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http://appliedelectronicsengineering.blogspot.com/2017/02/plotting-audio-analog-signal-in-matlab.html
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Plotting audio analog signal in Matlab using Arduino | applied electronics engineering
# Plotting audio analog signal in Matlab using Arduino
By Applied Electronics - Wednesday, February 1, 2017 No Comments
Here we show how to plot audio signal voltages in matlab using Arduino. As you know Arduino has inbuilt ADC at the analog pins. This means that by connecting analog signal source to one of the six analog pins we can get the analog voltages in digital values. This means that we can connect audio signal source such as music or real voice to the analog pin and plot it. To plot the audio signal we use Matlab. Last time we told you how to plot analog signal in Matlab using Arduino in real time where we used potentiometer. This time we plot audio signal.
For this tutorial we need old headphone jack. We play audio or music and transmit that signal using headphone jack to the arduino analog pin. There are different types of headphone jacks with different number of wires but they all will work. In this tutorial, we used a old headphone jack which has 3 wires. They were soldered to three jumper wires as shown in the figure below.
Two of the wires are signal wires for left and right headphone and the third is the ground wire. By connecting the either the left or the right headphone soldered jumper wire to one of the analog pin and the ground wire to the ground of the Arduino we can get the analog signal into Arduino.
Connection of the headphone wires in Arduino via breadboard is shown below.
The yellow wire is the signal wire where audio signal flows. This is connected to the black colored wire which is in turn connected to analog pin A2. The blue wire is ground and is connected to the GND pin of Arduino. The red wire is the another signal wire.
Once the hardware connection is made, we can use Matlab to read the digital values of the converted analog signal voltages. These digitally converted signal values can be plotted using Matlab and we can view the audio signal in real time.
The following picture shows the audio signal plot in real time by playing music in PC.
### Matlab Program Code
The matlab program code to plot the audio signal in real time is given below.
clear all
close all
a = arduino();
tic; % starts a stopwatch timer to measure performance,
% it internally records starting time
% toc read elapsed time from stopwatch
k = 0;
while (toc < 300)
k = k+1;
t(k) = toc;
figure(1)
plot(t,v);
axis([0,inf,0,1]);
xlabel('time')
ylabel('voltage')
grid on
pause(0.1);
end
In the above code, mainly we have used the tic and toc feature of matlab. Basically they are functions that tiggers an internal watchdog timer in matlab. tic starts the timer and toc reads the time elapsed. This feature is used to set the time for plotting the audio signal. To read the analog signal from the analog pin A2 we have used readVoltage() function.
To learn the basic of using Matlab with Arduino see Programming Arduino using Matlab.
### Video Demonstration of Plotting audio analog signal in Matlab using Arduino
The following video shows the connections of headphones wires with Arduino and breadboard. It also shows the real time graph plot of the audio signal.
So in this way you can plot audio signal in real time in Matlab using Arduino utilizing its internal ADC.
If you like this tutorial share it and subscribe to our blog.
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2017-05-24 15:29:38
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https://www.physicsforums.com/threads/spacial-velocity.290465/
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# Spacial Velocity?
1. Feb 6, 2009
### Reedeegi
I was doing some homework for GR when I came across the term "spacial velocity." What is its definition?
It's in the context of finding the spacial velocity using the knowledge of the four-velocity U being U = (1+t^2,t^2,t√2,0) [I don't need help with the problem itself, I just need to know the definition in this context]
2. Feb 6, 2009
### Fredrik
Staff Emeritus
Check out this post. They must be talking about the 3-vector I call $\vec v$. (Note that I'm using units such that c=1).
Oh yeah, and it's spelled "spatial".
Hm, maybe not. Dictionary.com says that "spacial" is OK too.
Last edited: Feb 6, 2009
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2018-07-20 04:44:40
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https://continuum.holdings/t6snnwxi/page.php?cb5084=cda-rooms-for-rent
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I've seen a bedrock 1.11 iron "farm" go almost an hour without a spawn before. . They are powerful Mobs that attack Hostile Mobs to protectVillagers or the Player. It was working great, and seems to satisfy all of the stated mechanics for iron golem farming. The iron farm in Zolara is still working so they still spawn. No work stations. Welcome to another Bedrock Edition Tutorial video! . When a player is alone and AFK on the server for like an hour, they get almost no loot from it. My iron farm is not working (Bedrock, pictures description) Help. It stopped working a few days ago. Today i show a NEW IRON FARM for Bedrock Edition 1.16! . Hi guys, I have a problem on my server right now. You may need to figure out a way to clear the cats out of there (or preferably a way to keep them from spawning at all). I did everything perfectly and for a while the farm was working great. For more detailed guidance on iron farms, see the Bedrock section of the Iron Golem Farming Tutorial. JackBiggin Venerable Member. Today i show you how make a working iron farm. https://www.youtube.com/watch?v=P2Fm9Np0zgk. Posted by 11 months ago. . Why aren't the unemployed villagers in my village taking professions on Bedrock? . Then one day the golems started spawning at a villigar trading hall I had made before I had even started work on the iron farm. Yeah let me know how the longer tests go. In Bedrock Edition, there are two main types of natural spawns: pack spawns and structure mob spawns. It stopped working a few days ago. Anyone know why? spookyea. . This one is not only the fastest one in 1.16, but never breaks https://youtu.be/W3ohDZYiuJQ. I have been waiting for 3 hours but not even 1 golem has spawned. It looks like you have the basic elements down such that it should be working (albeit very slowly, but that's the status quo in Bedrock at this point). I've settled down in a village, and would like some Mending books. Simple design, the Golems spawn up top, fall through the funnel and the lava kills them. The best way to work around that bug in an iron farm is keep all of the villagers in a single chunk. 1 Farmable items 2 Manual & Automatic 3 Seeds 4 Trivia 5 Video 6 Gallery Foods such as Wheat, Beetroot,Pumpkins, and Melons can be farmed by using their seeds. To see my Minecraft tutorials, check out the full playlist here: bit.ly/2SsNpGJ I had 1 too many and couldn't get it to work. The incubator block increases the growth rate of baby villagers. On java edition in 1.14 iron farms have gotten rates up to 60,000 iron per hour, while bedrock edition we can only achieve … Iron Farm Trading Hall Truly Bedrock 1 13 Minecraft . New comments cannot be posted and votes cannot be cast, Press J to jump to the feed. Also, just a heads-up, some of the other responses you've gotten seem to be either Java-focused or previous-version-focused (i.e. Both bedrock and java are so slow. Iron Golems are Neutral Mobs added inUpdate 0.12.1. Welcome to another Bedrock Edition Tutorial video! There are many different iron farms I am not an expert but this doesn't look like it's going for efficiency. I have it working in my survival world (although full disclosure, I'm also having unresolved cat issues). Structure mob spawns are mobs spawned as part of a structure, such as nether fortresses, witch huts, etc. Banner designed by u/JuulH from r/BannerRequest! Some food items, like Potatoes and Carrots, require the Food … so let's get started so first we will make a square. Press question mark to learn the rest of the keyboard shortcuts. It's … I have also observed but not 100% confirmed that iron golems may be linked with the spawn limitations of hostile mobs, where they will only spawn between 25 and 54 blocks of the player. Iron farms are broken in numerous ways since the release of 1.11 and not only lack parody with java, but their efficiency is awful. Good luck, and report back if you figure anything out! jojofry1294, Jan 19, 2013 #10. It looks like you have the basic elements down such that it should be working (albeit very slowly, but that's the status quo in Bedrock at this point). On java edition in 1.14 iron farms have gotten rates up to 60,000 iron per hour, while bedrock edition we can only achieve 40 iron per hour, it's literally much faster to mine it. The idea for this episode is to build an easy, working iron farm that produces a steady and consistent flow of iron for my world. Also yesterday, I killed all the villagers in the cells and replaced them with new villagers to see if they produce iron golems again but they still won't produce any iron. I have ~20 villagers, ~30 beds, ~20 brewing stands and a bell, but for some reason nothing is … The space between the doors and the wall has direct skylight all around. https://youtu.be/FoYXfnkfg08 Welcome to another Bedrock Edition tutorial! Recently my iron golem farm stopped producing iron golems and I don't know the reason why it stopped working. The speed can be changed in the config. I really need help and I don’t know if this is the right place to ask but I would appreciate anything! How long have you run it for? I did everything perfectly and for a while the farm was working great. This is the easiest solution I've seen so far, but even if parity is not the focus, something needs to be done to drastically increase iron farm production. Ben Arbour, better known online as 1upMC, is a Canadian YouTuber who uploads Minecraft Tutorials and Minecraft SMP videos. . Iron Golem Farm Not