Hello, I'm Jaroslav Škarvada, software developer at Redhead. And today I would like to talk about Q&A project and how it could help you with system tuning. Maybe you have already had some presentation mentioning Q&A or maybe you have already seen it in some performance tuning guides, but these papers usually do not focus on tuning in detail, so that's why I created this presentation to introduce the tool more. Regarding system tuning, if you are a system administrator, usually you don't are okay with the tunings, with the default settings that are in a Linux kernel and Linux system because you want to get the most from your expensive hardware, so that's why usually you need to customize some tuning knobs in the system to get the best performance. Also it depends what performance you need. For example, if you are running some high-performance computing cluster, you want to tune your system for the highest possible chip pad. So to be able to calculate more numbers on your system and in case you are running some message browser, you need to tune your machine probably for low latency. If you have some backup cluster, you probably may want to tune it to consume low power. So usually if you need to do some tuning, probably people consult guides and best practices forums and knowledge-based articles and there are some bunch of commands that they usually just copy and paste, or if they want to repeat these, they usually put it into scripts. So it can very, very soon get very complex and hard to maintain because there are many knobs on the typical system. You can tune. For example, cctl, ccfs, various tools. You need to call to do the tuning, the tools at configuration, usually in ETC. Also you may need to boot kernel with special parameters, run or tune system-d services and also there is, you may need hotplug. For example, if you attach new block devices to this system, you may need to tune it according to your needs. For example, change the IOU schedule or similar. So there are some more problems you can encounter with this approach. But this approach usually works because it's used for decays. And the other problems are the maintainability. It's especially a problem if you need to support multiple versions of operating systems, multiple versions of kernels because even the kernel interfaces and API are stable. They can evolve over time and then there can be changes and non-compatibilities. So usually you end up with several scripts for several machines in your network. If you have several versions operating systems, or you can do one very complex script that will handle it all. And the problem is that you can very easily get lost in it because you can just check some line and you can't remember why it is there. The other problem is how to verify that your system is tuning the way you already want. So usually you can't say that everything works as you wanted. So you probably need to run some benchmark to verify that the system behaves the way you want it. And there can be also interference with other tools because maybe you tune your ccpl somehow and then some other software is run and it changes the ccpl settings. And you will not notice and your system will be tuned differently than you wanted. And last but not least, the rollback. Usually with the script approaches you don't take it into account and if you need to go back with these settings you just provision the system, reinstall or temporary settings just reboot. So Tundi is a small project that tries to address this and help you with the system tuning. It has a plugin architecture, so it can be easily extended. Tundi is centralized in one place in so-called Tundi profiles. So you don't need to take care of all the settings, you just need to know what Tundi profiles to use. Rollback is supported, hotpack is supported, verification is supported and also Tundi can do some auto configuration of itself. It can detect the hardware or operating system versions and type and then can auto select the profile according to this detection. The tool can be controlled from a command line interface or through debas, so it can be easily integrated to existing solutions. For example, it's supported in cockpit. We have also an unseable role for it and the great thing is that it's available in Red Hat Enterprise Linux. In Red Hat Enterprise Linux 7 is already installed and enabled. So this is probably the most important slide for you if you are just ordinary user. People usually ask us for some magic button to just push and don't care about the details. So maybe the Tundi ADM profile command is near to it because all what you need is just to type Tundi ADM profile and then the profile you need and the profile will be loaded and all the system knobs will be set according to this profile. If Tundi is not running on your system, if you don't have Red Hat Enterprise Linux 7 or it's not enabled, like in Fedora, you also need to start it through system CTL or you can also enable it to auto start. The other important command is Tundi ADM list, which will show you all available profiles on your system that you can use that are installed and available. Tundi ADM active shows which profile is loaded and finally there is Tundi ADM verify command that just checks whether all the settings from the profile are applied. If there is something different, for example some pool change, some cctl knob or something, it will show that there is a difference and it will show what is different and you can use this command, for example, for scripts just to check the dash i parameter is there to ignore hardware, to ignore differences that are caused by a non-compatible hardware or that you have hardware that does not support the tuning. For example, if in the profile requested CPU Freq governor to be set to something that is not supported on your system or CPU Freq is not at all supported on your system then Tundi ADM verify will exit error but if you use dash i parameter it will ignore it because it knows that it's caused by not supported feature in the hardware or software. There is also a hack-ish example on this slide how to control it through debas using the debas sent debug command and this do the same as the Tundi ADM active in this example. So regarding the profiles, we have several profiles, I'm stream and these profiles have settings that are provided to us by performance engineers so the random benchmarks do the tuning know what the customers need and these tunings from performance tuning guides are put into these profiles. There are profiles for general goals like throughput performance or latency performance or latency power saving and balance in between. We also have profiles for various products for example for SAP, for database servers, for Atomic and also there exist some head-party packages providing Tundi profiles. Regarding profiles for products they are made from the documentation from the products and from knowledge bases and best practices articles. So exactly if you don't need to go to the knowledge base and tune it by hand you just select the profile and everything is set up. If you want to roll back and try different tuning you can do it, Tundi can roll back the settings so this is also good for benchmarking so you can just tune the Atomic profile change profile and benchmark or system with different settings and you don't need to reboot or reprovision. Regarding reprofiles there are two types of profiles factory or so-called system profiles and custom or user profiles. The system profiles are under user lip and usually there is a problem that some people directly edit them. Please don't do this because if you do it every update of the system profile by RPM, by new version of RPM will override your settings. So if you need to customize it the better way is to copy it to ATC Tundi which takes precedence when selecting the profile and then do your changes. I will talk about it more later. So what's inside the profile? The profile is directory that could be different files used by different plugins and the main configuration file of the profile is called Tundi corner file. If we look more deep on it it's just any file that has some main section and in the main section there can be summary and description what the profile did. This is what you see in, for example, cockpit. You will see that list of profiles and description what they are good for. All this is optional. You don't need to have it there. Even the main section is optional. And then there are plugins configuration. So here in this example I have enabled this plugin and CCTL plugin. In CCTL this is the same just for setting CCTLS. So I am setting serpiners to 5 which is quite low. It means that the system will not swap if not necessary. Regarding the disk plugin there is set really ahead to 4096 and each plugin has a bunch of these options