Welcome to this lecture. In this lecture, we are going to discuss about canonical forms for constant coefficient partial differential equations of course in more than two independent variables. The outline for today's lecture is we start discussing about canonical forms and then we actually do canonical forms for equations with constant coefficients. For linear PDEs in two independent variables, we derived canonical forms. Recall that we did not even define what does the word canonical form stands for. It was mentioned that we want the equation to look like wave equation, E.T. equation or Laplace equation as far as the appearance of the second order partial derivatives are concerned. Some books define what is a canonical form. They say that an equation is in canonical form if mixed partial derivatives do not appear. That is the definition. In the principal part, second order linear PDEs in the principal part, there will be only second order partial derivatives. C pinch over Rubinstein's book on PDEs. They hint this kind of definition. But if you adopt that definition, then w xi eta equal to 0 which is a canonical form for wave equation will no longer be a canonical form. If you adopt this definition, saying mixed partial derivatives do not appear in the principal part. And somehow we do not like this. Why is that? Because this equation w xi eta equal to 0 is far more easier to find its solutions than let us say u T t minus c square u xx equal to 0. u T t minus c square u xx equal to 0 is a wave equation. And there are no mixed partial derivatives. How do you solve it? I do not know. But when you convert that into w xi eta equal to 0 with xi and eta as the coordinate transformations which are coming by solving a characteristic equation, things are nice. So, it is not a canonical form if you follow this definition as in this book. Now, suppose we adopt such a definition. Let us say that does not matter. My definition of canonical form is that equation in which no mixed partial derivatives appear. Fine. Of course, very easy to define. Anything it is very easy to define. No problem. But can we guarantee that a canonical form exists? This is a natural question. Otherwise, there is no use of this definition. So, can we guarantee that a canonical form exists? It is a cumbersome task to transform a given equation into its canonical form. Remember what you need to do? We have to make sure that in the new change of coordinate system which we have to find, no mixed partial derivative appears. So, that is a system of nonlinear PDEs for determining p1, p2, pd which go on to define the coordinate transformation. And the system to be satisfied is this. Summation kl equal to 1 to d, akl dou phi i by dou xk dou phi j by dou xl equal to 0. And this should happen whenever i is different from j. Because aij is the coefficient of dou 2w by dou eta i dou eta j. You do not want mixed partial derivatives to appear. Therefore, when i is not equal to j, you want aij to be 0. How many equations are there? They are d into d minus 1 by 2. So, when d equal to 2, n of 2 is 1, n of 2 is 1. We need to determine two functions phi 1 and phi 2. Fine, no problem. Two functions, one condition. Looks good. n of 3 is 3. Three equations, three unknowns. Nonlinear equations, that is anyway there. But at least three relations, three conditions and three functions. Maybe looks reasonable. But d into d minus 1 by 2 equations to determine d functions. This number is much more than d if d is bigger. When d is greater than or equal to 4, number of equations is more, number of constraints to find the function phi 1, phi 2, phi d is bigger than d. So, more equations than the number of functions to be determined. So, therefore, the system is what is called a over-determined system of PDEs. More restrictions than what you need to find, the number of things that you need to find. In such cases, the natural thing to believe is that perhaps there are no solutions unless some magic happens, you may not have solutions. Okay, even if you have solutions, finding them is not easy because if d is bigger, n of d is also a big number. So, obtaining canonical forms is difficult. Perhaps impossible, we do not know, from d equal to 4 onwards. Therefore, we abandon this idea of finding canonical forms if the number of independent variables is 3 or more. We do not do that. Now, why are we discussing for constant coefficient case? When the equation is with constant coefficients, some miracle happens, things are easy, you can find. So, we understood the near impossibility of reducing linear PDEs to canonical forms in higher dimensions. However, for constant coefficient PDEs, finding canonical forms is easier. A second order linear PDE with constant coefficients in d independent variables is of this form, exactly as earlier DL, but now it is DLCC, therefore the coefficients A, I, J, B, I, C, and D are constants. In fact, this D need not be constant, does not matter because everything depends only on this. So, these are numbers. Let us take that. Anyway, we are assuming constant coefficients. Assume everything is constant. D need not be constant. D can be a function of x, it can be on the right hand side, does not matter. It does not change the discussion. So, assume that the matrix is symmetric as before. Now, since A is a symmetric matrix with real entries, there is an orthogonal matrix Q. What is the orthogonal matrix? Q transpose Q is identity. This stands for transpose. With what property? Q transpose AQ is a diagonal matrix with entries lambda 1, lambda 2, lambda d. So, when this lambda 1, lambda d just stands for lambda 1, lambda 2 on the diagonal integer d by d matrix, everywhere else it is 0 matrix. That is what is stands for. So, symmetric matrix is diagonalizable with an orthogonal matrix as this transformation, similarity transformation. How to get that Q? We know, we have to put the columns of Q as eigenvectors of the matrix A, that is from linear algebra. So, lambda 1, lambda 2, lambda d are eigenvalues. All of them are real numbers because the matrix is symmetric matrix. In general, for a matrix with real entries, eigenvalue can be a complex number. But if the matrix is symmetric, eigenvalues must be real numbers. Denote the ith column of the matrix Q by Q i. Ith column of the matrix Q by Q i. So, if this is ith column, that means it will be Q 1 i, Q 2 i, etc. Q di. This is what is called Q i, ith column of the matrix Q. Define phi i of x equal to Q i dot x. This is a dot product. Dot is hidden inside this. It is Q i, it is a vector dot x, Q i dot x. So, we have defined eta 1, eta 2, eta d. So, since the matrix Q is invertible, this linear transformation is also invertible. X 1, X 2, X d going to Q i dot x.  That is invertible. This map is invertible. The principal part of the PDE in the new coordinates is this. Summation lambda i dou 2 w by dou eta i square. Let us call this as new principal part, new PP i equal to 1 to d. Since the classification type is invariant under coordinate chain transformations, the type of the PDE DLCC which is given to us may be determined from using a new dot PP. So, classification for equations with variable coefficients is based on characteristic surfaces. Now, we will see what characteristic surface become when the coefficients are constant. Things become much easy and much more easy if you are in this new coordinate system eta i which is defined on the previous slide of this. eta i equal to Q i dot x. Things are much simpler. So, equation for a characteristic surface gets simplified for equations with constant coefficients using new PP. So, regular surface phi of eta 1, eta 2, eta d equal to 0 is a characteristic surface if and only if this is 0. Once you know the gamma in terms of beta i's, you can always write down in terms of x i's, x 1, x 2, x t. So, this is the equation for a characteristic hyper surface. Phi equal to 0 is a characteristic hyper surface if and only if this equation is satisfied. Now, if you observe if all lambda i's are of the same sign, okay, nonzero and same sign that means sin already means nonzero, then this will either be positive or negative. So, it will never be 0 which means there are no characteristic surfaces. If all lambda i's are the same sign. So, therefore the PDE dlcc is of elliptic type. If all the eigenvalues, what are lambda i's? They are the eigenvalues of A. If all the eigenvalues of A are same sign, then dlcc is of elliptic type. Now, how about parabolic type? When is it parabolic type? Parabolic type, what is the definition? It says one of the independent variables should be missing in the principal part. At least one of the eigenvalues A is 0. If lambda k is 0, then in the equation, dou 2 W by dou eta k square does not appear, okay. Yes. So, the PDE dlcc is a parabolic type. If at least one of the eigenvalues of A is 0 and all other eigenvalues must be of the same sign. So, the second order derivative dou 2 W by dou eta k square, it does not appear in new pp if lambda k is 0. Therefore, dlcc is a hyperbolic type. Now, we have to say it is hyperbolic type. If it is not elliptic, it is not parabolic. That is the definition. Now, what does that translate to in terms of the eigenvalues of A? This is the case when the matrix A has at least one positive eigenvalue and one negative eigenvalue, okay. Not elliptic means, elliptic means what? All eigenvalues of same sign. Not elliptic means eigenvalues of different signs. Not parabolic means no eigenvalue, at least one eigenvalue is 0. That is a parabolic. So, what do you mean by not parabolic? That also if you input, you will get this case. This will happen. When this will happen, then it is hyperbolic. So, as per our classification, this equation which is here is a hyperbolic equation. We have to ask what the eigenvalues are. They are minus 1, minus 1, 1, 1 because the matrix A is 1, 1, minus 1, minus 1 diagonal matrix. So, when compared to the wave equation, the above equation has two time-like variables because wave equation eigenvalues are like 1, 1, minus 1 or minus 1, minus 1, 1. That is all. But here there are two eigenvalues which are negative, two eigenvalues which are positive. So, we may say it has two time-like variables. So, some authors call such equations as ultra-hyperbolic. So, more precisely the definition of ultra-hyperbolic is a following. Some equation is called ultra-hyperbolic for which the matrix A has at least two positive eigenvalues and two negative eigenvalues and none of the other eigenvalues is 0. Our definition of hyperbolic will allow some eigenvalue to be 0. But ultra-hyperbolic, by definition, there are at least two positive eigenvalues, at least two negative eigenvalues and none of the other eigenvalues is 0. That is what is called ultra-hyperbolic. It is just for a definition sake. Now, let us look at an example and determine its type uxx plus uyf plus uzz plus 2uxy, 2uyz plus 2uxz equal to 0. So, what is the matrix here? The diagonal entries are 111 and these are off diagonals. They are also 111. So, this is the coefficient matrix. And we have to ask what are the eigenvalues. This is a very well-known matrix by now. Everybody knows its eigenvalues. This matrix is clearly singular. A rank is 1. Therefore, nullity is 2, which means 0 is an eigenvalue of multiplicity 2 and 3 is another eigenvalue, which is a sum. If you notice, sum of each row is actually the same constant. Therefore, if you look at 111, that will be an eigenvector with eigenvalue 3. So, we know everything very clearly here. So, the eigenvalues are lambda 1, lambda 2, 0. These are two eigenvalues. And we need to take eigenvectors, which are, if you look at carefully, I am putting a factor of 1 by root 2 and 1 by root 6 here to make the length to be 1. It is of unit length, this is of unit length and they are orthogonal to each other. This dot product with this vector is 0 because q is orthogonal matrix I have to construct, right? That is fine. And the other eigenvalue is 3 and eigenvector is 111. I put 1 by root 3 to get that length is 1. And of course, this is orthogonal to both of them. Now, I am going to consider q like this. The first column is actually the one of the eigenvectors for 0 eigenvalue. This is second eigenvector that we have written down for 0 eigenvalue. This is eigenvector for the eigenvalue 3. Now, q transpose A q will become the diagonal matrix 003. So, these are the change of variables phi 1 equal to x minus y by root 2, phi 2 is x plus y minus 2 z by root 6 and phi 3 is x plus y plus z by root 3, then the PDG transforms to this. This is what exactly we saw in the theory, right? Take a q such that q transpose A q is the diagonal lambda 1, lambda 2, lambda d, then introduce new change of variable zeta i equal to q i dot x. Exactly this is q i dot x. In this case, I have written down x, y, z. So, q i dot x, y, z is precisely this. So, you will end up with lambda 3 and dou 2 w by dou eta 3 square. Characteristic surfaces are eta 1 equal to 0 and eta 2 equal to 0 because they do not appear in the new PP. What is gamma 1 0? It amounts in x, y coordinates to x minus y equal to 0 and this is x plus y minus 2 z equal to 0. The given PDEs of which type? Parabolic. So, let us summarize what we did in this lecture. Impossibility of finding canonical forms for linear PDEs with variable coefficients was discussed. Impossibility or near impossibility. Canonical forms for linear PDEs with constant coefficients were obtained. Classification for linear PDEs with constant coefficients was understood more clearly. Thank you.