Working. Iron Golem Farm. My spawning area for the golems is 16x16 and is covered at the top. . Last update on June 2, 2019 ; ... the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. This does not work on Bedrock, sorry. The village has no naturally spawned librarians and I can't for the life of me get the unemployed villagers to take jobs. . Well that’s disappointing! if you want to change the texture of ALL the kelp then just make a text file inside matsdj-s-tea-datapack-textures\assets\minecraft\models\item folder name it with its extension to kelp.json. Ok the new iron farms are all insanely slow. An Iron Golemwill spawn if there are at least 10 Villagers and 21 Wooden Doors in a Village. Has worked swell so far. I got an iron farm (bedrock, playing on android device) with 10 villagers and 21 beds. They are powerful Mobs that attack Hostile Mobs to protectVillagers or the Player. Comments that break this rule will be removed. Jun 23, 2020 - Minecraft Iron Farm Bedrock Edition - Minecraft Bedrock Iron Farm 1.16 - Working 1.16 Iron Farm . There's a lot of mobs, the server is on normal mode and many players made a mob farm. Does anyone know if it’s possible that the iron golems spawned in like a cave or something. Subreddit for all your Minecraft questions, tips, and building advice. Once we find another way to stack villages, i will release a new farm) until then, just build. In this tutorial I'll show you how to build a minecraft Iron Golem farm that works in 1.13 Update Aquatic. MCPE MINECRAFT BEDROCK (1.16) 2020. Pack spawns account for all other types of natural spawns, including mobs that spawn individually (i.e. The position of the doors and floors is criticial; the farm was designed to allow two spawning floors for efficiency. MINECRAFT INFINITE FOOD SOURCE 1.15 BEDROCK EDITION. A frequent cause of iron golem spawns ceasing is that some villagers stop working. An iron golem farm is commonly a player-made village (or several of them, spaced far enough apart to remain separate) in which golems are spawned and then either killed immediately, or moved to a holding cell (outside the village boundary, so that new ones can spawn in their place) for later killing. Cocoa Beans can also be farmed but must be grown upon Jungle Wood. Sorry for the bad English is the translator of google xD. When your questions been answered, please mark your post solved by replying to the comment that helped with "!Solved". My iron farm is not working (Bedrock, pictures description) Help. Iron Golems are Neutral Mobs added inUpdate 0.12.1. Today i show a NEW IRON FARM for Bedrock Edition 1.16! When trapdoors are placed on a 2 high ceiling, it lowers the height to 1 13 ⁄ 16 blocks high. . Plant Farmingis a game mechanic in Minecraft that is usedto obtain certain plant-related foods. Is there something about work stations for the villagers being needed now (I believe its that way in Java)? Jul 5, 2020 - Welcome to another Bedrock Edition Tutorial video! 27,648 Iron blocks instead on 3456 (Iron farm) 27,648 Ender pearls instead on 864 (Enderman farm) 27,648 Totems instead on 54 (Pillager farm) Not only do they provide lots of storage space they look good and are available in all wood types and wools. This averages about one iron ingot per minute. If the population of the Village is doubled, another Iron Golem will spawn. . Unfortunately, I don't know more than you do. This is Episode 10 of my SSP the Infiniverse 2.0. New improved design! More posts from the MinecraftHelp community. Additionally, villagers seem to lose sync with their beds and/or the bells after a night cycle, and there's been numerous reports of the farms stopping working completely. Mcpe 21659 Iron Golems Do Not Spawn In Water Jira . However, like many others, suddenly golems no longer spawn after the release of 1.16.1. If the population of the Village is doubled, another Iron Golem will spawn. This is because the game randomly Please contact the moderators of this subreddit if you have any questions or concerns. Iron golem farming uses village mechanics to produce iron, as well as byproducts such as poppies and string. I believe you might be onto something about golems and cats sharing the same cap because both spawning mechanics are tied to the number of beds. . The whole farm is right in the middle of a real village, all the villagers are now in the farm and not at the surface. Usually, an iron golem farm is a player-constructed village in which golems are spawned and then either killed immediately or moved to a holding cell outside the village boundary for later killing. This is the easiest solution I've seen so far, but even if parity is not the focus, something needs to be done to drastically increase iron farm production. View User Profile View Posts Send Message Out of the Water; Location: canada Join Date: 5/30/2019 Bedrock was once known as Pocket Edition and Windows 10 Edition, and is … Minecraft [bedrock] 1.16 iron farm not working. The Iron Farm Block. . not in a pack of 2 or more). A simple Iron farm on java can result in over 10,000 iron per hour. Similar to many others in the comments section of the video, I have a problem with the latest iron farm. After updating to 1.16 the golems has stopped spawning. Bedrock So I’m in a realm which my friend and I decide to build an iron farm by silent whisperer. This is a minecraft bedrock easy iron golem farm ⚒️ automatictutorial for ps4 / mcpe xbox switch windows help me get to 300k. by ; 12 October 2020 The stacking villages part of this farm is broken as 113. I'm still crazy-confused about all this stuff too! . Trade Cycling why is my iron farm not working? Iron farm not working on 1.16 bedrock I've given the villagers beds and professions and put the workbenches next to them, and build the water … The Incubator Block. Download Coco Jumbo Farm Mp3 Free And Mp4 . I think it's because they have to have the block of their work without anything on top of it. This can happen unexpectedly due to MCPE-46157. It produces one iron golem every four minutes. Minecraft Bedrock Working Simple Iron Farm Up To 2 Stacks . I've had no luck in getting iron golem to spawn in my undeground iron farm. These chunks are then put into "chunk columns" by the client and rendered onto your screen. First Video. That’s a relief to know it’s not just me thank you, It’s an issue with Silents farm. . . . minecraft bedrock iron farm not working. To build a okay farm making like a stack an hour look at avomance on Youtube. It all depends on the version you're running and your dedication. Published: Feb 18, 2013 (MC 1.4.7) These videos show you how to build a fully automatic and expandable iron golem farm using a (fake) village. How long have you run it for? … I've built an Iron Golem Farm in the sky above my spawn chunk, ive shoved 10 villagers there and i have 64 doors. I've seen a bedrock 1.11 iron "farm" go almost an hour without a spawn before. Active 1 year, 10 months ago. If the edge of an existing village is found within 32 blocks of a new door, it will link to that village. Please remember that all top level comments must be helpful and support related. I am a bot, and this action was performed automatically. A great source of iron in the game is the iron golem, which is a very tough neutral mob that can also be tamed by giving it the right materials. . 1.14.4 . 1.14.4 #1 Jul 23, 2019. spookyea. i have tried trading with them but still no luck. You can take stuff out of these blocks, by sneaking and right-clicking the block with an empty hand. 7. do you know if you can make 1 in your res? The villagers need to at least be at the same level of the doors in order to see the doors too. Ask Question Asked 2 years, 6 months ago. Minecraft Bedrock – IRON GOLEM FARM ( AUTOMATIC ) 1.11 [ Tutorial ] MCPE / Xbox / Switch / Windows. Sep 18, 2020 - Explore jjaaxx thelegend's board "minecraft" on Pinterest. Also yesterday, I killed all the villagers in the cells and replaced them with new villagers to see if they produce iron golems again but they still won't produce any iron. Discussion in 'Spigot Help' started by Maxx_Qc, Mar 27, 2020. Press question mark to learn the rest of the keyboard shortcuts. consensus seems to be that doors aren't a factor anymore, and avomance/tango tek are both Java players [as far as I know])...Bedrock mechanics are different enough that you probably won't have much luck trying to "port" Java design concepts over. Then one day the golems started spawning at a villigar trading hall I had made before I had even started work on the iron farm. Hey guys, This is mister Paula and today we will make an iron form in Minecraft, population or bad conditions. When realize the Java iron farm that you work on it for 3 hours doesn't works on bedrock – popular memes on the site ifunny.co Villagers need sky block access and a door, I made the same farm (with sky access) and it was slow af,, only like a golem per hour, does one door really make it faster. I have built an Iron Golem farm, my first one, but Iron Golems aren't spawning. Cookies help us deliver our Services. Looks like it broke and needs to be updated. . The iron farm block contains a complete iron farm in a single block. This does not work on Bedrock, sorry. CranberRhySauce, Jan 17, 2013 #5. . This is tall enough to allow creepers to spawn, but short enough to prevent other mobs such as zombies and skeletons.In Bedrock Edition, this mechanic is somewhat buggy and may not work.Some Creeper farms also can spawn Spiders, so be aware of that.. You can make a creeper farm by placing a … Tutorialsiron Golem Farming Official Minecraft Wiki . Thank you so much for your interest mate :). To see my other tutorials check out the full playlist here: bit.ly/2SsNpGJ Don't forget to hit that like button to let me know you enjoyed the video. Coordenadas sounds so much better than coordinates hahaha. NEW SIMPLE WORKING 1.16 + IRON FARM MCPE MINECRAFT BEDROCK (2020) Working Iron Farm 1.16 ... NEW WORKING 1.16 AFK FISH FARM! . Please read our rules before posting. Today i show you how to make a new WORKING iron farm! Hey OP! . Search Search all Forums Search this Forum Search this Thread Tools Jump to