supported. In the form written there it will take all the disk devices or block devices non-removable on your system and tune it this way. If you need some more complex settings like tune different disk differently there is more for both form how to write it and these two are the same. So if you write more for both form you need to specify that it is a plugin type disk. This is the instance name it could be any arbitrary string but must be unique to describe your instance and there are devices the plugin will handle so it will handle all devices. On this slide you can see how to configure it for more instances. So this is the more complex form and you can see I have three instances of plugin disk. One I named disk system we are disk beta and the rest for the rest of disk on my system. So all are type of disk and I want my system disk I know it's SDA1 so I want SDA1 to be tuned this way SDA2 to be tuned differently. Here you can also see something called conditional change operator. This can be read as if just I want read ahead to be at least this number and read ahead is lower it's set to this number it's higher, it's not touched. So this way you can configure different devices. Also it's possible to do full udef regular expression matching. On this slide there are set two instances of the plugin to handle all these manufactured by Samsung so this udef property matched by regular expression and this second instance will handle all SSDs also it takes these devices and in udef it can be done by just checking that the rotation speed is zero. All properties you can match can be get from the udef by disk command, udef idm info udef property and the device you are interested in and all the properties written by disk command can be matched by sorry sorry so you can see that in the first example I am also setting I will schedule it to be deadline and the great thing about it is that it will not when this profile is applied it will not only tune your system all disks on your system but it will also tune later any devices so if you put in new Samsung disk at runtime and it will match any of this rule it will be tuned accordingly so there is another concept in the override which means you don't need to write the world profile, you can just base your profile on any existing profile so here you include the throughput performance profile it will take all the settings from it and you will just add the governor in the CPU plugin to be user space this syntax will disable all tuning from throughput performance for all disks and this will cause that the ccpl set in the throughput performance profile will be cleared and just this one will be so in the first form it will use anything and just modify what's written here and this is good for things called profiles chaining this is an example from the rpm package kundi profiles nfd which provide these profiles so it starts with the latency performance profile which tune your system for low latency then on top of it is based network latency profile that adds just tuning of network interfaces then the real time profile is based on it which adds tuning for real time kernel and finally the real time virtual host virtual host profiles so the good thing is that different teams can work and maintain these profiles and just focus on what's important for them and don't need to cope with the other details now how to customize the system profiles as I said you can just copy and update it but the problem is that you get just a snapshot of the profile provided in one time by the rpm package if maybe you are ok with it maybe you aren't so if you want the latest settings for the system profile to be in your customized profile you can use the overwrite feature this means just create new profile and include the profile you want to customize and customize it by overwrites so this is preferred by because you don't close your settings and also you will get the latest tuning from the rpm packages now I would like to show what we are also trying to solve in tundi to provide some abstraction to the changing interfaces so for example if you need to set transparency you can do it just by shell command but the command is different on different versions of kernel the path is this and on the seventh the path is this so if you need to copy in script you need to have some check there or two different scripts with tundi you just write this and it will take care about it automatically the tool is there for nearly 10 years so we are following the changes in these settings which are most needed and can provide abstraction layer for it there is another example for example if you need to change boot line boot kernel parameters if you do it by hand you will need to check whether it is bootloader specification enabled system in such case you need to call groupenable to edit the groupenable patch some entries check which bootloader is there whether it is grab2 in case it is not bootloader specification patch different files check whether it is EFI it can be quite complex with tundi you do not care you just write this it will set kernel boot command line out of the there iso CPUs we will set them to one which means that the kernel schedule is set to CPU por one so it is extended to more complex examples another thing in this profile is variables you do not need to customize the profile for example if the user needs to isolate kursi. Vse možete predstaviti stetik profil in drugi profil in počke počke. Vse možete predstaviti stetik profil in počke. Vse možete predstaviti stetik profil. Vse možete predstaviti stetik profil in počke. Ako počke počke počke počke počke počke počke počke počke počke. nr. one, this will return cores 2, 3, 4. And there are more functions supported in Tundi out of the box, and it's plugin-able, so you can also write your own plug-ins. For example, you can call external helpers, for example, to calculate parameters at runtime in the profiles applied. Another feature of Tundi is dynamic tuning. It's there to, initially, it goes at it to cope with things which wasn't supported in kernel. So, for example, if there is something, governance or policy doesn't exist yet in kernel, this can be done from user space. So, in Tundi, some plug-ins can do dynamic tuning. This is done, there are some performance counters, like CPU load, disk load, network load, which are provided by monitor plug-ins, so you can add other. And then the Tundi plug-ins can change these some settings in runtime according to these counters. This was experimental feature, and it's actually visible in the enterprise Linux, because we want to create two performance there. So, this will, this can change the tunings according to external factors. But if you want to play with it, you can enable it. You can be done in the minetune re-configuration files. If Fidora is actually enabled. Regarding the auto-configuration, Tundi can also check your system and preset, initially preset profile that it thinks is most appropriate for your system. You can do it by calling Tundi IDM auto-profile, or if you just want to check what Tundi thinks is the best on your system, you can call Tundi IDM and command. So, for example, if you have some product that needs some specific tuning, you can do Tundi profile to tune it, and provide the recommend file to automatically set your profile. Here is example of rules, which can be used. For example, this will set super performance on systems that have compute node, or server, in ETC system release, and are running on bare metal. So, no virtualization. This is output from the whipboard tool, and there are more checks supported. You can check for running processes. So, for example, if you find running debase server, it can assume that it's debase washing used for debase server, and can preset debase profile. So, if you have some rules, you can grant ETC Tundi recommend D, and it will be taken into account by the engine. Also, there is a feature called noDemon mode, because actually Tundi is a demon that listens on debase, and it can be a problem on embedded resources system, or some people just don't like another demon running on the system. So, you can set Tundi to run without demon by setting demon zero. And then Tundi will behave, just one shot. It will start, do its job, apply Tundi, then exist. Problem is, actually, it has less functionality in this mode. There is no debase control yet, but it's solable by socket activation. No clock support yet. It could be helped to do that. Just nobody write the support yet. No tuning of newly created processes. This is probably not solable in noDemon. Of course, no dynamic tuning, and no rollback. It shouldn't be problem to implement. So, regarding the improvements, we need better documentation, especially some reference manual, auto-degenerated, with the... All plugins and described options and what