Whether you're the type of person who has to deal with PDFs all the time or you're the kind of person who only has to deal with them Once in a while when you're doing taxes or something having a good PDF tool is something that is very important. So I Know personally that I hardly ever do with PDFs It's usually like a once every couple months kind of thing where I have to sign something for a client or I have to do my taxes whatever it has happens to be and Usually during that time period. I'm freaking out because there's not a lot of great PDF tools out there There's quite a few that do a very good job at viewing them There's a quite a few good ones that do a great annotations But outside of that it's kind of hit or miss in terms of what actually is good So what I thought I'd do today is take you through five Really great PDF tools now these all do things differently. They all do different things and Really only one of them is a jack of all trades So just keep that in mind as you go through that it's possible that if you're going to deal with PDFs all the time You may need more than one tool if you decide that you can't do what you need to do with one of these tools So let's go ahead and jump right in The first one on the list for today is called. I love PDF comm and this was recommended to me by one of my patrons Peter This website does some of the basic stuff that you'll probably need to do with a PDF if you happen to just be the occasional PDF editor slash whatever and The reason why I say that is because for the most part if you're dealing with this kind of stuff day in and out you'll probably want a Native tool and I'll talk about some of those tools that do some of this stuff in the rest of the list But if you're just the occasional user of PDFs this tool is really cool It's also useful for people who are on computers that they don't own So if you're on a work computer or whatever and you need to do something with a PDF But you don't have any native tools to do so and say you don't have access to actually install something You could go to this website do some of the stuff you might need to do with a PDF and then move on with your day So this website will allow you to merge and split PDFs It's not the only tool that I'll talk about that does that today But you could do that on this website you can compress it you could convert it to several different formats including word PowerPoint Excel things like that It'll also allow you to add a watermark if you needed to add a watermark You could unlock up a PDF if it's password protected There is the option to sign it as well if you wanted to sign the PDF and you had a digital ID Again, that's not the own This is not the only tool that I will talk about today that will allow you to do that But it is a good one. So just in case you don't have like I said access to a native tool This is a good option. So that is I love PDF comm Okay, so the next one on the list is ocular now ocular is a application that is mostly used for viewing PDFs and I say mostly because it does have a few extra features But for the most part this is what you'll want to use if you just absolutely need to read a PDF So say for example, you've downloaded a book or something and it's in PDF form ocular is a really good choice Now like I said, it does do a few other things so you can annotate to your heart's content in this So there's a highlighter thing here. You can select from underlines You can insert text you can do notes pop-up notes things like that It also has if you set it up the ability to Where is it right here digitally sign a PDF? So if you have to sign a document, you can do that within here you'd have to set up the signature and have a Signature certificate in order to actually do that and then it would be official obviously You can do that from right from here now The reason why I put this at number four is because for whatever reason for me It always appears full screen to begin with so I don't know why it does that You have to get out a full screen in order to actually do anything with it before you and that you know the keyboard shortcuts So I don't know why that does that maybe it's just because I'm in a window manager But this one is always kind of ragged it weirdly for me But it's a great little PDF viewer and it gives you access to the table of contents You can do all the unit like I said your annotations and stuff right here from ocular and it will get you Probably 90% of the way towards what most people actually need now the next one is also a PDF Viewer and the reason why I included two of these is because some of us Preferred to do our work in the terminal some of us prefer to have things that have them key bindings and There just happens to be a program that lets you do both of those things So if you want to view PDFs from your terminal, it's done through a program called Zathara now I'm going to CD into my documents folder here, and I'm going to open up as a thorough so Z A T H U R A and then I have a File here called example PDF dot PDF I'm gonna open that up and it will open up the PDF file that I was basically just in an ocular and you can Basically just do the things that you need to do here, but for the most part this is just for viewing It doesn't have the features of something like ocular. It's just meant for viewing But the cool thing here is that you can use the them key So up and down is J and K if you had the option you could use H and L in order to go side to side You can also search for things using the slash key. So let's just search for non here we know that that's in there somewhere and You can use the small end to go forward big end to go backwards just like you would in them GG goes to the top big G goes to the bottom and If there are links in your PDF, I don't know if there is one in this or not I don't think so when it looks like maybe there isn't a link right there You F and it will highlight the link and you could then hit enter and it would follow that link for you but that just happens to be a Random path link, but the point is is that if there was a link you could use F in order to do that now One thing that I highly recommend you do if you are going to use this thorough is Look at the man page just like you should with any Terminal-based application and it will give you the standard things that you can do so you can view Documents that have password protections. There are plugins for Zerothura. I don't know anything about those I've never tried them. Usually I just use this for just oh, I need to look at this PDF Open up in Zerothura do what I need to do, you know read or whatever and then go away It will all the man page will also give you the standard Keybindings that you'll need to know in order to navigate through a PDF So that is a thorough. It's actually really cool. It's something that I use quite often whenever I just need to view a PDF It's better than ocular for me simply because it doesn't have all the other stuff that I don't necessarily need The next one on the list is called PDF Sam and this does some of the same things as the website I showed you earlier, but it's a native application So what this will basically do is just a few things So it will allow you to merge and split PDFs So say you had two PDFs that you needed to merge together and make one into one PDF You could do that here if you have a very large PDF that you wanted to split into two smaller parts And you didn't want to use the command line to do this You could split a really large PDF into smaller parts that would enable you to send it via email if you wanted to and That way it's not you know too big in order to send via email. You can also Extract pages from the PDF document. So let's just say you needed to send pages four through seven or whatever in PDF to someone else, but you didn't need to send the whole PDF You could extract those pages using this you can also rotate and Split by bookmarks if you have bookmarks embedded into the PDF So if there's not all kind of stuff here that you can do for free There are some premium features that you could do if you needed to use those things But frankly some of the other tools that I've talked about do these things for free and you won't have to pay for them But PDF 7 is really good. It works really well, and it's available on most next distributions in their repos I know it was available in The arch repose so that is PDF Sam the last one on the list is the one that I was talking about at the beginning Where this is kind of the jack of all trades thing and it does everything Really well, and this is LibreOffice draw So this is part of the LibreOffice suite and what this thing does is just basically everything you can edit text So if I wanted to change this word here, I could change this word here to whatever just say I wanted to capitalize the word I could do that if I wanted to move around the parts of this chart I could do that, you know move it up and down if that's what I want to do because these are basically just shapes Whatever I wanted to do it does it you can this also allows you to sign PDFs You can create PDFs here if you needed to create one from scratch If you didn't want to create like a document for something convert it you could just create a PDF just as a PDF There's just a I mean I could sit here for days talking about all the features This is like the Microsoft Office of PDFs It has just a ton of different features and obviously it's free and open source This is the one that I never use honestly to be to be quite honest with you because I never have the need to Actually use this outside of like one time where I had to actually fill out a form So if you have like a form that comes in a PDF and you need to