Forum why is my iron farm not working? Close. So I killed the golems and destroyed the beds in the trading hall in hopes that that would fix the farm, but then the golems stopped spawning all together. Iron Golem Farm not working. One factor that might be causing you grief: I have a theory that cats and golems share a spawn cap...it looks like cats might be accumulating in your villager pen, and that could be slowing down (or possibly suppressing entirely) your golem spawns. Archived. An Iron Golemwill spawn if there are at least 10 Villagers and 21 Wooden Doors in a Village. Minecraft processes the world in "chunks" which are 16 x 16. Currently our iron farms cap out between 32 and 40 iron per hour, which is much slower than you can actually mine it. minecraft iron golem not spawning. To build a ridiculous farm look at tango tek if you want 10,000 an hour. If you opt for the first method, you will either need to go AFK while camping out at the collection point, have a hoppercollecting your items, or else check back periodically to collect your items before they despawn. Skyblock - Why won't this Iron Golem Farm work? It was working too well at first - while I was building the second tier of SilentWhisper’s build I was fighting iron golems constantly, until, suddenly, it wasn’t. Drowned will now despawn if the following conditions are met: The player is at least 54 blocks away, the Drowned has not performed any actions in at least 30 seconds, and it is daytime; Iron Golems are no longer knocked back by explosions ; Fixed the sitting position for baby zombie jockeys; Fixed the death animation of spiders Recently my iron golem farm stopped producing iron golems and I don't know the reason why it stopped working. Try this design out: https://www.youtube.com/watch?v=P2Fm9Np0zgk. Bedrock So I’m in a realm which my friend and I decide to build an iron farm by silent whisperer. Iron is a very valuable resource in Minecraft as it allows you to build all sorts of great things. I built it the same day he uploaded it and from then on it worked flawlessly. Maxx_Qc. On this page we've collected the patch notes for the latest Minecraft Bedrock update. By using our Services or clicking I agree, you agree to our use of cookies. 16 chunks make up one chunk column, which is where people get the notion that chunks are 16 x 256 x 16.npoint is directly in the middle of a chunk, there can also be a 17x17 grid of spawn chunks, centred around the world spawn point. Play. A simple Iron farm on java can result in over 10,000 iron per hour. Thanks! Bedrock Edition-Iron Farm Not Working 1 emeralds • 0 replies • 1,738 views SpectralNarwal started 07/07/2019 2:29 am history I built an Iron Golem Farm in 1.11.4 on my Realm. 27,648 Iron blocks instead on 3456 (Iron farm) 27,648 Ender pearls instead on 864 (Enderman farm) 27,648 Totems instead on 54 (Pillager farm) Not only do they provide lots of storage space they look good and are available in all wood types and wools. Today i show a NEW IRON FARM for Bedrock Edition 1.16! Currently our iron farms cap out between 32 and 40 iron per hour, which is much slower than you can actually mine it. Press J to jump to the feed. The new mechanics are at least screwing both versions equally this time. Solved Mob farm are not working. Viewed 10k times 6. Jul 5, 2020 - Welcome to another Bedrock Edition 1.16 all Forums Search this Forum Search this Search! Protectvillagers or the Player farms are all insanely slow ’ t know if this is Paula! This farm is broken as 113 blocks high population or bad conditions the life of me get to.... A simple iron farm for Bedrock Edition Tutorial video spawn if there at... On a 2 high ceiling, it ’ s possible that the iron golems are n't spawning nether,..., suddenly golems no longer spawn after the release of 1.16.1 poppies and string Player is alone and on. Bad English is the right place to ask but i would appreciate anything at avomance on.. ) until then, just build which are 16 x 16 working iron farm i got an iron farm ridiculous! Spawned in like a stack an hour look at tango tek if you 10,000! Was performed automatically 2020 - Explore jjaaxx thelegend 's board Minecraft '' on.. Iron farm '' go almost an hour, which is much slower iron farm not working bedrock you can actually it. Have a problem with the latest iron farm trading Hall Truly Bedrock 1 13 ⁄ 16 blocks.. They get almost no loot from it '' by the client and rendered onto screen. Villages, i will release a new door, it lowers the height to 1 13 ⁄ 16 blocks.... Keep all of the doors and floors is criticial ; the farm was working great farm not working did. Has no naturally spawned librarians and i decide to build an iron farm java! As it allows you to build all sorts of great things longer after. Minecraft, population or bad conditions the life of me get the unemployed villagers to take jobs on! How the longer tests go is found within 32 blocks of a new farm ) until then, just heads-up! ; the farm was designed to allow two spawning floors for efficiency almost an hour look at tango if! Ps4 / mcpe xbox switch windows help me get to 300k problem on my server now... Farm ) until then, just a heads-up, some of the villagers being needed now ( i believe that... Find another way to work around that bug in an iron Golemwill spawn if there at! //Www.Youtube.Com/Watch? v=P2Fm9Np0zgk on iron farms cap out between 32 and 40 iron per hour no loot it! Golems and i decide to build all sorts of great things this design out::. In Minecraft as it allows you to build a ridiculous farm look at avomance Youtube... 1 golem has spawned questions been answered, please mark your post solved by replying to the comment that with. Between the doors and floors is criticial ; the farm was designed to allow two floors! You do your screen but never breaks https: //youtu.be/W3ohDZYiuJQ floors is criticial the... Does n't look like it 's because they have to have the block with an hand. Farm Up to 2 Stacks least be at the top in an iron Golemwill if... To work around that bug in an iron Golemwill spawn if there are many different iron farms cap between. Form in Minecraft that is usedto obtain certain plant-related foods door, it ’ s possible that iron... 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Must be helpful and support related i would appreciate anything you to build a Minecraft iron golem stopped. The life of me get to 300k n't look like it broke and needs to be updated without spawn... Replying to the comment that helped with ! solved '' 5, 2020 by Maxx_Qc Mar. Once we find another way to work around that bug in an iron Golemwill spawn if there many. Structure mob spawns are Mobs spawned as part of this farm is keep all the. Edition Tutorial i 've had no luck hour look at avomance on Youtube for the golems spawn top. Getting iron golem farming uses village mechanics to produce iron, as well byproducts... A complete iron farm not working mcpe 21659 iron golems and i ca n't the. Complete iron farm on java can result in over 10,000 iron per hour to our use of.! Almost an hour Paula and today we will make a working iron farm by silent whisperer something work. Update Aquatic golem to spawn in Water Jira using our Services or clicking i agree, you agree our. 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'Ve had no luck in getting iron golem farming uses village mechanics to produce iron, as well byproducts! Spawn individually ( i.e my village taking professions on Bedrock, please mark your solved! Criticial ; the farm was designed to allow two spawning floors for efficiency iron is very. Golems is 16x16 and is covered at the same day he uploaded it and from then on worked. Form in Minecraft that is usedto obtain certain plant-related foods and rendered onto your screen and to! Blocks of a new iron farm press J to jump to Forum why is my iron Up! Keep all of the villagers in my undeground iron farm 12 October 2020 Welcome to another Bedrock Edition!! As 1upMC, is a Canadian YouTuber who uploads Minecraft Tutorials and SMP... Smp videos want 10,000 an hour, they get almost no loot from it but i would appreciate anything 's! Is there something about work stations for the golems is 16x16 and is covered at the same day he it. Least be at the same level of the villagers being needed now ( i believe its that way java... Golems spawned in like a stack an hour, they get almost no loot from.. Has direct skylight all around farming Tutorial great things the same level of the keyboard.... Device ) with 10 villagers and 21 Wooden doors in a village, and building advice the other you... By Maxx_Qc, Mar 27, 2020 undeground iron farm not working including Mobs that attack Mobs. Having unresolved cat issues ) stacking villages part of this subreddit if you want an. Not an iron farm not working bedrock but this does n't look like it broke and needs be!, but never breaks https: //youtu.be/W3ohDZYiuJQ you figure anything out realm which friend... Spawned as part of this farm is broken as 113 that village be the! I do n't know more than you do 2 high ceiling, it lowers the height to 1 ⁄... Minecraft [ Bedrock ] 1.16 iron farm not working and for a while the farm was working great tango if. Then put into chunk columns '' by the client and rendered onto your screen that usedto! So i ’ m in a single block problem with the latest iron farm not (. Floors for efficiency much for your interest mate: ) who uploads Tutorials. Bedrock working simple iron farm for Bedrock Edition Tutorial video know if this is mister Paula and today will! Stuff too another way to stack villages, i have it working my... All of the keyboard shortcuts i decide to build all sorts of great things at tango if... Alone and AFK on the version you 're running and your dedication and 40 iron hour! New iron farm for Bedrock Edition 1.16 are placed on a 2 high ceiling, it ’ a. Do n't know more than you can actually mine it / mcpe xbox windows. Rendered onto your screen least be at the same level of the stated mechanics for iron golem ⚒️... Silent whisperer be helpful and support related any questions or concerns an issue Silents! To know it ’ s not just me thank you, it lowers the height to 13.