the options mean. Because at the moment, there are some documentation online, but it's not complete. It's a bit outdated. And if you are a new user of Tundi, it is probably not that easy to find out all this information. Also, we would like to improve the noDemon mode, support more functions. And we was asked to add so-called simulation mode to just display what will be changed by the profile and don't actually write the changes. Also, there is a space for improvement regarding containers and much, much more. So, a conclusion. If you don't use Tundi before, give it a try. It's enabled and installed in Red Enterprise Linux. It's slowly finding its way to other distributions. And if your project needs specific tuning and you are doing it by some wild script, consider using Tundi. We, as upstream, can merge your profile, can maintain it to run with latest Tundi Core, Tundi Engine. And you can just benefit from the infrastructure which is supported by Red Hat. Also, if you find back or have some future, don't hesitate to open back report or contact us. Because there are some people saying, hey, this project looks interesting. We might use it in our use cases, but we found out that there aren't features we need, so we will not use it. Just in these cases, open backzilla, we are trying to implement the functionality if it's possible. So here you can see some context for the project. And, well, we have some time left. So I can show you another thing which could be useful for desktop users. Tundi has cover-top integration. If you know cover-top tool, it's a tool written and maintained by Intel. And as the name suggests, it shows you the processes that consume most power. Well, normally it shows you processes that do most wake-ups of T-class. But if you calibrate the tool, this is a thing that not everybody knows by running power-top dash-dash calibrate and keep it running for probably one hour, it will then show estimation for each process how much power it consumes in watts. And there is also a feature in power-top that can tell you what you could do for improvements and lowering power consumption of your system. There are a lot of requests to power-top upstream to add some auto-configuration to this tool for people just hitting the magic button and power-top configuring with everything for them. But the power-top upstream insisted a lot. But finally, the feature got there, and there is power-top dash-dash autotune feature that will enable all tunings. But it can cause problems on various systems because there can be incompatibilities like your mouse can die if it doesn't support power savings correctly and others. So, there is maybe a better way by using power-top to tune the tool. So, just install tune the tools and power-top. And by running this tool, it will generate new tune the profile that will contain all the power-top suggestions turned into tune the profile. And you can just edit this file and select what you really need or not by commenting or uncommenting it. And finally, by activating the profile, you will get all the power-top suggestions on your system. So, this is how to integrate power-top with tune the. So, I have some other slides about some tune the functionalities like PM quality of service and real-time tuning of processes. But these are more complex examples. So, you can see it in this presentation if you download it from the default site. So, probably, this is everything from me. And thank you for the attention. And if there are any questions, I am here to report them. Yes? So, you briefly mentioned the AC capability of tuning to be dynamic in frequency range system. Where does it take the input from, in that case, from the system, but how? You mean the dynamic tuning functionality. The question was from where it is taking the information for dynamic tuning. It is taken from the monitors plug-in, you can write. And currently, there are plug-ins to collect CPU utilization or CPUs utilization, network load for your network card interfaces. And also, you can write probably any monitor you need to fit your net well. The question was whether it will be possible to write some function to fit the TCP data. PCP data to, through the plug-in. Well, I think it could, the plug-ins are written in Python, so you can definitely write everything you need. Any other question?


We were doing normal mode analysis for perturbations about a spherical base state. We had a perturbation velocity potential outside as well as an inside and we had guessed the forms and we had arrived at all the boundary conditions. There were two boundary conditions coming from the kinematic boundary condition, the linearized kinematic boundary condition and then there was a boundary condition which was coming from difference of pressure. We have already used one of the equalities in the linearized kinematic boundary condition to achieve a homogeneous equation in E and B. So, let us call this equation A, where we have utilized this equality. Let us utilize the second equality. So, I want to set del phi in by del r at r 0 to be equal to del phi out by del r at r 0, r small r is equal to r 0 and I have to use those expressions for phi in and phi out and take the derivatives. If I do that, then you can see that for phi in I get l times. So, B l r 0 to the power l minus 1 B l e to the power i omega t, these remain intact is equal to del phi out by del r.  The P l and the P l will cancel, the e to the power i omega t will cancel because they are not 0 at all times and so the other side I will write A first.  This is my second homogeneous equation in the three unknowns A, B and E. I will call this equation equation B. So, I have one equation which is homogeneous in the unknowns which is equation A and I have one more equation. I need one more equation and that has to come from the pressure boundary condition that we have just written. So, equation 5 because equation 5 is a lengthy equation. So, I am going to rewrite this and then use the expressions for phi in phi out and eta to obtain a homogeneous equation in the three unknowns from equation 5. So, let us write the pressure boundary condition once again. So, rho out into del phi out by del t at r 0 minus rho in del phi in by del t also at r 0 minus t by r naught square twice eta plus cot theta del eta by del theta plus 1 by r naught square del square eta by del theta square. We have to remember that the expressions for phi in and phi out I will write it here so that you can follow the algebra.  So, we have to simplify this equation using these expressions. If I substitute it then I get rho out there is a derivative with respect to time. So, i omega r 0 to the power minus l plus 1 because it has to be evaluated at capital R 0 into A into p l of dot that takes care of the first term. Then we will have minus rho in again i omega r 0 to the power l B p l and then there is a e to the power i omega t in all the terms which I am going to cancel. So, I am not going to write it is equal to minus t by r naught square.  Again I am not writing the e to the power i omega t you can see that all the terms will have a e to the power i omega t and that can be cancelled out. So, I am not writing that plus the last term. So, there should be no r naught. So, the r naught square has already been taken common outside the bracket. So, that was a mistake. So, del square eta by del theta square. So, there will be an e here and then this is just d square p l by d theta square. Now, let us look at the right hand side of this equation. You can see that they there are derivatives with respect to. So, let us look at the right hand side the r h s of this equation. We will have to do something about the right hand side without which we cannot just get our dispersion relation because you see what appears on the left hand side is p l of theta in both the terms whereas what appears on the right hand side one term contains p l of theta but the other two terms contain the first derivative and the second derivative of p l with respect to theta. So, if you want a dispersion relation which is independent of theta, we will have to somehow convert the right hand side make all the terms proportional to p l of theta. Let us see how. So, I will take the right hand side of this equation and I will see I will write it as r 0 square. I will write the highest derivative first. So, there is an e over all. So, I am writing I am going to write the e at the end. So, every term has a e. So, I am just going to write the highest derivative which is the last term above then the next highest derivative which is cot theta times d p l by d theta and then the first term which is twice p l the whole thing gets multiplied by e. Recall that p l comes from the solution to an or second order linear differential equation that was my Legendres equation. We have written that earlier. So, p l comes from the solution to this equation. So, you can see that p l satisfies the equation.  