fill that out LibreOffice draw is actually really good because it will allow you to even tab through the form fields and Fill them out and then you can print them or whatever you need to do and just save it as another PDF You can do whatever you need to do that way So this is by far the most versatile of all the tools that I showed you on the list today And that's just simply because it has just a ton of features. So that is LibreOffice draw So those are the top five PDF tools for Linux and honestly out of all of them The one that I find the most useful is a thorough but that's just because for the most part when I deal with PDFs all I have to do is view them and I like the most minimal tool But I know that a lot of people use LibreOffice draw for viewing and editing It's just kind of like a jack of all trades. So if you have a favorite PDF tool or one of these is your favorite PDF tool Let me know in the comment section below. You can follow me on twitter at the linuxcast. I'm also on Mastodon again, it's a fostered on instance. The link for that will be in the video description as well You can support me on patreon at patreon.com slash linuxcast I'd like to thank my current patrons Robert Sid Devon Patrick Fred Kramer Meglyn Jackson I'm from Jules, Steve A. Sebrega Linux, Garrick Samo, KB, TGB, Keith, Andy and uncle bonehead trydevil Mitchell, J-Dog, Carpent Data, Jeremy, Sean, Odin, Marnie, Ross Eduardo, Art Stoner, Elliott, Merrick, Cam, Joshua Lee, Peter Ray, Crucible Dark Finance 6, Primes, and PM Thanks everybody for watching. I'll see you next time


Hello there, it's Sandy and today I'm going to be painting with fountain pen inks and using a little bit of bleach. These are two of my big bottles of ink. Most inks don't come in giant bottles like this, but that means I need to use them. So I thought I'd try doing some painting with them. And I've done a sketch here in which I'm using some bleach on it. I've dipped a glass pen, which is really just a piece of glass shaped into a pen. Dip it into a little container of bleach. Let it sit there for a second and then lift it off with a paper towel. It's a very easy kind of technique to do. The large blobs in the background were done using a cotton ball and the bleach. So you can apply it with lots of different things. Just don't use a brush on it. The stamps I'm going to use today are from Penny Black and they're two beautiful whales. And I'll be using these two inks that I cannot pronounce properly. I'm pretty sure I would get them wrong, so I will let you just read them on the bottles. I have a bottle of bleach, a glass pen, and a brush, which I'm only going to use on the inks. Don't use your brush with the bleach itself. So I'm going to start by putting some of the color onto a tile. You can do this on a plate, whatever kind of thing that you would like. I use tiles in my studio for lots of different things, so I keep a couple of them in the drawer. They're only like $0.89 or depending on what size, $1.29 at the hardware store. And I've put water down first so the ink color will move. For the most part, inks are relatively staining. And it doesn't apply to every single ink in the same way, but I didn't want hard edges. So I tried to put the water down first, which keeps the color moving. Inks are more intense in color than watercolors are. So if you want really strong, intense color, these are going to give you more of that effect.  So inks are helpful that way. They're not very cost effective though, because you need to buy a bottle of it. And sometimes those bottles can be expensive. These are high quality inks. They're going to cost a little more. And since I used them for my drawing as well, I thought I would try to do some painting with them. And they worked nicely. For the underside of the whale, I used a little more water and I'll barely touch the tip of the brush to the inks so that I don't pull too much in. Out of these two colors, the stronger one is definitely the bluer one as opposed to the green. The green is a much softer color. Each of them will react a little bit differently based on how much water you also use on the paper. So I'm using lots of water underneath before painting this one. You may have noticed a little bloop by the tail. I'm going to apply some bleach to that with the glass pen. And after it sits for a moment, dab that off and that will be gone. That is another nice feature of using inks. Not all inks will react to bleach, but test them out ahead of time and then you will know whether or not you can afford to goof up. On this one, I am not putting water down first. I'm just going to paint the inks themselves, see what happens. I want to watch how they blend with each other and how hard does that green edge stay. Because with some inks, they don't lift, well, most inks don't lift, meaning I can't go back in and soften it. I can go over top of it to blend an edge, but you can't really lift much of that color out unless you go to the extreme of using bleach. It's not like watercolor in that way, where you can just keep pushing it around while it's still wet. So here I'm going to add in some greens and blues together and try to mush them around a bit. The line that I got across the green was a little stronger than I wanted, so I just painted some extra green over top. That smoothed things out quite nicely, which was good. And the intensity of the color is definitely remaining. You don't tend to get a whole lot of really dark color by putting layer after layer of ink, like you do with some mediums as well. So that's another benefit to painting with ink, even if it's more expensive because you need to buy a whole bottle in order to have a little bit to paint with. After finishing up the whale, I moved to the technique that I had used in the previous whale and put the water down first so I could get lighter color on the water drops as well as in the thought bubble. I'm assuming it's a thought bubble because I don't know that whales can actually say ahoy there. And if they do, you might have been consuming a little too much rum on the ship that you are in. That's quite possible. But I wanted it to be readable, so just put some very light color in there. Next is to let them dry. And I did that for a while, went off and did a few things around the house, came back and was ready to get my fountain pen out to do some drawing. I had seen online quite some time ago an illustrator and I wish I had saved it. I just remember the idea of drawing a landscape inside of an animal drawing. And she had done this, I assume she, you know, maybe he, they had done this inside of, I think it was a wolf that I saw, some, some such. I can't quite remember what, but I want to see if it would work here because I do love drawing trees. I haven't had much time for doing drawing lately. I have been a little bit busy with lots of other things and my pens have been feeling loadsome and when I got the inks out, my fountain pen said, hey wait a minute, get back here. I want to also get in on the action. If you want some tips for how to draw pine trees like these, there is a whole video on just that topic, works for other mediums as well as fountain pen, but it's created in fountain pen. So downloadable with it as well. And speaking of drawing and pine trees and those sorts of things, I realized belatedly that I forgot to put other classes into my sale category. Every month I put different groupings of classes on sale and I just tossed a whole bunch of drawing classes, both pen and ink and pencil and charcoal and all kinds of things into the sale category at art-classes.com. So I will have a link to that in the doobly-doo as well as the pine tree video.  One of the best ones that I've seen people make the most improvement in their other mediums after taking is 30 days to more confident sketching. It's just done with a pencil and a sketchbook, but it gets you used to drawing things so that you don't panic when somebody says like this, draw some trees into a whale. It just helps you to feel more confident in your skills after spending 30 days in a row just drawing something, just 10 minutes a day. Just do something for a few minutes and that will really make a vast difference for you. So next up is the other whale and wanted to do something with the bleach on this one. So started to make some dots on the top. I was considering whether or not this would look like the shimmering of water on top of the whale. Could I make it do that? I don't get a lot of control with the glass pen. It kind of bloops out and sometimes you'll even need to tilt the glass pen really vertically to get it started because sometimes it stays in all of those curved shapes that are on the tip of the nib and then started looking like you had freckles. That seemed to be a small problem for this poor whale. Freckles are not something that I think they have undersea because they come from the sun, but there you go. I have instead chosen to watercolor over top of it with another layer of the inks to soften that so that at least it didn't look like freckles and it came out looking a lot more like slightly dappled water. Just a tiny bit underneath the color that I put for the top layer and you may decide that I should have left it alone but you could always go back in with another layer of the bleach if you needed to. A little heads up on these, you want to make sure that you're actually using paper that can handle the bleach. So do a few tests first before you dive headstrong into a project like this. I'm using Arches watercolor paper, which holds up well. All right, that's it for me. I will see you again very soon. Take care and have a wonderful day. Links in the doobly-doo to all the stuff I talked about.