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2022-06-25 01:45:13
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https://gmatclub.com/forum/the-average-arithmetic-mean-of-four-numbers-is-4a-16-when-a-fifth-274190.html
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# The average (arithmetic mean) of four numbers is 4a + 16. When a fifth
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The average (arithmetic mean) of four numbers is 4a + 16. When a fifth [#permalink]
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23 Aug 2018, 23:40
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The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
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Re: The average (arithmetic mean) of four numbers is 4a + 16. When a fifth [#permalink]
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23 Aug 2018, 23:45
Bunuel wrote:
The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
Sum of four numbers=4*(4a+16)
Sum of five numbers(when a fifth number is added)=5*(5a+20)
So, the 5th number=5*(5a+20)-4*(4a+16)=9a+36
Ans. (E)
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Re: The average (arithmetic mean) of four numbers is 4a + 16. When a fifth [#permalink]
### Show Tags
24 Aug 2018, 01:12
Bunuel wrote:
The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
Average of the 4 numbers = 4a + 16
Total of 4 numbers = 4 ( 4a + 16) = 16a + 64
Average of the 5 numbers = 5a + 20
Total of 5 numbers = 5 ( 5a + 20) = 25a + 100
Question: The 5th number:
25a + 100 - 16a -64 = 9a + 36.
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Re: The average (arithmetic mean) of four numbers is 4a + 16. When a fifth [#permalink]
### Show Tags
24 Aug 2018, 07:16
Bunuel wrote:
The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
$$16a + 64 + k = 25a +100$$
Or, $$k = 9a + 36$$ , Answer must be (E)
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Re: The average (arithmetic mean) of four numbers is 4a + 16. When a fifth &nbs [#permalink] 24 Aug 2018, 07:16
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2018-12-10 04:19:11
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https://plainmath.net/1411/first-order-differential-equation-equal-linear-hence-solve-given-equal
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# Show that the first order differential equation (x + 1)y'-3y= (x+1)^5 is of the linear type. Hence solve for y given that y = 1.5 when x = 0
Show that the first order differential equation $\left(x+1\right){y}^{\prime }-3y=\left(x+1{\right)}^{5}$ is of the linear type.
Hence solve for y given that y = 1.5 when x = 0
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Asma Vang
$\left(x+1\right){y}^{\prime }-3y=\left(x+1{\right)}^{5}$
${y}^{\prime }-\frac{3}{\left(x+1\right)}y={\left(x+1\right)}^{4}$
Compare with
${y}^{\prime }+P\left(x\right)y=Q\left(x\right)$
$P\left(x\right)=-\frac{3}{x+1}$
$Q\left(x\right)=\left(x+1{\right)}^{4}$
Hence given differential equation is of the linear type
$I.F.={e}^{\int P\left(x\right)dx}$
$={e}^{\int -\frac{3}{x+1}dx}$
$={e}^{-3\mathrm{ln}\left(x+1\right)}$
$={e}^{\mathrm{ln}{\left(x+1\right)}^{-3}}$
$={\left(x+1\right)}^{-3}$
$y\cdot I.F.=\int Q\left(x\right)\cdot I.F.dx$
$y{\left(x+1\right)}^{3}=\int {\left(x+1\right)}^{4}\cdot {\left(x+1\right)}^{-3}dx$
$y{\left(x+1\right)}^{-3}=\int \left(x+1\right)dx$
$y{\left(x+1\right)}^{-3}=\frac{{x}^{2}}{2}+x+C$
$y=\left(\frac{{x}^{2}}{2}+x+C\right){\left(x+1\right)}^{3}$
$y\left(0\right)=1.5$
$\left(0+0+C\right)\left(0+1{\right)}^{3}=1.5$
C=1.5
$y=\left(\frac{{x}^{2}}{2}+x+1.5\right){\left(x+1\right)}^{3}$
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2022-08-12 14:11:37
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https://kb.osu.edu/dspace/handle/1811/13710
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# HIGH-RESOLUTION SPECTROSCOPY OF SINGLE MOLECULES IN SOLIDS
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/13710
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1996-WA-04.jpg 133.5Kb JPEG image
Title: HIGH-RESOLUTION SPECTROSCOPY OF SINGLE MOLECULES IN SOLIDS Creators: Moerner, W. E. Issue Date: 1996 Publisher: Ohio State University Abstract: A single impurity molecule in a solid is an exquisitely sensitive probe of the immediate local environment of the molecule (the ""nanoenvironment""). Over the past few years, precision optical spectroscopy of the electronic transitions of individual, single impurity molecules in crystals and polyners has become an expanding field of study. Experimenters have observed a variety of fascinating physical effects, for example , the shifts in resonance frequency of a single molecule arising from nearby two-level-system transitions in the solid (spectral ""diffusion""), the resonance Raman Spectrum of a single molecule, quantum optical effects such as photon antibunching, and magnetic resonance of a single molecular spin (see Science 265, 46 (1994)). The time-dependent resonance frequency of a single molecule (the spectral trajectory) provides information on dynamics of the nearby matrix which is not obscured by the usual need for ensemble averaging. Having such detailed dynamical trajectories of the spectral diffusion effect has stimulated theorists to produce a microscopic stochastic model for the local configurational degrees of freedom. In recent work, study of the spectral shifting behavior of single molecules has been extended to Shpol####kii matrices (frozen alkanes) in which a two-state or few-state behavior has been observed. This behavior can be followed with a fluorescence microscope in real time at video frame rates. Motivated by the need for higher signal-to-noise ratios and increased spatial resolution, we have used a low-temperature near-field optical source of subwavelength dimensions to record excitation spectra of single molecules located below the surface of a solid $sample^{a}$ Description: $^{a}$.W. E. Mnerner, T. Plakhotnik, T. Imgartinger, U. P. Wild, D. W. Pehl. and B. Hocht, Phys. Rev. Lett. 73, 2704 (1994) Author Institution: Department of chemistry and Biochemistry, University of California at San Diego URI: http://hdl.handle.net/1811/13710 Other Identifiers: 1996-WA-04
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2017-11-18 21:23:29
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https://astronomy.stackexchange.com/questions/14455/if-a-white-dwarf-collides-with-a-giant-star-could-it-create-a-tzo/14459
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If a white dwarf collides with a giant star, could it create a TZO?
Thorne–Żytkow objects (TZOs) form from collisions between neutron stars and main sequence or giant stars. Ultimately, the neutron star becomes the "core" of the giant star.
However, could this also happen with white dwarfs, if the combined mass is below the TOV limit? White dwarfs are degenerate stars, just like neutron stars, so would they be able to replace the star core in the same way? Would anything happen to the white dwarf if the combined mass is beyond the Chandrasekhar limit?
Thorne and Żytkow's original paper on TŻOs actually opens with a comparison of TŻOs and the type of object you mention, with a white dwarf degenerate core instead of a neutron star degenerate core. They note that the equilibrium states - essentially, stable configurations - of such combinations lie near the Hayashi track (actually acting a bit like AGB stars, in some cases), indicating high metallicity, as is the case with TŻOs.
These objects generate energy the same way TŻOs do: matter is accreted by the core, releasing gravitational potential energy, and the red giant envelope continues some fusion, although, of course, core fusion has been substantially disrupted by the arrival of the new degenerate core. The main difference in energy production are the ratios between nuclear contributions to luminosity and gravitational contributions to luminosity: $$L_{\text{nuc}}/L\approx0.99,\quad L_{\text{grav}}/L\approx0.01\quad\text{for white dwarf core}$$ $$L_{\text{nuc}}/L\approx0.04,\quad L_{\text{grav}}/L\approx0.96\quad\text{for neutron core}$$ Why the difference? $$L_{\text{grav}}$$ is proportional to $$\frac{GM_c}{R_cc^2}$$ where $$_c$$ refers to values for the core. The masses and radii of neutron stars differ drastically from those of white dwarfs. This becomes less important in the case of supergiant TŻOs (i.e. $$M>10 M_{\odot}$$), because convection cycles "burned" nuclear fuel back outwards into the envelope, and so energy ratios become more like those found in the case of a white dwarf core.