All I am doing is just taking p l and replacing it in this equation which I have put inside a red rectangle. You can see that all I have done is I have just replaced capital F by p l. Why? Because I know that the solution to this equation one of the solutions to this equation is p l of cos theta. So, p l of cos theta must satisfy this equation. So, I know that this is the equation that p l of theta satisfies.  This just comes from this equation. I have just rearranged this equation. What do I gain by this? I have seen this expression earlier. We have made this expression earlier. This is exactly this expression in my boundary condition. So, it allows me to replace the second derivative and the first derivative with just minus l into l plus 1 p l. So, the whole term on the right hand side of this equation becomes proportional to p l because on the left hand side both the terms already have a p l. I can cancel out the p l and what I will get is an equation in A, B and E whose coefficients do not depend on theta. That will be my third equation in A, B and E. Let us do the algebra. So, I am just going to take this identity that we just wrote and I am going to replace this term plus that term. There is a E common. So, I can pull that out and I can replace the sum of those two terms using this. If I do that, then this is what I obtain. So, we obtain. So, the left hand side remains the same.  I am just rewriting the left hand side A into p l of dot and I am not going to write the E to the power i omega t because that will get cancelled out minus rho in i omega r 0 to the power l B into p l of dot is equal to the right hand side. The right hand side has 3 terms. The first term is left as such because the first term is just 2 times E times p l of dot. So, the first term is just this. We do not do anything with this and we replace the next two terms using the identity that we have just obtained. So, we obtain inside 2 minus l square minus l. It is just l into l plus 1 with the minus l into p l of dot into E. You see the Legendres equation has helped us simplify the expression drastically on the right hand side. Now, you can see that there is a p l everywhere. I can cancel it out. Once I have done that the coefficients of this equation which contains A, B and E become independent of theta. So, I can get an equation which looks like rho out to i omega r 0 to the power minus l plus 1 into A minus. So, I can keep this in a bracket to remind us that this is the coefficient of A. Similarly, a coefficient of B rho in i omega r 0 to the power l into B minus. I am shifting the term on the right hand side to the left. If I do that and I will keep it as minus because I am swapping I am pulling out a minus from here.  You can multiply and convince yourself that this is correct. So, that is my third equation. So, I will call it C. We had 3 equations. So, let me write it again. So, we had i omega E minus l r 0 to the power l minus 1 into B is equal to 0. This was my equation A. Then I had an equation again. So, this was obtained from the linearized kinematic boundary condition.  This is equation B. And then we have equation C. So, those are our 3 equations in 3 unknowns. Not all the unknowns appear in all the equations, but they are linear homogeneous equation, algebraic equations in the 3 unknowns. Once again, we can write it as a matrix equation, as a homogeneous matrix equation and the unknown vector will be A, B and E. The determinant has to be equal to 0 in order to obtain non-trivial solutions to A, B and E. If we do that, I leave it to you to work out the determinant. I will just tell you the dispersion relation. It is a little bit of algebra. It is not difficult. You can try it out for yourself. If you work out the determinant of this, you have to be careful. You have to rewrite these equations such that in every equation. So, if you write it in the order A, B and E, then you have to make sure that you are writing down the coefficients correctly. So, for example, equation A has to be written with B first and the term with E as next. Similarly, equation B, equation B is already written in the correct form. So, equation A has to be, the two terms have to be switched. If we work out the algebra, then it just turns out that the dispersion. So, you can see that it will give us a quadratic equation in omega and that quadratic is the following.  You can see where this is coming from. The l plus 2 and the l minus 1 was already there.  I can shift everything to the right hand side except omega square and I can write it as t by r naught cube and I will pull out a rho in because t by r naught cube into density has the dimensions of frequency squared. So, whatever is left must be a non-dimensional quantity.  It is a density ratio divided by rho in because I have taken rho in common into l. Once again, we achieve the same form. These are surface tension driven oscillations. So, I can write a non-dimensional frequency as t by r naught cube into rho in. And this is some non-dimensional function of the density ratio and l. So, this is some non-dimensional function g of l and density ratio. And we have determined the form for g. So, this is our dispersion relation. Let us compare this dispersion relation with all the other pure capillary driven dispersion relation that we had obtained so far. So, we had obtained earlier for pure capillary waves on a pool of finite depth and hyperbolic. The right hand side is non-dimensional. This was for capillary waves, tangular pool. We have seen this before. Then we had waves on a cylinder, on a liquid cylinder. This was t by rho r0 cube. I am writing the non-dimensional frequency on the left hand side and whatever is left on the right hand side is a non-dimensional function of its arguments. So, this was kr0. We had found an instability here kr0 square minus 1, the modified Bessel functions i1 and i0. This was for capillary waves liquid cylinder ignoring the gas outside of radius r0. Then we have found in the same problem we have found t by rho r0 cube is equal to the same formula kr0 into kr0 square minus 1. But now the other Bessel function, modified Bessel function and these are capillary waves on a cylindrical gas bubble of radius r0. Here too there was instability. Here in this third formula we are solving for the liquid outside. We are ignoring the effect of the gas inside. In the second formula we are solving for the liquid inside. We are ignoring the gas outside.  This takes into account the density of both the fluids. So this should give you an overall sense of what we have looked at so far. The first problem that we looked at was a Cartesian geometry. The second and the third problem was a cylindrical geometry. The fourth problem was a spherical geometry. These three are the most common geometries that we encountered typically in engineering applications and we have looked at waves on quiescent base states in all the three geometries. With the exception of the first we have ignored gravity in 2, 3 and 4. In the first problem we have included gravity as well and we have found what is the effect of gravity. We have looked at capillary gravity waves. In writing the formula 1 I have just said g is equal to 0. So these are the various formulas that we have found until now. Let us look a little bit in more detail at this dispersion relation. Recall that l is a positive integer. So 0, 1, 2, 3 and so on. This comes from the subscript of the Legendre function. I have told you the form of p0 of x, p1 of x, p2 of x and so on. So you can see that for l is equal to 0 and l is equal to 1 this frequency is 0 because there is a l and l minus 1. So the frequency is 0 for l equal to 0, l equal to 1. Apart from these two for everything else for all other positive values of l, l equal to 2, 3, 4, 5 and so on. You can see that this will never give you omega square negative, omega square is always positive. So the first conclusion is that that this base state, the spherical base state unlike the cylindrical base state, the spherical base state is stable to small amplitude perturbations. We always get oscillations or waves, we never get instability. So this dispersion relation does not contain any instability. Now we will understand the l equal to 0, the l equal to 0 and the l equal to 1 limit. So because the both of these predict that omega square is 0, 0 frequency relation. Okay. In one of the assignments early on in the course, we have seen examples where examples of mechanical systems where the one of the normal mode frequencies was 0. One of the cases here is related to that. Let us look at this dispersion relation in slightly more detail now. So we will write two limits of this dispersion relation first. So one is the drop limit. The drop limit is the limit where we are saying that the outer fluid is a low density fluid, typically a gas. And so we can ignore the density of the outer fluid compared to the inner fluid. So it is a liquid bubble surrounded by let us say air. So a water bubble in air, raindrop is a good example. So the drop limit we set rho out to 0 retaining rho in. If we do that, then the dispersion relation simplifies. So our dispersion relation is, so I am just going to write it in dimensional form t by r naught cube and I am going to push the rho in inside so that it is easier for me to set things to 0, l plus 2 minus 1 divided by, there was a rho in. So this is rho in into l plus 1 plus if I push the rho in inside then this ratio just becomes rho out into l. So now if I take the drop limit of this dispersion relation, so then omega square of drop is equal to, so I just set rho out equal to 0.   