You need to find out the number of moles of A to B2 and C2. Yes, I tried doing that. So, they were asking average molar mass. Correct. So, m of A1, m of A into number of moles of A plus m of B into number of moles of B plus C by N in the center. Yes, but it was not working. Is it coming? What is the reaction? A2 gives B2 plus C2. Yeah. So, Kp is given. You find Kc from that. No, this Kp Rd. I mean Kd by N. Alright. And that would be Kp equals to Kc into Rd. N is 1, the time is 1. Okay, I will try this. So, you write on this question and solve this. The reaction is given. A2 gas, try this one, then we will discuss. The molar mass of A2 is given. It is 70 molar mass of B2 is given. It is 49 and molar mass of C2 is 21. The unit is gram per mole. You need to find out the average molar mass in gram per mole. Average molar mass in gram per mole. Sir, Kp was 9 and B was 7. Yeah, Kp is 9 is given. Kp is given. It is 9 and 7 MOSFET expression, 300 Kelvin. 7 MOSFET expression, 300 Kelvin. Try this one. So, this is B carried out with that pressure. No. In this, the equilibrium constant, Kp is 9 in this reaction. That is given. And the reaction is carried out at 7 atmospheric pressure and 300 Kelvin. Equivalent constant, Kp atmospheric is given for the reaction in this question. It is written that Kp for the reaction is 9 at 7 atmospheric and 300 Kelvin. Means, when Kp is 9, the atmospheric pressure is 7 atmospheric. It means that is the equilibrium pressure we have. Means, when you write down suppose, initially we have only 8 to present. Pressure of this is what? P, 0, 0. At equilibrium, what will happen? P minus x, x and x. So, when you add this pressure at equilibrium, what you will get? P plus x.  So, P plus x is 7. That is given. We need to find out x first. What happens? What is x? 3. We need to factorize this x by minus 32. And what is P? Initial pressure? 4. 4. When pressure is 4, P, M is equals to DRT you can write. All of you got x? See, I will just do it now. The initial pressure I am assuming, that is P and this is 0 and 0. So, when it dissociates, it forms P minus x, this forms x and this forms x. The question says when Kp is 9, pressure is 7 at 300. This is the language we have. So, when Kp is 9, pressure is 7 atmospheric. It means Kp when we are saying, it means the equilibrium has to be established. So, equilibrium pressure is 9 at this given. So, this is the equilibrium pressure. So, when you add this, the total pressure Pt is equals to P plus x and this is equals to 9. Now, once you know this x, you can find out P. And what is the relation we have? Initial pressure is P divided by the equilibrium pressure. We know pressure and molecular mass is what, inversely proportional. We have this relation P, M is equals to rho RT or density RT. PV is equals to NRT. N is what, mass by molecular mass and mass by volume is what? Density. Mass by volume is density. So, P into molecular mass goes to DRT. So, once from this what we can write is pressure and mass is inversely proportional. Because density R and T is constant. So, we can write the initial pressure by equilibrium pressure is equals to the equilibrium molecular mass divided by the initial molecular mass. Can you understand? Okay. Okay. And this is because of only A. Initially, we do not have B and C. At time T is equals to 0, we have only A. Right? So, if you know this, you have to find out this. This you already know and equilibrium you know. No, sir, that only you have to find. No, you ask it. At a pressure, it is here. This you know. That is the pressure because of A, no. This is what? This P plus X. No, P is this. This P that we have. Yeah. P equal to P plus X. So, you know this. If you know this X, you know this P. Yeah. So, you have this P. You have this P equilibrium. That is 7. You know the initial mass that is because of only A. So, mass of A will take here and this you have to find out. So, objective is what? Objective is to find out this X when everything is done. Now, for this we will write down the expression of KB. So, KB expression what will happen? P2. X square divided by P minus. C2 divided by A2. That will be X square divided by P minus X. Then you can substitute. So, P. Yeah. 9 minus X. P is 9 minus X. Yeah. Okay. And KB is 9. So, 9 is equals to 9 into 9 minus. Which is 9 or 7? No. P is 7. PT is 7. PT is 7. PT is 7. So, it is 7 minus 2X. Yes. So, it is X square plus 18X minus 63 is equals to. Okay. X equals to 3 you will get from this. Okay. So, this P is equals to what? The initial pressure P is equals to 4. So, the expression will be 4 pi equal to pressure is 7. M equilibrium divided by. 7. This is 70. This way also we can do. It should be 40. Yes. How much it should be 40? Sir, why those marks B2 and C2? That formula also we can find out. M of A into number of moles of A plus M of B into number of moles of B. But that will be more complicated because this is pressure. Yeah. We have to convert this into number of moles. So, better we will use that. Okay. 30 it also. Yes, sir. One more question you see. Equivalent mixture of 2 gases K2 and B2 is taken and is it reselected at 10 to 300. Reaction is given. Kp3 is given. 2. If the initial pressure in the container is too atmospheric. Initial pressure in the container is too atmospheric. The final pressure developed at equilibrium is 2.75 atmospheric in which the equilibrium partial pressure of gas AB was 0.5 atmospheric. Calculate the ratio of Kp2 by Kp1. Calculate the ratio of Kp2 by Kp1. One information is given. Degree of dissociation of B2. Alpha of B2 is more than to that of Kp2. So, initially there is only A2 and B2. Yes. The reaction is the last one. But it takes place by three different steps. First, A2 converts into 2A, B2 into 2B and then the reaction takes place. So, that is still A2 plus B2. Is that A plus B2 or A2 plus B2? A2 gas gives 2A gas. A2 plus B2 gives 2AB. So, the final pressure AB is given. It is 0.5. No, partial pressure of AB. Yes. Partial pressure of AB is more complex. See, A2 gas gives 2A gas. So, suppose initial pressure I was assuming is 1 and it is 0. So, it is 1 minus xn 2x. So, Kp1 is what? So, you can just assume that it is 1. Yes, you can take it as 1. You don't do that. You always assume it is 1. I will discuss in the class also. Nothing is given. You can take it as 1. Why wouldn't like P1 P2 or P1 plus P2 plus 2 in the next? For that, the required data is not given. If you take any random value of pressure, it is very difficult to solve this question. It is more complex. So, nothing is given. You can take it as 1. So, Kp1 is 2x square pi 1 minus x. Similarly, this reaction can be written. But this dissociation constant is different. Correct? So, why are you doing this? So, Kp2 is 2y square pi 1 minus y. Now, I will find out Kp2 by Kp1. So, X or Y relation is required. Since it is simultaneous, there will be some Z which is used over there as well. Z. Like in the A2 plus B2 plus 2AB, I can say that like some Z comes out from A to Z. Exactly. Because AB also dissociate, B also dissociate. So, Z of A comes out, Z of B2 comes out and just comes out. Coming to that point. But point I am trying to make is, Kp2 by Kp1 you have to find out. So, our objective is what? X and Y value. Now, the next thing was Kp3 is given. Kp3 given is obviously this and this to combines and forms this. So, we can write 1 minus X to A2 and Z dissociate. 1 minus Y to A2 and Z dissociate. And this forms. 2 Z is equal to 0.5. 2 Z is equal to 0.5. Because this is our pressure. So, we know the value of Z. What is the pressure of AB? 0.5. 0.5. So, 2Z is equal to 0.5. So, what is the value of Z? 0.25. Okay. Okay. 0.25 over Z. So, what is this? Square N. Total pressure. Here, total pressure is this plus this plus this. So, and you see one more thing. It is a simultaneous equilibrium. So, in the reaction vessel AB will be present, AB will be present and ESR will be present. It means K2, B2, AB, AB. All are present in reaction vessel. So, all these molecules will contribute to the pressure of the equilibrium mixture. So, pressure of A2 is what? 1 minus X1. Pressure of B2 is what? Pressure of A is what? A is 2X. Pressure of B is? Ui. Pressure of AB is? Ui. Happy Diwali. Happy Diwali. Total pressure, what is the value of this? It is my childhood. Diwali is the question. See again. This will solve the problem. This plus this.  Yes. And this is 2.75. Now, it is getting easier. X plus Y is in relation. X plus Y is what? 0.75. Is this Kp given? Finally, X2 is given. Sir, Kp3 is given. Kp3 is given. Yes, Kp3 is given. 2. See, X and Y will have one relation. And we need to find out the value of X and Y. So, one more relation if you get it to X and Y, then we can solve those equations. Find X and Y and we will substitute it. Okay. A buskel here, we haven't used. Till now, we haven't used this particular. Okay.  So, 1 minus Z is 0.75. So, in that denominator, we can write 0.75 minus X 0.75 minus Y. Is that what? 0.25 into 2.5, so it is 0.5. Square. Okay. So, we can substitute Y as 0.75 minus X in that equation. Yeah. And then you just have whatever you have. It will be quadratic in X. Y is 0.75 minus X. Yeah. And then you can solve that. Okay. Equal equation from percent. That also you can do. Y is 0.75 minus X. So, 0.75 will get cancelled. You get X into this and then you can solve this quadratic. You will get X prices. So, solve it. So, also for Kp1 and Kp2, you will have to change that.  For this relation, see what is A2? A2 is 1 minus X for this equation. So, for this equation, it is only this Kp1 for this equation, not for the entire thing. So, for the equilibrium pressure, that is 1 minus X minus Z. 1 minus X minus Z. Yeah. No, no. See, in this reaction, what we are taking? 1 minus X minus Z we should take. Sir, because it is a simultaneous equilibrium pressure. Oh, yes. Yes, correct. So, it should be minus Z also here. So, can I write this 0.75 minus X? Yes. It should be 0.75 minus X. Equilibrium play has always been 1 minus X minus Z. Yes. Okay. So, one thing is what you can substitute this Y as 0.75 minus X and you will get this X value. One other way also, we have to solve this. See, our use the law of multiplying, Kp1 into Kp2. That is what I was thinking actually. Kp1 into Kp2. The denominator will get the same. Okay. Okay. So, what we are doing here? 4 into 416. X square Y. X square Y square divided by 0.75 minus X into 0.75 minus Y. We are just solving this to get X and Y. So, this is what 0.5 is squared by Kp3 and Kp3 is divided by 2. So, we can write the score. 