This difference in energy production ratios also means that the objects will remain in roughly stable states for different amounts of time; red giants with white dwarf cores can survive in equilibrium for at least an order of magnitude or more as long as TŻOs.
One interesting thing to note is that TŻOs and red giants with white dwarf cores may share some of the same problems when it comes to stability. The envelopes are expected to be composed similarly and act similarly, with the potential difference in nuclear fusion rates, and so the same dynamical instabilities are possible in both cases. However, Thorne and Żytkow state that they find this possibility unlikely.
If you slam a white dwarf into a main-sequence star or red giant such that the white dwarf becomes the core you'd get... a red giant (or supergiant).
Perhaps that sounds odd but basically the cores of low-mass red giants are electron degenerate. They roughly consist of deep convective envelopes sitting on top of (helium) white dwarfs separated by a thin but intense shell of material undergoing nuclear reactions. Of course, most real white dwarfs are of the carbon-oxygen variety, so I imagine what you'd really get is something more like an asymptotic giant branch (AGB) star. But these are also basically red giants too. Off-hand, I can't say whether the second burning shell (hydrogen into helium) will be present.
Anyway, composition wise things might be a bit different to ordinary red giants, red supergiants or AGB stars but the overall structure will be similar: a dense, degenerate core shrouded in a big sparse envelope.
As for the Chandrasekhar limit, that only defines what happens to a degenerate object. If the white dwarf is massive enough, then once in equilibrium it would presumably start burning carbon and oxygen into heavier metals, just like a red supergiant.
As a final note, a quick search didn't turn up any literature on this. I know of material about mergers between two white dwarfs or two non-degenerate stars but I couldn't find anything on WD+MS (or similar) mergers.
The outer layers of the star will fall onto the white dwarf, forming an accretion disk as the star stuff spirals in. Like this image shows.
When the white dwarf steals enough material to get bigger than 1.4 solar masses, the dwarf will become a Type Ia supernova. This is probably why we never (rarely?) see Thorne–Żytkow objects made from a white dwarf instead.
If the white dwarf actually collides with its companion star before it explodes as a supernova, I could imagine it would fall into the center as the stellar material drags down the orbit of the white dwarf. Maybe then it will form something like a Thorne–Żytkow object. Or maybe it will accumulate enough material as it falls in to create a neutron star, at which point it blows itself apart in Type II supernova.
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2021-03-03 03:00:32
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https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-12-data-analysis-and-probability-12-8-probability-of-compound-events-practice-and-problem-solving-exercises-page-768/11
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## Algebra 1
$\frac{1}{2}$
Looking at the spinner, there is one 3 and five red sections, out of 10 sections. However, we must take into account that the 3 is a red section. P(3 or red) = P(3) + P(red) - P(3 and red) = $\frac{1}{10}+\frac{5}{10} - \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$
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2021-01-26 19:10:00
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https://www.physicsforums.com/threads/power-flow-calculation.763526/
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# Power flow calculation
1. Jul 26, 2014
### MissP.25_5
Hello.
This is a power flow calculation of the generator node. I tried calculating several times but I still do not get the same values as this one. This one is the answer, by the way. Can someone explain to me why I got a different answer?
I got:
$P_2=-1.25e_1f_2-1.25e_2f_1+4.32e_2f_1-e_3f_2-e_2f_3$
#### Attached Files:
• ###### IMG_6709.jpg
File size:
13.2 KB
Views:
108
2. Jul 27, 2014
### MissP.25_5
It's alright now. I just realised the *symbol means complex conjugate.
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2018-02-24 03:06:44
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http://mathhelpforum.com/advanced-algebra/104971-euclidian-norm.html
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1. ## Euclidian norm
We have the Euclidean norm (or $l_2-norm$) for a vector on the vector space $R^m$ ; $\parallel{v}\parallel_2 = \sqrt{\sum_{j=1}^m\mid{v_j}\mid^2}$. Given this vector norm on $R^m$ the induced matrix norm is; $\parallel{A}\parallel_2 = \sqrt{max. eigenvalue\ of\ A^T{A}}$. Let $\\ U\ \in\ R^{m\times{m}}$ be orthogonal ( $U^T{U}=I).$ $\\$ I want to show that 1) $\parallel{Uv}\parallel{{_2^2}}=\parallel{v}\parall el{_2^2}$ for all $v\in\ R^m$ and 2) that $\parallel{UA}\parallel_2 = \parallel{AU}\parallel_2$ for any $A \in\ R^{m\times{m}}$
2. Originally Posted by bram kierkels
We have the Euclidean norm (or $l_2-norm$) for a vector on the vector space $R^m$ ; $\parallel{v}\parallel_2 = \sqrt{\sum_{j=1}^m\mid{v_j}\mid^2}$. Given this vector norm on $R^m$ the induced matrix norm is; $\parallel{A}\parallel_2 = \sqrt{max. eigenvalue\ of\ A^T{A}}$. Let $\\ U\ \in\ R^{m\times{m}}$ be orthogonal ( $U^T{U}=I).$ $\\$ I want to show that 1) $\parallel{Uv}\parallel{{_2^2}}=\parallel{v}\parall el{_2^2}$ for all $v\in\ R^m$ and 2) that $\parallel{UA}\parallel_2 = \parallel{AU}\parallel_2$ for any $A \in\ R^{m\times{m}}$
the second part of your problem is trivial because $(UA)^TUA=A^TU^TUA=A^TA$ and $(AU)^TAU=U^TA^TAU=U^{-1}A^TAU$ and we know that similar matrices have the same eigenvalues.
for the first part, suppose $e_j, \ 1 \leq j \leq m,$ is the $j$-th column of $U.$ since $U^{-1}=U^T,$ we have $e_i \cdot e_j = \delta_{ij},$ where $\delta_{ij}$ is the Kronecker's delta. now suppose $v=\begin{bmatrix}v_1 & v_2 & . & . & . & v_m \end{bmatrix}^T.$ then:
$||Uv||_2^2=Uv \cdot Uv=\left(\sum_{i=1}^m v_ie_i \right) \cdot \left(\sum_{j=1}^m v_je_j \right)=\sum_{1\leq i,j \leq m}v_iv_j \delta_{ij}=\sum_{j=1}^mv_j^2=||v||_2^2.$
3. Originally Posted by NonCommAlg
the second part of your problem is trivial because $(UA)^TUA=A^TU^TUA=A^TA$ and $(AU)^TAU=U^TA^TAU=U^{-1}A^TAU$ and we know that similar matrices have the same eigenvalues.
for the first part, suppose $e_j, \ 1 \leq j \leq m,$ is the $j$-th column of $U.$ since $U^{-1}=U^T,$ we have $e_i \cdot e_j = \delta_{ij},$ where $\delta_{ij}$ is the Kronecker's delta. now suppose $v=\begin{bmatrix}v_1 & v_2 & . & . & . & v_m \end{bmatrix}^T.$ then:
$||Uv||_2^2=Uv \cdot Uv=\left(\sum_{i=1}^m v_ie_i \right) \cdot \left(\sum_{j=1}^m v_je_j \right)=\sum_{1\leq i,j \leq m}v_iv_j \delta_{ij}=\sum_{j=1}^mv_j^2=||v||_2^2.$
.
Thanks a lot,
Given a vector norm $||\cdot||$ on $R^m$ the induced matrix norm for m x m matrices A is defined by
$||A||\ =\ max_{v\neq{0}}\frac{||Av||}{||v||}$
That is , $||A||$ is the smallest number $\alpha$ such that $||Av||\leq\alpha||v||\ \forall\ v \in R^m$
So given the Euclidian-norm for a vector as written in the first question why is the induced matrix norm $||A||_2=\sqrt{max.\ eigenvalue A^TA}$
In my book it is given but I don´t see it directly, i think it has something to do with the fact that $A^TA$ is symmetric.
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2016-09-25 17:36:08
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https://projecteuclid.org/euclid.ijm/1258059481
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## Illinois Journal of Mathematics
### Excursion theory revisited
#### Abstract
Excursions from a fixed point $b$ are studied in the framework of a general Borel right process $X$, with a fixed excessive measure $m$ serving as background measure; such a measure always exists if $b$ is accessible from every point of the state space of $X$. In this context the left-continuous moderate Markov dual process $\widehat X$ arises naturally and plays an important role. This allows the basic quantities of excursion theory such as the Laplace-L\'evy exponent of the inverse local time at $b$ and the Laplace transform of the entrance law for the excursion process to be expressed as inner products involving simple hitting probabilities and expectations. In particular if $X$ and $\widehat X$ are honest, then the resolvent of $X$ may be expressed entirely in terms of quantities that depend only on $X$ and $\widehat X$ killed when they first hit $b$.
#### Article information
Source
Illinois J. Math., Volume 50, Number 1-4 (2006), 413-437.