This is a very well known dispersion relation. It is used frequently in analyzing the natural oscillations of liquid droplets. There is a bubble limit also, bubble limit. Here we set rho in to 0. We are saying that there is a liquid outside and there is a gaseous medium inside. So we are going to solve for the liquid outside ignoring the gas inside. That is the bubble limit. You can think of an air bubble in water. In that case the density of air is negligible compared to water. So we will set the reverse. We will set rho in to 0. So omega bubble square is equal to, so now we are going to set rho in to 0. So I will get a t by r naught cube into rho out.  This is the dispersion relation for bubble. Note that these govern what are known as, these are all oscillations. These are frequencies which tell us the frequencies of small amplitude oscillations. Note that these are shape oscillations. What does that mean? This implies that there is a shape, but at linear order there is no change in volume. So these are shape oscillations. In particular in the case of bubbles, volume oscillations are also possible when the air behaves as a compressible medium inside. The gaseous medium behaves as a compressible medium inside. These dispersion relations govern shape oscillations and not volume oscillations. So let us understand the origin. So as I said earlier the full dispersion relation gives omega square is equal to 0 at l is equal to 0 and 1. Why is the case? Let us understand this in a little bit more detail. For this we will need to calculate the volume of the perturbed drop. In spherical coordinates, the volume of the perturbed drop, the volume of the perturbed drop in spherical coordinates has to be computed through integration. In r theta phi coordinate system that is spherical coordinates, the volume of the perturbed drop is given by this this integral. So r goes from 0 to r naught plus eta and eta itself is a function of theta and t and theta goes from 0 to pi and psi goes from 0 to 2 pi. Nothing really is a function of psi. So the psi integral will be the easiest to evaluate. So this is r square sin theta dr d theta d psi. You can look this up in any textbook on calculus. This is the volume of the perturbed drop. We have put some surface perturbation at the drop and we are calculating what is the volume of this perturbed drop. So the psi integral is the easiest to do as I said earlier. That is because none of these quantities depend on psi. The eta here is a function of theta and time. So I can do the psi integral and that will just give me a 2 pi because the limits of psi is 0 to 2 pi. So the psi integral goes out and I am left with let me write the theta integral theta equal to 0 to pi because that will be the integral which will be done last into d theta. And then we have the r integral which is 0 to r naught plus eta which is a function of theta. So it will affect the theta integral and this one will be r square I should keep a sin theta here and then r square dr. If I do this then this just becomes 0 to pi d theta sin theta and r cube by 3. So this will become r 0 plus eta whole cube. We will continue with the integral in the next video.


Today, on International Women's Day, we celebrate the achievements and contributions that women and girls have made to society all over the world. Indeed, women's contributions to society are immense, but often go unrecognized. Twenty-five years after the Beijing platform for action, a lot has been achieved globally and in different areas, but we all know more needs to be done. We can all do better, and we must. We need to ensure that IOM interventions, from their inception, consider and respond to the diverse needs, roles, responsibilities and experiences of people of different genders. In this way, we can make sure our actions meet everyone's needs and remove barriers to gender equality. Promoting gender equality also means having a hard look at our own practices. We need to work on our organizational culture to better operationalize the concept of equality. This also means preventing abuses and reacting accordingly when they are reported. We need to accelerate our strategy to achieve gender parity at all levels and in all IOM functions. Allow me to take this opportunity to thank all IOM colleagues of all genders for what you have achieved around the world through your own actions. By being gender sensitive, your work is making a positive difference. Let us be generation equality. I am generation equality.


Yeah, the Australian government's looking at me right now that someone's researching this and going I don't think he was looking for jobs during that time He owes us quite a lot of money Yeah, I can pay it now In that moment, I was not prepared. I didn't know I did not have all the tools. I wasn't feeling cool enough I wasn't alpha enough. I didn't have the right shoes or whatever else I Had been preparing in the sense that I'd made a decision. I wanted to be better with women I was out there doing it with friendly fives and like, you know Nice sevens and like arty chicks and like girls that I could handle and then suddenly next level appeared and I became ready by doing it In that moment I changed that behavior of not me not being able to do this or not this girl was too good to me or whatever else That was the moment where I had an evolution and you look at Zen Buddhist because that's the the traditions that I come from in terms of my spirituality That constantly striving through daily practice to reach instantaneous breakthroughs Yeah, in terms of seeing the nature of reality And that's what you guys are doing when you're learning seduction. You are taking daily action You're going out there.  There's supposed to be a thing that says how much time out someone took it away so one last story Once again, I was on Euro to a couple of years ago. I was on this island paradise called Havar off the Croatian coast and I was walking In the dappled sunlight through an olive grove with a couple of students and I was wearing my Daniel Craig swimming suit Which looks much better on him than on me with my skinny white body in my hairy chest and My students were equally well endowed with the gifts of nature And we were strolling through the dappled sunlight Across slightly pebbly ground Across this island and there was this outdoor cafe and all these beautiful people Croatian couples are sitting around sipping espressos And I said to my student see that over there and He looked in the direction and he went to see what and I said the most beautiful one on the planet And he went oh Yeah, yeah, right like he's trying to avoid the fact that in the middle of this and well away from everyone else Is the most beautiful woman on the planet Obviously a Russian.  He's like man.  It's a weird existence that we dating coaches living and um so he strides up to this to this girl and I see him like lean over and like put his hand on the table and go and this girl just looks up and like withers at him and opens her mouth like this To deliver one withering word probably and I see him sort of there tentatively and he just like backs off and he just walks back He comes back to me and I just give him a little hug And he says man, she was really not very nice. She was really nice. That was really bad I don't want to do that.  He opens his eyes and I said That was really good.  I don't like that was enough for me today. I'm like all right My turn watch and so I'm walking over