16 X square Y square divided by this entire thing is 0.5 square into 3 or d2. Okay? Okay. Sir, but you don't get anything from this. Yeah. We should get 5. We need Kp1 divided by Kp2. Sir, you can do that. Solve the problem. Solve the problem. We can solve like that. But I have done this. This way also I have done this. You could say that Kp1 into Kp2 is equal to Kp1 divided by Kp2 into Kp2 square. Okay. You solve this quantity there. What are you getting? Check this. Solve this quantity. You know what? One thing is missing in this problem. You know what is that? It's a2 in between. One thing is missing in this question. What mistake we have is there in this question is this should be A of gas and B of gas. Exactly. It makes more sense. Because those reactions don't exactly do it. Yeah. Two of this and two of this. Okay. Correct. Then only it makes sense. Because when you add these two, you'll get this. Like the reaction is proceeding with A2 and B2. So you should get the final reaction with the help of the intermediate reactions. Okay, sir. And then we have this. Then if you add these two, you'll get this. So we can write this into this is equal to Kp2. Yes. Then the solution will be easier. Okay. That's what I was thinking. Kp1 into Kp2. So this you let it be. And then we can write this Kp1 into Kp2 is equal to Kp3. So you add the equation, you still don't get that. We'll get now. So A2 and B2 will still do that. Yeah. So there's no AB in those two reactions. We can't get it. Why? If you add all these three equations, sorry, if you add all these three, you know. So you get A2 plus B2 equals 2AB. Correct. 2A plus 2B we'll get. A2 plus B2 we'll get 2AB. Okay. If this one I let it be like this. A2, B2, A2, AB. So then we can solve it. So we can solve the equation for this. I got the answer. 3 plus 0.5 plus 0.5. Yeah. You solve like that only. I'll just check this out. Okay. Did you solve this quadratic? Yeah. We're not getting one value for X, one value for Y. X and Y can be either 0.5 or 0.5. So the condition is given. Degree of dissociation of B2 is greater than to that of it. So Y is more than X. Yes, so Y is more than X. Accordingly you find out. What is getting Y and X value? So Y is 0.5 and X is 0.2. Yeah. 0.5. So 1 by 2. Yeah. So Y is 1 by 2. X is 1 by 2. X is 1 by 4. X is 1 by 4. If you substitute it here, you'll get Kp1 and Kp2 ratio. Take it. So we'll start organically. Sir. Oh, by starting? How will you see? We just solved this. We haven't discussed this yet. Substituted. Polyporting as it will see. Minus X as Y. Yeah. X to the support. Minus X to the support. Minus X to the support. Minus X to the support. Minus X to the support. Minus X to the support. Minus X to the support. Minus X to the support. Alpha 1, alpha 1. HSO4 again dissociates and gives H plus and Hso4 to minus. See polyprotein acid is my subject. H2SO4 you have. So when it dissociates, it forms HSO4 minus and H plus. So if it is 1, 0, 0. So it's called your 1 minus alpha 1, alpha 1 and alpha 1. Polyprotein acid means what? More than 1 H plus sign it can give. Okay. So when one dissociation gives, it gives you this. HSO4 minus can further dissociate. It gives you SO4 2 minus plus. H plus again. What was this? 1 minus alpha 1. Okay. This was 0. This was 0. Again it dissociates also. 1 minus alpha 1 minus alpha 1. H plus is alpha 1. H plus is alpha 1. Okay. When this dissociates.  Okay. Then it forms. HSO4 minus 1 minus alpha 1. Alpha is the area of dissociation. It will just be alpha 1. Yeah. Where? HSO4 minus in second. No. First. Yeah. It is alpha 1 correct. It is alpha 1 only. So it is alpha 1. Alpha 1 minus alpha 1 alpha 2. And then it is alpha 1 alpha 2.  So HSO4 will write on KPL expression. So we will discuss that polyprotic acid. This is a simultaneous equilibrium. Similar to that. Yeah. Two reactions giving the same ions. So in polyprotic acid you can assume that a simultaneous equilibrium and you can write down the expression. We haven't done this. So cutting after. Alpha 1 minus alpha 1 alpha 2 HSO4. Because degree of dissociation is divided by the unison number of moles. We haven't multiplied by the unison. Alpha is out of one what is reacting. Out of one mole. So our C concentration as C alpha will react. See as a. So you can say in terms of alpha if you write down then you can say 10 minus 10 alpha is the concentration which is left. Means what is reacting? 10 alpha is reacting. Because alpha is defined out of one mole. So 10 minus 10 alpha reacting. In other way what you can say. 10 minus 3 moles is reacting. This is the number of moles reacting. In terms of amount. What amount is getting reacted? This is for one mole really. So in terms of alpha we always write concentration into alpha. C minus C alpha. So this we will discuss. I will share the solution of ionic equilibrium of the center model. So you can take the equilibrium. It should be there. You want I can share that. So because the question is much harder than the previous question. Chemical equilibrium. Chemical equilibrium is easier. Yeah it's a good job. But I'll share it.


Today history was made in Chesapeake Bay, amid the crash of exploding bombs, obsolete battleships were sunk by airplanes for the first time. Veteran Army pilot General Billy Mitchell did what he said he would do. American battleships which once sailed proudly round the world with a great white fleet and only yesterday were detaining America from her enemies are at the bottom of the sea. The nations have agreed to build no more battleships for 15 years, probably forever. The shipyards are empty. The scrapyards are thundering to the sounds of destruction of whole squadrons of battleships. Does this mean the end of the Dreadnought battleship? This is what General Billy Mitchell claimed today. And that's what people will be saying all over the world. More than four decades have passed. Men have fought and died on land and in the air. On the sea too, a new generation of battleships have fired their guns in anger again and again, have triumphed and then disappeared from the oceans. This is a battleship grave, a memorial to an era of magnificence. The silence that hangs like a pole over these Dreadnoughts holds many memories of combat.  She was built because men wanted her. She fought magnificently and with the end of her era she was forgotten. Here lie three of the last and greatest of this super breed of fighting ship, waiting for perhaps one more call to duty. Their names are Iowa, Wisconsin and New Jersey. Their home through these lost years, a remote pier in the Philadelphia Navy Yard. The ancestry of these sleeping men of war stems from the first Dreadnought ever. It is a fearsome name in naval history. Dear God and Dreadnought, the family motto of the English Admiral Lord Fisher, who created the first all big gun battleship early in this century as a challenge to anyone who might dare to dispute England's rule of the world's oceans. Now these American Dreadnoughts look back on the honorable record of their ancestors with names like Valiant and Warspite, Michigan, Texas and Tennessee. The nations of the world built 175 of them at a cost of countless billions. They met their ends in various ways, in combat blasting the pieces each other's steel hulls, or was sent to the bottom by mine, torpedo or bomb, or they were broken up in times of peace and national economy. Their rusting, mud shrouded skeletons litter the bed to the Atlantic, the Pacific, the Mediterranean, the North Sea. In less than the lifetime of a sailor, they had all gone, all but these few kept in reserve, or as mammoth and melancholy memorials to their former greatness, and to a vanished age before missiles and jets deprived the world's armories of nobility. In the years of uneasy peace and depression, the United States Navy had still kept its faith in the older battleship she had built from 1910 to the 20s. Linked now with the new carriers, they were the nation's first line of defense, and their omnipotence brought reassurance to a troubled generation. In a stately line of steel towers and artillery, they signaled to the world their power to deter any future enemy. The funeral pyre of Pearl Harbor changed all that. More brought together the old veterans with a new generation of bigger-than-ever dreadnoughts, graceful, swift, invulnerable. The big gun was still needed. There were ten new ships in all, the greatest concentration of artillery the world had ever seen. One of these giants was destined time and again to etch her name in black gunsmoke and white wake across the battle-contested Pacific Ocean. Maybe with us who follow his leadership that our loyal team may never be slack and our courage never wanting, especially in the day of battle be close to us. We do not pray for easy lives, but we do pray to be stronger men. We do not pray for tasks equal to our powers, but we pray for powers equal to our tasks. Amen. The commandant is authorized to place in commission the United States ship New Jersey, the Navy Yard Philadelphia, May 23rd, in accordance with the foregoing authority and now direct to New Jersey be placed in commission. The year was 1943 and the New Jersey, a steel miracle of speed and firepower, was ready to join the United States Navy for Pacific War service. Her gun crews were behind armor 16 inches thick. There was 17-inch steel over other vital parts of the New Jersey. Her 16-inch guns could hurl 2,700-pound shells 23 miles with unerring accuracy. More than 100 lighter guns could blast any raider out of the skies and she was strong enough to resist the worst the enemy could throw at her. Wither, oh splendid ship, thy white sails crowding, Leaning across the bosom of the urgent west, That fierce nor sea rising nor sky clouding, Wither away, fair rover, and what thy quest. Robert Bridge's white sails had given way to 212,000 horsepower turbines and the quest of the New Jersey and her sisters Iowa, Wisconsin, and Missouri was victory in the Pacific. There was no pause after her shakedown training before the New Jersey's baptism of fire. She steamed into the full fury of the battle for the Marshall Islands at the end of January 1944 and the fiercely defended Japanese fleet base at truck. Her great guns created devastation to shore. Her 5-inch 40 and 20-millimeter artillery stamped the sky with hectic patterns of dark puffs and streaked it with arching tracers. Day by day in the tumult of battle, the men became more skillful and the guns synchronized with the rhythm of destruction and the enemy planes tumbled down in awful balls of fire to a hissing death in the ocean. From Quageline to truck, from Panapay across the Equator to New Guinea, from the damp chill of a north wind to the feverish heat of the southern Philippines, the officers of the New Jersey once lived off duty in this ward room, talking of the routine problems of the day, or maybe that big shoot when the brown stain of their shell bursts at all but screamed off the island of Guam before the invasion craft went in, or what the captain had said when that kamikaze grazed the four mast and exploded 50 yards off the port bow. Through the