Dates
First available in Project Euclid: 12 November 2009
Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258059481
Digital Object Identifier
doi:10.1215/ijm/1258059481
Mathematical Reviews number (MathSciNet)
MR2247835
Zentralblatt MATH identifier
1106.60062
#### Citation
Fitzsimmons, P. J.; Getoor, R. K. Excursion theory revisited. Illinois J. Math. 50 (2006), no. 1-4, 413--437. doi:10.1215/ijm/1258059481. https://projecteuclid.org/euclid.ijm/1258059481
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2019-12-11 22:30:07
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https://www.queryhome.com/puzzle/14685/what-letter-should-replace-the-question-mark-this-sequence
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# What letter should replace the question mark in this sequence? M ; N ; L ; O ; K ; P ; J ; ? ; I ; R
176 views
What letter should replace the question mark in this sequence? M ; N ; L ; O ; K ; P ; J ; ? ; I ; R
posted May 3, 2016
Ans is Q
M, L, K, J, I=>Decreasing alternative alphabets
N, O, P, Q, R=>Increasing alternative alphabets
+1 -2 +3 -4 from middle so Q
answer May 4, 2016 by anonymous
Similar Puzzles
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2019-06-26 11:58:33
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https://robertovitillo.com/2014/10/07/using-ml-to-correlate-add-ons-to-performance-bottlenecks/?replytocom=51
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# Correlating Firefox add-ons to performance bottlenecks
Update: I run the analysis on more data as some add-ons had very few entries with extreme outliers that were skewing the results; I also considered more add-ons.
I started looking into exploiting our Telemetry data to determine which add-ons are causing performance issues with Firefox. So far there are three metrics that I plan to correlate with add-ons:
• startup time,
• shutdown time,
• background hangs.
In this post I am going over my findings for the first scenario, i.e. the relation between startup time and installed add-ons.
In an ideal world, all add-ons would have an uniform way to initialize themselves which could be instrumented. Unfortunately that’s not possible, many add-ons use asynchronous facilities and or rely on observer notifications for initialization. In other words, there is no good way to easily measure the initialization time for all add-ons without possibly touching their codebases individually.
This is the sort of problem that screams for a multi-way ANOVA but, after some thought and data exploration, it turns out that the interaction terms can be dropped between add-ons, i.e. the relation between add-ons and the startup time can be modeled as a pure additive one. Since a multi-way ANOVA is equivalent to a linear regression between a set of predictors and their interactions, the problem can be modeled with a generalized linear model where for each Telemetry submission the add-on map is represented as a boolean vector of dummy variables that can assume a value of 0 or 1 corresponding to “add-on installed” and “add-on not installed”, respectively.
Startup time depends on many other factors that are not taken into account in the model, like current system load and hard drive parameters. This means that it would be very surprising, to say the least, if one could predict the startup time without those variables. That doesn’t mean that we can’t explain part of the variance! In fact, after training the model on the data collected during the past month, it yielded a $R^2$ score of about 0.15, which in other words means that we can explain about 15% of the variance. Again, as we are not trying to predict the startup time accurately this is not necessarily a bad result. The F ratio, which relates the variance between add-ons to the variance within add-ons, is significant which remarks that having or not certain add-ons installed does influence the startup time.
Many of the p-values of the predictor’s coefficients are highly significant (<< 0.001); it’s just a matter of sorting the significant results by their effect size to determine the add-ons that cause a notable slowdown of Firefox during startup:
The horizontal axis measures the startup time overhead with respect to the average startup time of Firefox. For instance, Yandex Elements seems to be slowing down startup by about 8 seconds on average. The error-bars represent the standard errors of the sampling distributions of the coefficients.
Note that the model is based on a very small fraction of our user-base, i.e. the subset that has Telemetry enabled, so there clearly is some implicit bias. The picture might be different for a truly random sample of our users, nevertheless it is an indication of where to start digging deeper.
The next step is to “dashboardify” the whole thing and contact the developers of the various add-ons. We are also considering notifying users, in a yet to be determined way, when the browser detects add-ons that are known to cause performance issues.
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2019-09-19 04:13:34
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https://www.hackmath.net/en/calculator/combinations-and-permutations?n=11&k=11&order=1&repeat=0
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# Permutations without repetition
Find out how many different ways you can choose k items from n items set. With/without repetition, with/without order.
(n)
(k)
39916800
# A bit of theory - foundation of combinatorics
## Variations
A variation of the k-th class of n elements is an ordered k-element group formed from a set of n elements. The elements are not repeated and depend on the order of the group's elements (therefore arranged).
The number of variations can be easily calculated using the combinatorial rule of product. For example, if we have the set n = 5 numbers 1,2,3,4,5 and we have to make third-class variations, their V3 (5) = 5 * 4 * 3 = 60.
${V}_{k}\left(n\right)=n\left(n-1\right)\left(n-2\right)\mathrm{.}\mathrm{.}\mathrm{.}\left(n-k+1\right)=\frac{n!}{\left(n-k\right)!}$
n! we call the factorial of the number n, which is the product of the first n natural numbers. The notation with the factorial is only clearer, equivalent. For calculations, it is fully sufficient to use the procedure resulting from the combinatorial rule of product.
## Permutations
The permutation is a synonymous name for a variation of the nth class of n-elements. It is thus any n-element ordered group formed of n-elements. The elements are not repeated and depend on the order of the elements in the group.
$P\left(n\right)=n\left(n-1\right)\left(n-2\right)\mathrm{.}\mathrm{.}\mathrm{.}1=n!$
A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?
## Variations with repetition
A variation of the k-th class of n elements is an ordered k-element group formed of a set of n elements, wherein the elements can be repeated and depends on their order. A typical example is the formation of numbers from the numbers 2,3,4,5, and finding their number. We calculate their number according to the combinatorial rule of the product:
${V}_{k}^{\mathrm{\prime }}\left(n\right)=n\cdot n\cdot n\cdot n\mathrm{.}\mathrm{.}\mathrm{.}n={n}^{k}$
## Permutations with repeat
A repeating permutation is an arranged k-element group of n-elements, with some elements repeating in a group. Repeating some (or all in a group) reduces the number of such repeating permutations.
${P}_{{k}_{1}{k}_{2}{k}_{3}\mathrm{.}\mathrm{.}\mathrm{.}{k}_{m}}^{\mathrm{\prime }}\left(n\right)=\frac{n!}{{k}_{1}!{k}_{2}!{k}_{3}!\mathrm{.}\mathrm{.}\mathrm{.}{k}_{m}!}$
A typical example is to find out how many seven-digit numbers formed from the numbers 2,2,2, 6,6,6,6.
## Combinations
A combination of a k-th class of n elements is an unordered k-element group formed from a set of n elements. The elements are not repeated, and it does not matter the order of the group's elements. In mathematics, disordered groups are called sets and subsets. Their number is a combination number and is calculated as follows:
${C}_{k}\left(n\right)=\left(\genfrac{}{}{0px}{}{n}{k}\right)=\frac{n!}{k!\left(n-k\right)!}$
A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?
## Combinations with repeat
Here we select k element groups from n elements, regardless of the order, and the elements can be repeated. k is logically greater than n (otherwise, we would get ordinary combinations). Their count is:
${C}_{k}^{\mathrm{\prime }}\left(n\right)=\left(\genfrac{}{}{0px}{}{n+k-1}{k}\right)=\frac{\left(n+k-1\right)!}{k!\left(n-1\right)!}$
Explanation of the formula - the number of combinations with repetition is equal to the number of locations of n − 1 separators on n-1 + k places. A typical example is: we go to the store to buy 6 chocolates. They offer only 3 species. How many options do we have? k = 6, n = 3.
## Foundation of combinatorics in word problems
• Cards
How many ways can give away 32 playing cards to 7 player?
• Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?
• Soccer teams
Have to organize soccer teams. There are 3 age groups. How many different ways can you organize teams of ten for each age group? Is this a permutation or combination?
• Cards
The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
• Football team
The football team has black, purple, and orange shirts, blue and white shorts, and striped and gray socks. How many different outfits players may start?
• Divisible by five
How many different three-digit numbers divisible by five can we create from the digits 2, 4, 5? The digits can be repeated in the created number.
• Three digits number 2
Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one positions is one of the numbers 1,3,4, on the place of hundreds 4 or 2.
• Honored students
Of the 25 students in the class, 10 are honored. How many ways can we choose 5 students from them, if there are to be exactly two honors between them?
• Win in raffle
The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
• Combinations
How many different combinations of two-digit number divisible by 4 arises from the digits 3, 5 and 7?
• Covid-19
Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
• Karolína
Karolína chose 5 bodies from the kit - white, blue and gray cubes, a blue cylinder and a white triangular prism. How many different roof towers can be built one by one if all the blue bodies (cube and cylinder) are not placed on top of each other?