as we sing together. Ahim that we rarely sing but it speaks about the golden morning when Jesus Christ shall come. Him two hundred and five. Let us rise on our feet as we sing together. Bless us in a special way. Be with us now for the rest of the day and the program because we ask it all in Jesus' name. I want to welcome each and every one of you this afternoon for the afternoon program. We had a beautiful morning shared by our speaker Pastor Mahanu and this afternoon I'd like to invite him again to share with us in our dream living and looking into eternity. Thank you all for coming and for those who are online wherever you are we want to welcome you to share in the word of God. At this time I would like to invite our speaker Pastor Mahanu who will take us through living for eternity. Thank you. Okay good afternoon. Good afternoon everyone. You're welcome brothers and sisters. It's a privilege and honor again to stand before you. I hope we all had good lunch and I want to welcome you on our first day of our stewardship week of prayer and the title of our presentation the whole of this week is living in view of eternity. Living in view of eternity. I'll be speaking on this subject every evening and at the end of this presentation I'll share with us the topics as they will be running each day at the end of this presentation. But for this evening I would like to welcome us to consider this subject living in view of eternity and our key text is taken from the book of Ecclesiastes. Okay there are those who pronounce it as Ecclesiastes. Okay chapter three and we are looking at verse 11. That's where our our text of study will be coming from this particular afternoon. Chapter three verse 11 are we there? Verse 11 says he has made everything beautiful in its time. He has also set eternity in the human heart. My version says in the human heart. Others will say in the hearts of men. Yet he says no one can fathom what God has done from beginning to end. That is the reading. Let us pray. Our Father in heaven every time we get a chance to sit at your feet and to consider your word that is eternally in nature. Whose effect is eternal? Whose consequences are eternal? Whose power is infinite? Whose authority is unlimited? We shudder and we close our eyes because it is beyond what we can understand. In the stillness of your voice in the coming few minutes as we consider this which belongs to the realm of eternity yet we belong to the realms of the finiteness. Help us to comprehend this thing your word that has power to save even power to heal and to create hope in a state of hopelessness is our prayer in Jesus name. Amen. You see there are questions that we need to answer in life. These questions will never be set by anybody at your place of work. These questions may not be set by the curriculum developers in the KIC. They may not. They may not be considered as part of what you need to do for you to get married. In fact it will never be part of the interviews that you will ever attend on this other side of life for any job that we're looking for. There are questions that human beings are and must of necessity answer to and these questions part of them are this that we are going to look at this afternoon. The questions are why am I here and if you have never asked yourself that question you do not have the legis you you do not have the privilege of of simply glossing over it is a question that you must answer why am I here especially for those of us who are serious men and women in this life. The other question is what difference does it make for me to be here? Suppose I was I was born dead. What difference would it make? Suppose I died before I went to school or I died before I got married. Suppose I died before I got my job. What difference does it make? It's a hard question. What is it that will ultimately satisfy the curious and the longing of my heart? What is it? I am not claiming to have absolute answers to this question but in this study this afternoon we intend to respond somehow principally to them not exhaustively but principally to them. The order of this book is called Solomon, the wisest man who ever lived. If you look at this man his credentials and I wish I had time to give us the credentials of Solomon but suffice it just for me to say at this time he is the president. He is the president of the greatest superpower on the planet earth called Israel seated on the throne. He is a wealthy man stinging rich with you know things he has. He is a man of means. He has acquired knowledge. He has tried to know this and why this is like this and not like that. He has gotten to that. He doesn't know so much but he knows at least something about everything. Most of the subjects that are you know going on at his time he has something he can contribute. He can tell them no guys if you've got this direction this is what will happen and because of this don't go this direction. That is Solomon. He's a man whose heart was open to get satisfaction from anything that his hand would lay on. He has tried knowledge. He has it but his heart is more vacuous and empty. He has said no you know the passion of the flesh you can't just starve the passions of the flesh. You need to satisfy you need to feed your flesh. He has tried to feed his flesh and and and ensure that every passion that comes is well taken care of. He has 1,000 wives. He must have been a very strong man. 300 legally married and about 700 Kongiubines. He keeps them all of them are funded by the state coffer. He is one man who you know will come from this house and go to this house. He sleeps in this house today sleeps in the other house tomorrow. He has all of them coming in different shapes in different colors in different sizes. He is allowing it to be the only moment to satisfy the passionate longing of his flesh and he has tried it and and and and and he comes to this text by the way if if you get time just go and read again you know his book Ecclesiastes just go and read and you will enjoy you know he comes and says man I have discovered that these things are vanity. In fact he doesn't say some things he says all everything else that you can do under the blue sky he says it is vanity.  That is how he sums it up in fact that's how he begins this particular book. You can imagine you're writing a book and you start by saying all his money. This is a man who has hit a dead end and God allows him to write like this because to some of us who think that we can live by things and I repeat that statement intentionally.  It is a sharp rebuke because things and the things we live for and buy do not add even a single iota to the life that we have and so Solomon has been enumerating all various of vestitudes of prosperity and adversity. He has talked about construction and destruction here. He has talked about society and solitude. He has talked about love and hate and he talks about these things all coming in time and place for a reason and within its own season and then he comes down and in verse 11 that we are considering he puts it he says he has made everything beautiful in its time. Everything is beautiful only in its time. Everything is good in its time. Everything is appropriate only in its own time. Done practiced outside its own time. It is not. It is not and so Solomon says in the text he says there are two antagonistic facts here. Man himself is transient meaning we are on transit we are passing by we are temporal but what God has done is that he has said something called eternity in your heart and in my heart so man is a bipolar being man is schizophrenia if you may choose to call it he he is two personalities in one he is both temporal and yet in his heart is eternity set in it. I think God was wise I think he was wise so he allows eternity to be that which controls the transient and not the other way around and I'm going to explain that in a little while so then it goes on he says that God has made everything so there is nothing that we have there is nothing that we are that was not made by him nothing is that was not made by him nothing we are and nothing we have that was not provided for by him we and all that we have and are belong and come from him he God has made everything everything but beautiful in its own time it's outside its own time it will happen when it happens in its own time beautiful all natural things are so beautifully in their seasons consider summer and winter spring and autumn all these seasons coming each one in their place in their time is beautifully in its own consider darkness and light in its own whenever the natural cause of things is left to bear there is a strikingly beautiful results whenever natural cause is allowed to in other words there is only a challenge in the life of men whenever that which is natural is turned into unnatural every time everything is happening in their own cause and order of nature everything is beautiful any time there is an interference with the natural order any interference with the natural order of things I can assure you everything goes amese and these is where we are allow me ladies and gentlemen to let us know that if God has set eternity in the man in the in the heart of man or in the human heart it simply means that man is in possession of a stifled and misinterpreted