tedium, the discomfort, the frequent sharp dangers, there was the talk and from it grew the bonds which secure the friendships of fighting men. And the captain himself, alone with his responsibilities, obiter of 3,000 lives, at once warrior, chieftain, patriarch, and judge, as well as commander of one of the most powerful vessels of war ever devised by man. The price of the battle stars earned by the New Jersey and her sister battleships was paid in the lives and injuries of good American sailors and the sorrowing of wives and families. The tide had flowed in every combated sea since Actium. Only the nature of war at sea had changed and the role of the battleship with it. Billy Mitchell, like so many prophets, had been only half right. The battleship was no longer the ship of the line whose war was to pound the enemy fleet in a slamming duel. The aerial bomb and torpedo had finished all that. It was a near impregnable steel fortress with great guns to strike with weighty high explosives at land targets and small guns to clear the skies for the new queens of the Navy. Those floating airfields, the carriers upon whom the battleship depended for her own survival. Now the battleship was the fleet's armed bodyguard, sharp of eye and quick on the trigger. Bull Halsey himself hoisted his flag on the New Jersey, wove his webs of strategical genius and leapt on the flies as they flew into trap after trap. The battles did not cease with the end of the day. For when the sun went down and the stars came out far over the summer sea and never a moment ceased. Ship after ship the whole night long with her battle thunder and flame. God of battles was ever a battle like this in the world before. It was the summer of 1945. The end was near. Under the masterly command of Bull Halsey, the New Jersey had fought at the Marianas, the Philippine islands at Iwo Jima. Like Sir Francis Drake on Plymouth Ho, awaiting the Spanish armada, Fleet Admiral Halsey had time for a game before the final and decisive trial. The enemy was crumbling fast. The New Jersey was steaming at flank speed to participate in her final annihilating battle, Okinawa. Down here on that day the smell of danger was as acute and penetrating as the scent of the hot bearings and racing turbines. No less because it was the last battle. And the courage of the men was of a very special kind as they exercised their subterranean skills. Learning of the battle above only from the sounds and shocks, knowing that if the outcome was defeat, their chances of survival were the slimmest of all. Man, man, man, man, man, man, man, man, man, man, man, man. But these brave men of the New Jersey survived. And after that last battle they raced up from the darkness of war into the dazzling light of victory to join those who had worked the guns. Yes, at last it was all over. The hot days of war turned to the cold days of peace. Old enemies became new allies. Old allies became less friendly. In the troubled air of the late 1940s, many an American battleship went to the breakers. But some of the greatest were kept just in case. Even in this new missile and jet in nuclear age there might still be a place. You never knew, not with a dreadnought. Invincible dreadnought. Suddenly the New Jersey's big guns were needed again. They had not lost their power. Off the Korean coast in 1951, the shells span out explosively from the barrels, in salvos and broad sides, the pinpoint shore installations, and the new enemy and foxholes among the Quezon Hills. On July 26, 1953, a decade after she was first commissioned, the New Jersey fired her guns in anger and many thought it was for the last time. It seemed right and proper that this great battleship should be the last in the world to fight. Again, the old warrior was retired with affection and deep respect, but without ceremony. One more decade passed in the life of the New Jersey. She lay forlorn between two of her sisters, a threesome of forgotten men of war. Through winter snows and gales, the unfulfilled promise of every spring, the heat of summer and the renewed melancholy of autumn, the New Jersey still floated. Her guns trained fore and aft in the posture of peace. When you mounted the gangway and stood on those muscular decks, looking up in awe at the towering superstructure, the cacophony of war was as distant in time as the ship's history. Now there was only the cry of wheeling gulls and the squabble of pigeons about their nests in the funnel tops. With the touch of a late fallen leaf, a fragment of peeled paint falls to the scarred deck. And yet, here was where sweating gunners beat each other's backs and cried joyful obscenities when that kamikaze had hit the sea just forward of midships. And here, aft on the port side, was where that North Korean shell hit and killed. And this is where Bull Hallsy played his last game of deck tennis. I'll bet he won that too. It was so old a ship, who knows, who knows, and yet so beautiful. I watched in vain to see the mast burst open with a rose and the whole deck put on its leaves again. It is the summer of 1967 and the air is full of new national anxieties. The New Jersey is suddenly alive again, throbbing to the activity of duckyard workers who have come to prepare the old warrior for sea. Yet again, the battleship has to be called back to active duty. In August, the New Jersey is detached from her old consorts and drawn in slow dignity from her birth into dry dock. Neglected for ten years, she is again the center of attention. The men that work on her in the Philadelphia Naval Shipyard are another special breed, as tough in their own way as those who man a battleship in action. They are all weathermen who can work high above the deck in winter like a mariner furling a windjammer's topsel or deepen the chilled bowels where it's as dark and claustrophobic as a Pennsylvania coal mine. They are men who may have worked on the New Jersey back in 1950, or even when she was first built in the early 1940s. They all know her and now with their expertise and strength they come on board again to graft their wondrous computers, sophisticated communications, modern lighting and air conditioning to the complex structure and organs of the battleship. As the seasons turn and the low autumn mists over the Delaware give way to the chill and damp of a dockyard in winter, the complex organism is reawakened, stage by delicate stage. New life comes to the ship as her crew gathers, some fresh to battleship service, others who've known it all before. This man and this ship may be rich in memories, but today is when history starts again, yet still chained with the past by links of men and links of steel. On the New Jersey men like this fought and saw others fall 24 years ago and 17 years ago and now perhaps they may endure it all again. For this ship which has experienced the forces of nature and man will soon be echoing again to the feet of men who have tasted action and others who thought that war was something out of history books. The New Jersey's guns are exercised. The massive turbines turn over once more, paint work is cleaned down, and steel that was chipped with age is turned first red, then a clean purposeful gray. A year's work is over. For so long the graveyard memorial, she will soon be a pulsating reality. Man control stand by to answer all bells, take in all lines. That is clear to shift, sir. On the way. It's the first time I've seen that fan tail clear four months. Surely the old ship knows that a new dawn is breaking for her. That again after such a long, long silence, the crisp orders of our new commander are ringing out from her bridge. That is stern, sir. Very well. Starboard engine ahead one third. Starboard engine ahead one third. This is a testing time when a hundred specialists must check a thousand minute perfections. Main control, bridge, engine seem to be answering nicely. So the New Jersey is off on her trials at first slowly and gently downriver. One long blast on a whistle. Then she feels again the heady sensation of speed and the swift caress of the 33 knot water sweeping along her hull. In a few days time the Navy and the people will come to pay their homage and the band will strike up in joyful unison with the cheers at her recommissioning. And so this is the day of days. Senior officials, important guests, gold braid. Today we recommission the battleship. New Jersey is most welcome. A touch of the formality, the pump and the color the New Jersey deserves to celebrate the start of a new life. Philadelphia, May 16, 1968. A cold steel gray dawn. Just a quarter of a century since the New Jersey first sailed away to war. The last act has been played. There remains only the finale. Her stage is the boundless ocean, her true element where all the great roles in her long and dramatic life have been enacted. Released at last, she seems to cry out in triumph I am going to see again, to see, to see. And from across the water comes the anguished echo from the dreadnought's forgotten sisters. As she slips majestically down the waters of this river which is known the shape of her keel for so long heading for deep water and freshening winds she bears the inheritance of every dreadnought that ever fought on the oceans. Of the invincible that once annihilated a whole squadron and was later blown to pieces at Jutland the Bismarck that once destroyed the greatest dreadnought in the world and went to the bottom 48 hours later the Nevada sunk at Pearl Harbor yet lived to fight again. The New York Admiral Rodman's flagship in World War I the Tennessee, Texas and California the Dunkirk from France the Vittorio Veneto, Italy's greatest Washington, Wisconsin, Prince of Wales Colossus and Conqueror, Revenge and Royal Oak Maryland, Mississippi and Missouri Oklahoma and Arizona The New Jersey is the last in a long line of a still unvanquished breed of fighting ship New Jersey, noble American dreadnought born on American soil bred in a century of combat at sea sail then New Jersey sail again out to the seas that have missed you for so long may your tasks be honorable and peaceful may your destiny be as proud as it always has been sail away great ship Godspeed and safe return


