down the detention centers and not housing the women and children in those arrangements. I've said both to the President, to Jay Johnson, who is the head of Homeland Security and to the Justice Department. In fact, Lloyd and I joined in a letter with, I think, about 135 of our colleagues expressing that to President Obama and the administration that we believe there should be alternative arrangements. And those can include other things besides an ankle monitor. The point is, and we know from the numbers, that the overwhelming majority of these folks are coming back for their court hearings when they're supposed to. And that's what's important, right, that there be a process here so that they can make their claim for asylum. And so I fully support that. In terms of campaign contributions, I'm not aware if I have received, I don't think I've received any from the private prison companies. I have to be honest, I wasn't too familiar with GO or CCA before all of this, basically before the last year. You think about it, I know over the years the function of imprisoning folks has been turned over to private contractors, but most of that had been for folks who are criminals within the United States, as opposed to the detention of immigrants. And so it's not something in the legislature, for example, that I dealt a lot with, or even in my time in Congress so far, until this came up. And so I think I've only used about two minutes. Now I want to speak for a minute, four minutes. I still have four minutes, all right. I won't use all of them, but I think I've answered the questions now, those four questions. So I want to say this. We are right now facing a moral test as a country. We're going to have to decide what kind of nation this is going to be in the coming years. There are tonight a few hundred of us gathered here in San Antonio, Texas. And in the other part of the country in New Hampshire, there are 1500 people who showed up tonight for a presidential candidate who is leading the charge to end birthright citizenship in violation of the United States Constitution. And we've got to stand up against that, because that's not what our country stands for. When the migrants arrived from Central America last summer, as Jonathan said, many of us understood right away their purpose.  They're not even folks who were trying to get around Border Patrol. They were going up and presenting themselves as folks seeking asylum in the United States. Now, I agree with Jonathan that the laws, as we understand them, would give a strong chance for many of those folks to stay on as assailees in the United States. But I think you'll also agree that that's not how most of the nation perceived this situation. Part of that was because of a lot of the politicians who were stoking fear, who were claiming that this was a kind of invasion in our country. Even a week and a half ago, at a debate with many of the presidential candidates, the governor of Louisiana said that immigration without assimilation is an invasion. You think about that for a second. Who gets to decide whether somebody has assimilated in the United States? Who's going to make that determination? That's where we are now. And another part of the reason that it wasn't perceived as an assailee or refugee situation is because the Red Cross and other organizations, and I'm sure some of the ones here, were having problems going in there and volunteering their time and donating clothing and furniture and offering housing. And that affected the way the news coverage and how this was perceived by Americans. And so I had a few amendments to an important bill that didn't, my amendments didn't get on, but I want you to know that I made an effort to change the way that we handle these situations. Because I think that we should have sent the Red Cross down there and not the National Guard. And then finally, as we think about this, two things. First, we want to close the detention centers for the sake of the women and children who were still there today. But just as important, looking down the road, we want to make sure that for God's sake, if we have another wave of immigrants who comes here, another group of asylum seekers who comes here a year from now or 20 years from now, that the United States government handles it differently next time and doesn't put them in jail like facilities. And then with one minute left, my last point. You know, when we think about our asylum and our refugee laws, we still think about offering asylum to people who were fleeing communist dictators from the 1950s and 60s and 70s. I think that's what most Americans still think of when they think of an asylum. We have to update that for the 21st century. These people are facing violence and desperation and the kind of violence that's been perpetuated on them, perpetrated on them from gangs is just as harmful as any that is perpetuated by a dictator across the world. So thank you for caring. Thank you for your passion and every single thing that you're doing on behalf of these people. Thank you very much.