longing something in our hearts that pushes us too long to yarn for something we cannot interpret even ourselves we don't know what it is because that eternity must make us to focus at a place beyond anything else the transitory however setting it may appear sometimes it may not be very active depending on your relationship with God if you haven't cultivated it over and over sometimes it's like that longing seems to disappear but that is never true it does not disappear forever there are moments when you are on your own at your best then you see and you feel and you sense it coming a misinterpreted longing in our hearts it will set in by God eternity is to be conceived as a long indefinite period of time God has placed in the inborn constitution of man the capability of conceiving of eternity and the struggle to apprehend the everlasting the longing after the eternal that will be man's portion for the rest of his life we may sometimes try to switch off the engine that seems to be propelling you towards longing for eternity but even when you have switched it off the engine will still be rolling inside you inside your heart there will be something that you need and that is determined by what we are doing in fact the reason why you woke up in the morning is because you're looking towards eternal you should have remained in bed the only reason why you ate food in the morning is because you had transient you had dying you want to eat so that you can that's the only reason why you went to the bathroom and showered and put on some good clothes the reason why you'll wake up every morning and go to work even though sometimes it's not very good it's because you are thinking of tomorrow eternity is set into our minds so man is nourished by two worlds the temporal world and the eternal world the temporal world with its all temporal things that we can see and the eternal world that none of our hands has ever laid on anything of it poor writing he says i has never seen ear has never heard that which belongs to the realm never when john the revelator is writing using andropomorphic language he he simply says he simply says i saw a city that was four square he says the city has gates of power and and he says and the city has streets of gold he doesn't know that he's interfering with our imaginations how can i imagine a city whose pathways are made up of gold he's interfering with our imaginations that's the language that could possibly be understood at that time that is a gentleman allow me to say this that god himself is eternal he has no beginning or ending he sees the end from the beginning he is omnipotent meaning all powerful he is omniscience or omniscient meaning he knows everything science then of course he is omnipresent meaning he is everywhere at the same time god he is eternal he has set this thing called eternity in the heart of man he has set the cycle and the clock that goes beyond the chronological clock that we have that is why we are living for next week and for next year even when we may die tomorrow our clock does not stop we plan as if we will be here for 1000 years even we know when we know that we'll be here only for two months it is because inside our heart there is a clock that was set that goes beyond the chronological time that we have today are you listening to me ladies and gentlemen it is important to know that this is how god created us he created us to last forever and what did he do he took the dust and then he breathed in the dust eternal spirit then man became a living soul so a human being is a composite is or a combination of that which is transient and that which is eternal at death that which is eternal lives and goes back to the realm of god and the body remains because of that my brothers and sisters you will always struggle to live in between these two and to balance how to live in this transient world yet looking forward to living in eternity is the greatest science of the soul this is not the science of the mind this is the science of the soul that is where we are we are above eternal and temporal now in the garden of Eden when god creates Adam he takes Adam and his wife Eve who are both temporal and eternal puts them in the garden and he wants to teach them to live a life within this temporal realm but living in view of eternity then he plants in the garden several trees and in the garden plants three kinds of trees or of roots one is the tree of life you eat of it you live forever the second one is the tree of knowledge of good and evil you eat of it you die and then he creates another one the third one is the tree that has fruits for food on daily basis and he tells men this third one you can eat of it it does not have any consequence but this too you eat of this one you live forever you eat of this one you die you eat of this you will live forever even as you continue subsisting on this temporal one you eat on this tree of life you live forever you test of this particular fruit of good and evil that one you die you end up god was teaching men on how to balance between temporal nature and the eternal nature now Adam chose to go for the fruits which are for this life they have no consequences but because of a lie that he believed in he thought that this one of eternity is good let it let it stay for a while this one i'm not pursuing it let me pursue this one first which has been prohibited because in it there seems to be some benefits and those benefits are going to make me great those benefits are going to be immediate they are not like have to wait and wait and wait i'm going to get them right now so he went for this tree and the moment he went for it he ate the bible says he died as a matter of fact the only reason why we are sitting here hello the only reason why we are sitting here is because they chose to go the temporal way and forgot about the eternal way the only reason why we are sitting here our loved ones some of them are dead it is because of what happened at that time the only reason why our sick loved ones are in the woods and hostels in beds in our houses it is because these guys are them and his wife the only reason why there is pain in your life the only reason why you have to quarrel with your husband and quarrel with your wife the one with whom you covenanted on the altar and said god our love comes sunshine or rain the only reason why that that challenge is there is because Adam and Eve chose to go the shortcut the temporal way as opposed to and i think for those of you who are in your lesson quarterly you must have discovered something about the choice that this great man lord made and the the author of the lesson said you know lord looked at the the green foliage of the plains he looked at the bamboo leaves when the wind is passing through the whistling voice he saw music in itself and he looked at the well the waters that run through the plain the rivers and he said man this must be the place he was going and living by the temboralness and not considering eternity which had been set in his heart you know i don't know if this has been your experience when i was a small boy one of the things i used to tell god god if you can just help me get 20 shillings because by then tembo would be available and tembo was enough to get me uniform tembo was enough to buy me a shirt and a shirt for my schools i would say god if you just help me get 20 life will be over i will i will be satisfied i got 20 i discovered that the moment i got 20 that was mine 20 that calls me father and a mother and i said oh my god if it is just 50 50 50 all my problems in the world will be over sometimes during a school break you know we would go gleaning from people's farms after harvesting would get maize and then we go to sell and i got 50 when i got 50 when i sat down to work on what i consider to be what i needed i said i wish it was 100 100 shillings was the highest you know denomination of our notes when we were growing up so then i got 100 i said i wish it was 200 then it got on going up you know until one day i was a millionaire but not you know kenyan money i went with pastor to rope to do some some call pota work down south and went to Botswana south africa and coming back we came to zambia and we had to exchange you know my friend you know our kenyan money i mean the dollars of course changing into zambian money you you got to carry a back that you you know we i think we had a note of almost a hundred thousands or something like that you know it's a it's you know it's a one note of about a hundred thousands and you know so i was a millionaire at some point of course when i was in zambia when i left zambia pastor to rope i left you there i don't know you know whether you also became a millionaire or a billionaire maybe yeah interestingly the more you get the more you wish you would get is that your