السلام عليكم ورحمة الله وبركاته بسم الله الرحمن الرحيم والصلاة والسلام على أشرف المرسلين سيدنا ونبينا وشافيعنا ومقائدنا وقرة عيوننا سيدنا محمد وعلى آله وصحبه وسلم يا ربنا لك الحمد كما ينبغي لجلال وجي كواضي من سلطانك اللهم افتح علينا فتوحى الارفين اللهم اعلمنا ما ينفعنا وانفعنا بما علمتنا يا رحمة الرحيمين كما يكتبنا last week المرسلين من هذه المرسلين سيدنا مقائدنا لما ينبغي اللهم سبحانه وتعالى لذا هذه اليوم نريد أن نكون لدينا مرسلين نحن ننبغي هذه الدنيا ونذهب إلى اللهم سبحانه وتعالى لذا هذه كانت مرسلةنا المرسلين من هذه المرسلين كانت فقط مرسلين من المرسلين لما ينبغي اللهم سبحانه وتعالى حتى ينبغينا لذا هذه المرسلين المرسلين من هذه المرسلين كانت فقط مرسلين من المرسلين لما ينبغينا مرسلين لما ينبغي اللهم سبحانه وتعالى لقد نواجهنا أن نحن نحصل على 10 فرقات لما سيساعدنا لما ينبغي لذا اليوم سوف نتحدث عن أول من هذه 10 فرقات التي سيضعنا أكثر إلى اللهم سبحانه وتعالى وذلك سيجدنا أكثر مستعدة لما ننبغي هذه الدنيا هذه المرسلين هي المرسل السلام المرسلين التي سوف نتحدث عنه now يتحدث عن فرقات الأولى السلام لكن يتحدث عن فرقات الأخرى والثلاثة والأثير من هذه المرسلين لذا يتحدث عن السلام يتحدث عن ذكاء يتحدث عن فاستين ويتحدث عن حلش معازل رضي الله عنه قال قلت يا رسول الله أخبرني بعمل يدخلني الجنة ويباعيدني من النار لذا معاز بن جبال رضي الله عنه يتحدث عن ذلك كان مع سيد محمد صلى الله عليه وسلم وقالت يا رسول الله أخبرني بعمل ويدخلني ويباعيدني من النار لذا سيد محمد صلى الله عليه وسلم قال لقد سألت عبن عظيم وإنه لا يسير على من يسره الله تعالى عليه لذا لقد سألت عن مدينة بشكل جيد أمرا عظيم ولكن it's easy for one whom الله سبحانه وتعالى makes it easy for so what is this that the person is asking about what is this a lean thing what is this great important thing so سيد محمد صلى الله عليه وسلم added تعبد الله لا تشرك به شيء you worship الله سبحانه وتعالى and you associate nothing with him in worship وتقيموا الصلاة so you offer or you perform الصلاة وتأتي زكا you pay the زكا وتصوم رمضان and then you observe the song fasting when you observe the song during رمضان at the last point he mentioned وتحج البيت استطاعت إليه سبيلا and perform حج to the house of الله سبحانه وتعالى if you can afford it let's say سيد محمد صلى الله عليه وسلم said ألا أدولك على أبواب الخير shall I not guide you or shall I tell you what are the gates of goodness so he added he said وصلتك تفعي الماء ونور وصلاته روا جولي من جق في الليل so the the gates of goodness are these three items الصوم وجنة fasting is a screen a screen from hellfire it's a shield there's a screen so there is there is a door in الجنة that is called باب الريان so those who perform the who fast who are or fasting the نفل fasting it's not صوم رمضان it's the extra fasting then they would enter from this باب الريان so الصوم وجنة وصدقات تطفي الخطي أكما يطفي الماء ونور so the other point is charity and Allah SWT is mentioning that سيد المحمد صلى الله عليه وسلم is mentioning that that charity extinguishes the sins the same way that water extinguishes fire and that's why the people of Allah say when you when you sin ask Allah SWT for forgiveness do a lot of stuffar and pay charity so this charity extinguishes the sin the same way water extinguishes fire and the last point that of the of the gates of goodness is صلاة الرجولي من جاوف الليل standing in prayers during the last third part of the night you know that Allah SWT said it descends down to the first to the lower the lowest sky and he talks to us ألا من مستغفل فقافر الله ألا من تائب فأتو وعلي ألا من so he repeats is there is there anyone who is asking for forgiveness I will forgive him is there anyone who is doing توبة now will accept his توبة is there anyone who is asking for anything and I will grant him his wish so this is صلاة الليل this is the night prayer so if you need anything from Allah SWT do it at this time walk up before Fajr ميكدو perform two rakhads and ask Allah SWT whatever you need make dua Allah said أدعوني أستجب لكم ask me and I will I will answer your calls I will answer your prayers so this is صلاة الليل صلاة الرجول من جوا في الليل the night prayer then سيدنا محمد صلى الله عليه وسلم bread the two eyes of surah al-sajdah تتجاف جنوبهم عن المضاجع يدعون ربهم خوفا وطمعا ومن ما رزقنا مجرد العمل so these people those who wake up at night they arise from their beds and they supplicate their Lord in fear and aspiration and from what we have provided them they spend and you know there is something called صدقة الفجر this is they say that this is the highest of صدقة that you get your charity at فلا تعلم نفس ما أخفي لهم من قررتي أعيون so no soul knows what has been hidden or what has been prepared for them of the kindness of night this would be the reward جزاءا بما كانوا يعملون a reward for what they used to do and then he ended the حديث by saying ثم قال ألا أخبرك برأس الأمر وعموده وذروة سنامها قلت بلا يا رسول الله so he said رأس الأمر الإسلام وعموده السلام سيدنا محمد صلى الله عليه وسلم قلت هل سأخبركم about the root of the matters and the pillar and he said yes سيدنا محمد صلى الله عليه وسلم قلت the root of this matter of this foundation is Islam وعموده السلام is prayer so the whole Hadith concentrates or focuses on صلى الله عليه وسلم whether it's the obligation صلى الله عليه وسلم or whether it is the night prayer or the extra prayers so the prayer is an essential guide to improving one's relationship with the creator and the creation how when someone prays then his relationship with Allah سبحانه وتعالى is getting stronger and when his relationship with Allah سبحانه وتعالى is stronger then his relationship with the creation that Allah سبحانه وتعالى has created gets better so now we might say how or what should be observed in صلى الله عليه وسلم there are five elements that should be observed in صلى الله عليه وسلم these are very important elements so what are these elements what are these elements the first element is performing good you say we are praying why is performing good important I'll tell you أبه ريرا رزق الله عنه قال صلى الله عليه وسلم صلى الله عليه وسلم and this is narrated by أبه ريرا إذا توضأل عبد المسلم أو المؤمن فغسل وجه so when a Muslim or a believer washes performs with him he washes his face so when he washes his face خرج من وجهه كل خطئة النظر إليها بعينه مع المد so every sin which he committed with his eyes will be washed away from his face with water or with the last drop of water so when you when you wash your face the last drop of water will include your sins فإذا غسل يدي خرج من يدي كل خطئة كان شتها يدى معلمة so when he when he washes his hand then every sin which he committed by his hands will be a face from his hands with the water or with the last drop of water then he goes on فإذا غسل رجلي خرج كل خطئة نشتها رجله مع الماء and when he washes his feet every sin his feet committed will be will be washed away with the water or with the last drop of water حتى يخرج نقيا من الذنوب until he finally emerges cleansed of all his sins سبحان الله سبحان الله so this is the importance of وضوء it purifies us it wipes away all sins عثمان رضي الله عنه said سمعت النبي صلى الله عليه وسلم يقول so عثمان رضي الله عنه reported that I heard the messenger of Allah صلى الله عليه وسلم saying so when the time for a prescribed Salah for Salat Al-Fard is due and a Muslim performs it to his وضوء so the act of bowing making sujud properly so performing this Salah will be an expiation for his past sins no more sins as long as he does not commit major sins and this is applied forever so imagine that between each Fard prayer your sins are being wiped out سبحان الله so this is the second element performing وضوء the second element to be observed in a Salah is pray the sunnah before you pray the Fard why when you do something extra then you get your heart ready you get yourself ready to pray the Fard and when you pray the sunnah before you pray the Fard then it is a preparation for the heart to focus on the Fard so you feel you are more alert you are more aware of your Fard prayer when you perform the sunnah before it the third element to be observed in Salah is maintain sincerity so this element is actually the result of the previous element we said that we want to perform we want to pray the sunnah so we get our hearts ready now we are in the prayer we have to maintain sincerity we have to maintain awareness during the prayer so we have to remember that this prayer is a connection with Allah سبحانه وتعالى it's not just an exercise of standing bowing going up and down no it is a connection with Allah سبحانه وتعالى one of the companions when he wanted to to pray while he was making wudu they would see that his face became pale and they would ask him what's wrong with you he said don't you know who I am going to stand before who I am going to talk to so his heart is aware even before starting the prayer now when you lift your hands and you say remember that you are leaving everything behind and you are starting a private meeting with Allah سبحانه وتعالى when you have a meeting with your boss with someone special then you focus on this meeting 100% now praying is the time when we when we focus on this private meeting with Allah سبحانه وتعالى so we have to maintain sincerity during this private meeting we have to maintain awareness full awareness during this meeting Allah سبحانه وتعالى is the one whom we are talking to so the words mean Allah is the greatest there shouldn't be anything in our heart greater than Allah سبحانه وتعالى and greater than our love to Allah سبحانه وتعالى so this is just saying now when we read the opening supplication the opening then this should be a direct point of our hearts toward Allah سبحانه وتعالى we are asking Allah سبحانه وتعالى for a dua we have to be sincere in that dua after the opening then we start with الفاتحة and الفاتحة is called the opening of the Quran the opening of the Quran that's why it's called الفاتحة it is also called السبع المثاني why because it is repeated every each and every of our prayers so what is the importance of الفاتحة what is this فاتحة so if we look at the فاتحة we find that it's a conversation between Allah سبحانه وتعالى and the one who is reciting it and the one who is performing the prayer so رسول الله صلى الله عليه وسلم and this is حديث قدسي and we mentioned that the حديث قدسي is the words of Sayyidina Muhammad صلى الله عليه وسلم which was revealed to him by Allah سبحانه وتعالى it's different than the Quran in the Quran we pray using the Quran but we cannot pray with حديث قدسي so Allah سبحانه وتعالى says قسمت الصلاة بيني و بين عبدين صفين و لعبد ما سأل so Allah الله says I have divided the prayer into two halves into two parts between me and my servant and my servant will receive what he asks so what do we say in the فاتحة فإذا قال العبد الحمد لله رب العالمين قال الله تعالى حمدني عبده so when the servant says praise be to Allah then the Lord of the universe then Allah سبحانه وتعالى the most high would say my servant has praised me so what is حمد the meaning of حمد is praise it comes from gratitude and حمد is to acknowledge the blessings we praise because we are acknowledging we are grateful for the blessings that we have been given this is what the word الحمد الحمد حمد means to be grateful to Allah سبحانه وتعالى for all the blessings that he has given you so الله سبحانه وتعالى will say my servant has praised me when we say الحمد لله رب العالمين then we go on الرحمن الرحيم so وإذا قال الرحمن الرحيم قال الله تعالى أثنى علي عبده and when the servant says the most compassionate الرحمن the most merciful الرحيم الله the most high would say my servant has lauded me وإذا قال مالك يوم الدين قال الله تعالى مجدني عبده ومرتا قال فوضى