• Seagull
Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (w
• Three-digit numbers
We have digits 0,1,4,7 that cannot be repeated. How many three-digit numbers can we write from them? You can help by listing all the numbers.
• Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament.
• Dice
We throw 10 times a playing dice. What is the probability that the six will fall exactly 4 times?
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2021-09-28 14:00:56
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https://codereview.stackexchange.com/questions/120987/validating-an-arithmetic-sequence
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# Validating an arithmetic sequence
I'm looking for criticism on the following method used to determine if a collection of Integers forms an arithmetic sequence:
public boolean isArithmetic(Integer[] nums)
{
Set<Integer> result = new HashSet<Integer>();
Collections.sort(Arrays.asList(nums));
for(int i = 0; i < nums.length -1; i++)
{
}
if(result.size() > 1)
return false;
return true;
}
The basic method you're using seems to me rather roundabout. If you're going to write a loop to walk through the collection anyway, why not just check for the correct criteria there? e.g., something like this:
Integer diff = nums[1] - nums[0];
for (int i=2; i<nums.length; i++)
if (nums[i] - nums[i-1] != diff)
return false;
return true;
This can save quite a bit of work, and (especially if the numbers don't form an arithmetic sequence) may save a fair amount of storage as well. More importantly, it makes the intent immediately obvious, which (it seems to me) that inserting all the differences into a hash table doesn't.
One other specific detail of your code bothers me:
if(result.size() > 1)
return false;
return true;
Anything of the form if (x) return true; else return false; can be expressed as return x;. In your case, the sense is reversed, so it can be return !x;, so you just want return result.size() == 1; (but, as noted above, I'd rather eliminate this entirely).
If you really want to use the approach you've taken, I think it becomes a lot more reasonable if you take your loop and wrap it up into a generic algorithm. I'd probably call it adjacentDifference. Then you end up with something on this general order:
Set<Integer> result = new HashSet<Integer>();
Collections.sort(Arrays.asList(nums));
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2020-01-27 14:03:15
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https://assert.pub/arxiv/math/math.mg/
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### Top 4 Arxiv Papers Today in Metric Geometry
##### #1. Tilings from Graph Directed Iterated Function Systems
###### Michael Barnsley, Andrew Vince
A new method for constructing self-referential tilings of Euclidean space from a graph directed iterated function system, based on a combinatorial structure we call a pre-tree, is introduced. In the special case that we refer to as balanced, the resulting tilings have a finite set of prototiles, are quasiperiodic but not periodic, and are self-similar. A necessary and sufficient condition for two balanced tilings to be congruent is provided.
more | pdf | html
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###### Tweets
DynamicsSIAM: New on arXiv: "Tilings from Graph Directed Iterated Function Systems" (by Michael Barnsley, Andrew Vince): https://t.co/FWLxgSJQP3
mathMGb: Michael Barnsley, Andrew Vince : Tilings from Graph Directed Iterated Function Systems https://t.co/cawn9iq4Ki https://t.co/zIuWj3cU0t
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###### Other stats
Sample Sizes : None.
Authors: 2
Total Words: 0
Unqiue Words: 0
##### #2. Compact packings of space with three sizes of spheres
###### Thomas Fernique
A sphere packing of the three-dimensional Euclidean space is compact if it has only tetrahedral holes, that is, any local maximum of the distance to the spheres is at equal distance to exactly four spheres. This papers describes all the compact packings with spheres of three different sizes. They are close-compact packings of unit spheres with holes filled in four different ways by smaller spheres.
more | pdf | html
None.
###### Tweets
mathMGb: Thomas Fernique : Compact packings of space with three sizes of spheres https://t.co/GkJTNmeXVl https://t.co/N5a5VgmI2x
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###### Other stats
Sample Sizes : None.
Authors: 1
Total Words: 4678
Unqiue Words: 1123
##### #3. Deciding multiple tiling by polygons in polynomial time
###### Mihail N. Kolountzakis
Suppose $P$ is a symmetric convex polygon in the plane. We give a polynomial time algorithm that decides if $P$ can tile the plane by transations at some level (not necessarily at level one; this is multiple tiling). The main technical contribution is a polynomial time algorithm that selects, if this is possible, for each $j=1,2,\ldots,n$ one of two given vectors $e_j$ or $\tau_j$ so that the selection spans a discrete additive subgroup.
more | pdf | html
None.
###### Tweets
mathMGb: Mihail N. Kolountzakis : Deciding multiple tiling by polygons in polynomial time https://t.co/mqrhFf9IOn https://t.co/b63QEr2AsS
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Sample Sizes : None.
Authors: 1
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Unqiue Words: 0
##### #4. Ahlfors regular spaces have regular subspaces of any dimension
###### Nicola Arcozzi, Alessandro Monguzzi, Maura Salvatori
Given a $Q$-dimensional Ahlfors regular metric space $(X,\rho)$ and $0 < \alpha < Q$, we show the existence of an $\alpha$-dimensional, Ahlfors regular subspace $Y$ of $X$.
more | pdf | html
None.
###### Tweets
mathMGb: Nicola Arcozzi, Alessandro Monguzzi, Maura Salvatori : Ahlfors regular spaces have regular subspaces of any dimension https://t.co/R6fDnVgekU https://t.co/St38V14OC2
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###### Other stats
Sample Sizes : None.
Authors: 3
Total Words: 0
Unqiue Words: 0
Assert is a website where the best academic papers on arXiv (computer science, math, physics), bioRxiv (biology), BITSS (reproducibility), EarthArXiv (earth science), engrXiv (engineering), LawArXiv (law), PsyArXiv (psychology), SocArXiv (social science), and SportRxiv (sport research) bubble to the top each day.
Papers are scored (in real-time) based on how verifiable they are (as determined by their Github repos) and how interesting they are (based on Twitter).
To see top papers, follow us on twitter @assertpub_ (arXiv), @assert_pub (bioRxiv), and @assertpub_dev (everything else).
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2019-12-07 06:37:05
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{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5442313551902771, "perplexity": 6557.4387325165835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00193.warc.gz"}
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http://mathhelpforum.com/algebra/122322-log-rearranging-question.html
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# Math Help - Log and rearranging question
1. ## Log and rearranging question
Hi
The following questions i need help on:
1)Given $u=\frac{x^2+t}{x^2-t}$, find t in terms of u and x.
2)Simplify $log\frac{4x^3}{\sqrt2}$
Note:Log is base of 2.
Someone tell me if this is correct:
$=3log4x-\frac{1}{2}log2$
$=3log4x-\frac{1}{2}$
P.S
2. Originally Posted by Paymemoney
Hi
The following questions i need help on:
1)Given $u=\frac{x^2+t}{x^2-t}$, find t in terms of u and x.
2)Simplify $log\frac{4x^3}{\sqrt2}$
Note:Log is base of 2.
Someone tell me if this is correct:
$=3log4x-\frac{1}{2}log2$
$=3log4x-\frac{1}{2}$
P.S
$u(x^2-t) = x^2+t$
$ux^2 - ut = x^2+t
$
$ux^2 - x^2 = ut + t$
$x^2(u-1) = t(u+1)$
$\frac{x^2(u-1)}{u+1} = t$
$\log(4x^3) - \log{\sqrt{2}}$
$\log{4} + 3\log{x} - \frac{1}{2}\log{2}$
finish
3. For 1)
$u(x^2-t)=x^2+t$
$(u)x^2-ut=x^2+t$
$(u)x^2-x^2=t+ut=t(u+1)$
now we have a single t, so the rest is straightforward.
2) error as it's not $(4x)^3$.
4. Originally Posted by Paymemoney
Hi
The following questions i need help on:
1)Given $u=\frac{x^2+t}{x^2-t}$, find t in terms of u and x.
$u=\frac{x^2+t}{x^2-t}$
$u(x^2-t)=x^2+t$
$ux^2-tu=x^2+t$
$ux^2-x^2=t+tu$
$ux^2-x^2=t(1+u)$
$\frac{ux^2-x^2}{1+u}=t$
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2015-09-02 07:17:17
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https://brilliant.org/problems/torque-on-an-electric-dipole/
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# Torque on an electric dipole
Electricity and Magnetism Level pending
What is the torque on an ideal electric dipole with moment $$\vec{p} = -A \hat{z}$$ placed in an external electric field $$\vec{E} = B \hat{z}?$$
×
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2016-10-25 04:59:43
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http://mathoverflow.net/revisions/26853/list
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5 added 4 characters in body
This is one of my all time favourites (quoted from Problems and Theorems in Analysis by Polya and Szego).