experience also hello am i speaking to real people here has that been your experience too yeah then you know i said then of course i left i said no you know uh if i go to school and i i i i just finished primary i just managed to finish primary god i'll be so grateful i finished primary you're going on went to secondary after second i said man god i hear people go to college help me go to college once i get to college my life will be sorted out with my bachelor's there and i was still looking for another paper you know when went to went to school did my masters i was still looking for another paper went for my phd finished i was i'm still looking for actual i'm thinking of doing a second and third phd you know and and then the question you ask yourself then when does it become enough that is the question it's because everything else that is temporal will never satisfy fully your soul never satisfy fully your senses never you get it and you wonder what you are doing you see a beautiful dress and you you come sleep you go buy it and when you buy it you put on once and you wash it is on the line you look at it it's like i mean what what was it it is the beauty of this life god has set eternity in our hearts to help us live while subsisting on temporal things but our ultimate goal is focused on eternal things that balance is what we need to strike and so how do we do that god introduced men to a relationship in that garden of Eden he told adam adam you take care of this garden that does not belong to you take care of it take care of it turn it it doesn't belong to you it is mine but take care of it while you are taking care of it the choices and decisions that you are making those choices will under god they will define our my relationship with you they will that relationship and the choices you make will help you know who i am and who you are who you are is determined by the choices you make on how to balance between the temporal and the eternal things and who god is to you is equally determined by the choices you make when you're trying to balance between eternal and temporal things this particular thing that under gods or determines or defines our relationship in real in relation to god is what we call stewardship that we are learning this particular week man was to exercise his god-given powers to choose which way to go eternal way or temper away he chose temper away and by extension all of us choose temporal way adam was not stupid he was not foolish he just did it this particular relationship that helps us to know what is eternal what is temporal who am i and who god is is what stewardship is all about therefore i want to propose to you ladies and gentlemen that stewardship is a relationship subject it is not about your money it is a relationship subject it deals with who you are in relation to god and who god is in relation to you that is what stewardship is in a broad sense this subject of stewardship will facilitate the choices either for temporal or for eternal to live for things that are here today and tomorrow they are gone or to live for things that will be there forever and ever stewardship is a signboard that points either towards eternity or towards temporal because of eternity in our hearts we will never ever get satisfied with anything that our hands can lay on what satisfies is that which is eternal that we haven't seen with our eyes which we only exercise our faith to hold onto it that is what fills and satisfies our hearts he is not a fool therefore who gives out what he or she cannot keep in order to acquire that which you cannot lose because of eternity in our hearts few things we need to know one life is short it is not long i had a chance of going to view the body of our late president and i stood there and looked at this man the body is still being guarded by the great man the most powerful and the might man in this country the navy the air force and uh and i looked at the body and i was asking myself the difference between this body and me what is it and i came to a conclusion the conclusion was this the only difference between the body of a dead person and you who is alive is that there is that spirit of god that is still within you it has nothing to do with what you have it has nothing to do with what you do it has nothing to do with your position in society it has nothing to do with your agenda it is that spirit of god in you life is short it is in fact compared to a breath and suddenly life comes to an end suddenly or unexpectedly make the most out of this time especially in how you relate with the timber of things we should affect others in a very positive sense do that which once you have done you leave a mark behind let someone say yes there came a man or a woman who ever lived knowing that we are living in view of eternity should make us know that this life we live the choices we make on daily basis on how we relate with the timber of things around us determines how finally and where finally we will be eternally and finally the decisions have eternal consequences chalice lewis said this about those men and women living in view of eternity said we should always have heaven in our minds and he says it is because we should have heaven constantly in our mind so as to have an impact in this world in fact he says it is since christians have largely seized to think of the other world that they have become so ineffective in this world in other words those men living in view of eternity are so much full of heaven that they are so good to their neighbors they are so good to their environment because they are so heaven minded and when christianity suffers from the blow of forgetfulness of their eternity in their hearts then you will see them being so full of us so absolutely minded that finally they don't even get the earth and they don't get heaven these are the things that we are going to study the whole of this week day one tomorrow we'll be looking at the principle of ownership our real worth what is your worth day two the principle of management being all that god has called us to be on day three the principle of character development they will simply look at your stewardship is your theological statement about life on day four the principle of responsibility walking with a full cup how can you without spilling over day five principle of accountability and here we're talking about partnership with god or enmity with god day six principle of sacrifice where we say give according to your earning or you will earn according to your giving and on Sabbath we'll talk about the principle of reward where we talk about faithfulness until the end this will form the structure of our interactions and discussions this week may the lord bless us all there may be a question that i want to respond to before we wind up any question maybe online viewers although seated here any question there being no question i'll ask that we pray and then we usher in the choristers let's pray gracious father in heaven how can we thank you better for not letting us wallow in misery and disappear into the thin air how else can we thank you for putting eternity in our hearts that will constantly remind us that even as we feed on the temporal things there is something that our hearts are longing for that is so indescribable but that largely and ultimately satisfies us as we go home as we meditate on these things about eternity having it having been set in our hearts we pray that this week speak to us speak to us and and correct us oh god rebuke our evil ways bring us back into the way of righteousness leaders into into eternity when you will come to usher as home may our minds ever focus on the path that leads towards eternity never to forget never to be distracted to live today as if we are living tomorrow we thank you and we praise you in jesus' name amen we shall if you saw nita kuandama kote rainbow number miamoya talatini nanane let us all rise through this week we bless lord in a special way that we may understand that i will for us bless every one of us even those of us who have been watching online wherever they are bless us in a special way and encourage us that this week we may fellowship together for the good of our own being in this world to this end i pray and seek thy face in jesus' name we pray please be seated thank you pastor for blessing us with those special words and we have come to the end of our program this afternoon i'd like to remind you that tomorrow we are starting at four o'clock and for the rest of the week we start at five thirty may god bless you all as we dismiss now and i hope to see you tomorrow at this time at four o'clock sorry and for those who are for any reason unable to come it will be live so you can tune in online and still enjoy the blessings of the lord god bless you all and we can dismiss now thank you