إليك عبده and when the servant says master of the day of judgment مالك يوم الدين then الله says my servant has glorified me and in another narration he said my servant entrusted his affairs to me مالك يوم الدين is the master of the day of judgment فإذا قال مالك نعبد وإياك نستعين قال الله هذا بيني وبينا عبده ولي عبده ما سأل and when he says when the worshipper says you do we worship and of you do we ask help then الله سبحانه وتعالى would say this is between me and my servant and my servant will receive what he asks for so what is it that we are going to ask الله سبحانه وتعالى فإذا قال اهدنا الصراط المستقيم صراط الذين أن عمت عليهم غير المغضوب عليهم ولا الضالين قال الله وتعالى هذا لعبدي ولعبدي ما سأل then when the worshipper would say guide us to the straight path guide us to the path of those to you whom to you have been gracious not those whom you have incurred displeasure not those whom who have gone astray so when the worshipper says this then الله سبحانه وتعالى would say this is for my servant and my servant will receive what he asks for so this is صورة الفاتحة this is the seven that we recite each and every now when you read when you recite imagine yourself having a conversation with Allah سبحانه وتعالى you are saying something and Allah is replying back to you so this would get us more alert will get us more focused on our prayer so the prayer is a connection with Allah سبحانه وتعالى and it is highly rewarded but do you know what is more rewarded what is multiplied in a word not sure عن ابن عمر رضي الله عنه قال قال رسول الله صلى الله عليه وسلم صلاة الجماعة يتفضل صلاة الفذ بسبع وعشرين درجة this is the answer ابن عمر رضي الله عنه يتفضل that the messenger of Allah صلى الله عليه وسلم صلاة صلاة صلاة is 27 27 times more excellent than the prayer performed by a single person so try to pray all your prayers in jama'a if you can pray always with your husband pray with with your father pray with your son pray in jama'a try to have your prayers always in jama'a just to get this multiplied reward from Allah سبحانه وتعالى and we all know that the best time to pray is immediately after you hear the الان عن ابن مسعود رضي الله عنه قال رسول الله صلى الله عليه وسلم أفضل الأعمال الصلاة وفي أبودي وقتها so this is narrated by ابن مسعود رضي الله عنه نيسان the messenger of Allah صلى الله عليه وسلم one of the best deeds to offer one of the best needs to perform is the prayer being performed in its early times so when you hear the call for the event when you hear the just performing the event just bring you will immediately go pray this is the best of the deeds to perform the salah at its earliest time imagine that your phone rings you go immediately and answer it so the call for the prayer is just a call from Allah سبحانه وتعالى to us so that we have to answer immediately so we might say what are the reasons for a Muslim to pray five times a day you know that when ص. محمد صلى الله عليه وسلم went for the إسراء and معراج journey Allah سبحانه وتعالى at that time he ordered ص. محمد صلى الله عليه وسلم to order all Muslims to pray and it was 50 times but ص. محمد صلى الله عليه وسلم was descending down he met ص. محمد صلى الله عليه وسلم he said what has Allah سبحانه وتعالى told you he said he ordered me to give the order for my umma to perform the salah and he said how many rakats he said 50 he said no no no you cannot they cannot they will not be able to do it just go up again to Allah سبحانه وتعالى and ask him to reduce it then he went up and he talked to Allah سبحانه وتعالى and he reduced it five times and he went down again ص. موسى told ص. محمد صلى الله عليه وسلم your umma will not be able to do it go up and ask him to reduce it and then he was coming up and down until it was reduced by five but when we perform five salah five prayers during the day it's as if we will get the reward of 50 prayers so there are five reasons why Muslims pray the five times a day the first one is it's a religious duty so the salah is one of the five pillars of Islam and we know that Allah سبحانه وتعالى سيد محمد صلى الله عليه وسلم سيد محمد صلى الله عليه وسلم بني الإسلام على خمس شهادة أن لا إله إلا الله وأن محمدا عبدوه ورسوله وإقام الصلاة وإتاء وحجل بيتي وصمي رمضان so these are the five pillars that سيد محمد صلى الله عليه وسلم said justifying that there is no God but Allah سبحانه وتعالى and محمد is his messenger is his slave and messenger and to establish the prayer to perform the prayer to pay the zikaa to go to pilgrims of Allah سبحانه وتعالى and to fast during Ramadan so these are the pillars of Islam and these are so this is the first the first reason why the Muslim pray these five times that it's a religious duty and those who do not pray سيد محمد صلى الله عليه وسلم said بين القفل والإيمان تلقص صلاة so between disbelief and faith is abandoning the the the sonak so the mark the sign for إيمان is the second reason is love and thankfulness to Allah سبحانه وتعالى so the daily prayers are a way for a Muslim to show his thankfulness to Allah سبحانه وتعالى and to get the opportunity to be in coming in with Allah سبحانه وتعالى so Allah سبحانه وتعالى says in سورة البقرة I-152 فاذكروني أذكركم وشكروا لي ولا تكفرون remember me and I will remember you be thankful to me and do not be ungrateful to me and we said that the first word of سورة الفاتحة أمدو لله thank you الله سبحانه وتعالى the third reason to perform the Salah is the five third Salah is the purification the Quran tells us that prayers refrain one from a person an individual from indecency wrongful actions in سورة العنكبوت الله سبحانه وتعالى says إن الصلاة تنهى عن الفحشاء والمنكر prayer surely restrains one from indecency and from manifesting evil so the purpose of our lives as Muslims is to grow closer to Allah and the daily prayers purify Muslims and remove inclinations to sin so this is the fruit of Salah تنهى عن الفحشاء والمنكر keeps a person away from doing evil and gets a person closer to Allah سبحانه وتعالى the Salah purifies the heart of the Muslim now the fourth the fourth reason for performing the Salah is the spiritual nourishment so prayers are like spiritual food we eat but our soul also needs to eat our soul needs to be nourished so you cannot live without without food and establishing the Salah is a connection with Allah سبحانه وتعالى that will nourish our soul so just as our physical body needs needs nourishment several times a day so it stays strong in the same way our souls need nourishment several times a day also to keep strong and this spiritual nourishment is obtained through the daily prayers so why do we need to keep strong you know that in the dunya there are so many afflictions there are so many tests we have to be strong so to face the arrows that are always being shot against us so when we are strong we can prove ourselves at that, at the time of hardship we have the support from Allah سبحانه وتعالى with us at the time of hardship what's the fifth reason that we perform the prayers we know that the prayers comes naturally so the when you need something from Allah سبحانه وتعالى immediately you would say when you want to talk to Allah سبحانه وتعالى you just pray you just perform your prayers to talk to Allah سبحانه وتعالى so this is how we we get connected to Allah سبحانه وتعالى it's a natural connection so Islam teaches us that prayers prayers are very important for discipline ourselves for getting spiritual strength for ourselves and do you know where the best place to pray in the masjid but which masjid سيدنا محمد صلى الله عليه وسلم and he said صلاة الرجولي في مسجد بخمسين ألف صلاف وصلاته في المسجد الحرام بمئة ألف صلاف so a man's prayer in my mosque which is the mosque in Medina is equivalent to 50,000 prayers imagine here in مسجد رسول الله is equivalent to 50,000 prayers and his prayer in the sacred mosque in the Kaaba is equivalent to 100,000 سبحان الله so when you are invited by Allah سبحانه وتعالى to perform Hajj or Umrah pray and you know some people some of the Awliya for Allah سبحانه وتعالى when they go to to visit Sayidina Muhammad صلى الله عليه وسلم to visit the the Masjid النبوي the Masjid of Sayidina Muhammad صلى الله عليه وسلم they do they perform one day of previous missed Salah when you go when you are invited to to the house of Allah سبحانه وتعالى perform one day of the previous previous missed Salah that you did not pray earlier try to do it during the Hajj of time try to do it during the day try to do it during the night do it anytime at least once one day when you are visiting these sacred places and try to do it every day when you are there and I will end with this that Sayidina Muhammad صلى الله عليه وسلم صلى الله عليه وسلم صلى الله عليه وسلم بمن كبي فقال كن في الدنيا كأنك غريب أو عابر سبيل فهو أخذ رسول الله صلى الله عليه وسلم بمن كبي فقال كن في الدنيا كأنك غريب أو عابر سبيل عبد الله ابن عمر رضي الله عنه ساد المسجل of Allah took me by the shoulders he said be in this world as though you were a stranger or one who is passing through وكان ابن عمر يقول إذا أمسيت فلاة انتظر الصباح وإذا أصبحت فلاة انتظر المساء ابن عمر used to say in the evening do not expect to live till the morning and in the morning do not expect to live till the evening and that's why sayidina Muhammad صلى الله عليه وسلم said صلى صلاتك وانتم وادع pray as if it were your last prayer because you don't know if you will live till the next prayer or not so with this we just covered a little bit that can be said about prayers about performing the prayer and we we said that when you pray always remember it's not just an exercise of going up and down doing suju, doing raku'a it is a connection between you and Allah سبحانه وتعالى so perform your prayer pray with full awareness pray the way that that is as much perfect as you can and until we meet next week Insha'Allah I send my salam to sayidina Muhammad صلى الله عليه وسلم وسلام عليكم ورحمة الله وبركاته


A lot of times people ask me, do you represent people if they're actually guilty every day? But that's where people miss the point. The goal of a lawyer is a couple things. Number one, sometimes to mitigate the circumstances. That means instead of the client doing a year in county jail, they do 30 days. Or sometimes instead of going on probation for two years, they pay a fine and pay restitution, pay the victim back up front. Many times the lawyer is there to navigate the client through the difficult maze of the criminal justice system, even though they're guilty. There are many circumstances where the person committed a crime and there is a good legal basis to defend the case. Sometimes a person suffers from a mental illness. Sometimes they're addicted to a drug where you can help them get the help for that and counseling so that they you've solved their life problem. But every person is guilty is entitled to the presumption of innocence and also the government to prove them guilty beyond and to the exclusion of any reasonable doubt.