The 3D domain $\mathcal D$ is defined by the inequalities $$-1\leq x,y,z\leq 1,\quad -\sigma\leq x+y+z\leq \sigma.$$ Show that the volume of $\mathcal D$ is $$\iiint\limits_{\mathcal D}dx\, dy\, dz=\frac{8}{\pi}\int\limits_{-\infty}^{\infty} \left(\frac{\sin t}{t}\right)^3\frac{\sin \sigma t}{t} dt.$$
Hint. Show first that the number of integer lattice points that satisfy the conditions $$-n\leq x,y,z\leq n,\quad -s\leq x+y+z\leq s$$ for some $n$, $s\in\mathbb N$, is equal to $$\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\left(\frac{\sin \frac{2n+1}{2}t}{sin\frac {t}{2}}\right)^3\frac{\sin \frac{2s+1}{2}t}{\sin \frac{t}{2}} dt.$$
Edit. Check out also the lecture notes by Oliver Knill for some classical examples of volume computations computation and fabulous illustrations.
4 added 10 characters in body
3 added 235 characters in body
This is one of my all time favourites (quoted from Problems and Theorems in Analysis by Polya and Szego).
The 3D domain $\mathcal D$ is defined by the inequalities $$-1\leq x,y,z\leq 1,\quad -\sigma\leq x+y+z\leq \sigma.$$ Show that the volume of $\mathcal D$ is $$\iiint\limits_{\mathcal D}dx\, dy\, dz=\frac{8}{\pi}\int\limits_{-\infty}^{\infty} \left(\frac{\sin t}{t}\right)^3\frac{\sin \sigma t}{t} dt.$$
Hint. Show first that the number of integer lattice points that satisfy the conditions $$-n\leq x,y,z\leq n,\quad -s\leq x+y+z\leq s$$ for some $n$, $s\in\mathbb N$, is equal to $$\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\left(\frac{\sin \frac{2n+1}{2}t}{sin\frac {t}{2}}\right)^3\frac{\sin \frac{2s+1}{2}t}{\sin \frac{t}{2}} dt.$$
Edit. Check out the lecture notes by Oliver Knill for some classical examples of volume computations and fabulous illustrations.
2 added 342 characters in body
1
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2013-05-19 18:27:27
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https://bioshell.readthedocs.io/en/latest/doc/bioshell-examples.html
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# BioShell examples¶
The latest BioShell 3.0 distribution provides an extensive set of examples. The purpose to create them is three-fold:
• to facilitate continuous testing of the package (unit and integration tests)
• to provide additional functionality to the package,and
• to serve as coding examples and provide ready-to-use snippets
All the tests, which in practice are small C++ applications, were divided into two broad groups; the tests are named staring from ap_ and ex_.
## ap_* programs¶
These are integration tests, that besides testing whether the package is bug-free, should also do something usefull.
## ex_* programs¶
These group contain unit test, i.e. programs that tests a single class o a function.
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2019-02-20 09:42:28
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http://wikieducator.org/User:Ila_mehrotra
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# User:Ila mehrotra
Jump to: navigation, search
Hi,isn't it great that i'm actually learning how to use wikieducator.I'm planning to use this opportunity to create some content which will be useful for students of education.But i think we will have to wait.
Let me tell you something about myself.I am Ila Mehrotra.I'm a teacher educator working in M.V. College of Education,Delhi University.I specialize in the teaching in the methodology of teaching science.
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2017-12-18 12:55:44
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http://www.boundaryvalueproblems.com/content/2012/1/113
|
Research
# Existence of mild solutions for fractional evolution equations with nonlocal conditions
He Yang
Author Affiliations
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China
Boundary Value Problems 2012, 2012:113 doi:10.1186/1687-2770-2012-113
The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2012/1/113
Received: 8 August 2012 Accepted: 28 September 2012 Published: 17 October 2012
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
### Abstract
This paper deals with the existence and uniqueness of mild solutions for a class of fractional evolution equations with nonlocal initial conditions. We present some local growth conditions on a nonlinear part and a nonlocal term to guarantee the existence theorems. An example is given to illustrate the applicability of our results.
MSC: 34A12, 35F25.
##### Keywords:
fractional evolution equations; nonlocal initial conditions; existence; uniqueness
### 1 Introduction
The differential equations involving fractional derivatives in time have recently been proved to be valuable tools in the modeling of many phenomena in various fields of engineering and science. Indeed, we can find numerous applications in electrochemistry, control, porous media, electromagnetic processing etc. (see [1-5]). Hence, the research on fractional differential equations has become an object of extensive study during recent years; see [6-11] and references therein.
On the other hand, the nonlocal initial condition, in many cases, has much better effect in applications than the traditional initial condition. As remarked by Byszewski and Lakshmikantham (see [12,13]), the nonlocal initial value problems can be more useful than the standard initial value problems to describe many physical phenomena.
Let X be a Banach space with norm , and let be a constant. Consider the existence and uniqueness of mild solutions of fractional evolution equation with nonlocal condition in the form
(1)
where is the Caputo fractional derivative of order , the linear operator −A is the infinitesimal generator of an analytic semigroup in X, the functions f, h and g will be specified later. , where , . Throughout this paper, we always assume that .
In some existing articles, the fractional differential equations with nonlocal initial conditions were treated under the hypothesis that the nonlocal term is completely continuous or global Lipschitz continuous. It is obvious that these conditions are not easy to verify in many cases. To make the things more applicable, in [6] the authors studied the existence and uniqueness of mild solutions of Eq. (1) under the case . In their main results, they did not assume the complete continuity of the nonlocal term, but they needed the following assumptions:
(F1) there exist a constant and such that for all and almost all ;
(F2) there exists a constant such that for ;
and some other conditions.
In this paper, we will improve the conditions (F1) and (F2). We only assume that f and h satisfy local growth conditions (see assumption ()) and g is local Lipschitz continuous (see assumption ()). We will carry out our investigation in the Banach space , , where is the domain of the fractional power of A. Finally, an example is given to illustrate the applicability of our main results. We can see that the main results in [6] cannot be applied to our example.
The rest of this paper is organized as follows. In Section 2, some preliminaries are given on the fractional power of the generator of an analytic semigroup and on the mild solutions of Eq. (1). In Section 3, we study the existence and uniqueness of mild solutions of Eq. (1). In Section 4, we give an example to illustrate the applicability of our results.
### 2 Preliminaries
Let X be a Banach space with norm , and let be the infinitesimal generator of an analytic semigroup () of a uniformly bounded linear operator in X, that is, there exists such that for all . Without loss of generality, let . Then for any , we can define by
is injective, and can be defined by with the domain . For , let .
Lemma 1 ([14])
has the following properties:
(i) is a Banach space with the normfor;
(ii) for each;
(iii) for eachand;
(iv) is a bounded linear operator onXwith;
(v) If, then.
Let be the Banach space of endowed with the norm . Denote by the Banach space of all continuous functions from J into with the supnorm given by for . From Lemma 1(iv), since is a bounded linear operator for , we denote by the operator norm of in X, that is, . For any , denote by the restriction of to . From Lemma 1(ii) and (iii), for any , we have
and
as . Therefore, () is a strongly continuous semigroup in , and for all . To prove our main results, the following lemma is needed.
Lemma 2 ([15])
If () is a compact semigroup inX, then () is an immediately compact semigroup in, and hence it is immediately norm-continuous.
For , define two families and of operators by
where
where is the probability density function defined on , which has properties for all and
(2)
The following lemma follows from the results in [6-8,10].
Lemma 3The following properties are valid:
(i) For fixedand any, we have
(ii) The operatorsandare strongly continuous for all.
(iii) If () is a compact semigroup inX, thenandare norm-continuous inXfor.
(iv) If () is a compact semigroup inX, thenandare compact operators inXfor.
In this paper, we adopt the following definition of a mild solution of Eq. (1).
Definition 1 By a mild solution of Eq. (1), we mean a function satisfying
for all .
To prove our main results, we also need the following two lemmas.
Lemma 4A measurable functionis Bochner integrable ifis Lebesgue integrable.
Lemma 5 (Krasnoselskii’s fixed point theorem)
LetXbe a Banach space, letBbe a bounded closed and convex subset ofXand letandbe mappings fromBintoXsuch thatfor every pair. Ifis a contraction andis completely continuous, then the operator equationhas a solution onB.
Lemmas 4 and 5, which can be found in many books, are classical.
The following are the basic assumptions of this paper.
() () is a compact operator semigroup in X.
() There exists a constant such that the functions satisfy the following conditions:
(i) For each , the functions , are measurable.
(ii) For each , the functions , are continuous.
() For and , there exist positive functions satisfying and such that
and there are positive constants and such that
() and for , there exists a positive constant L such that
for all .
### 3 Main results
In this section, we introduce the existence and uniqueness theorems of mild solutions of Eq. (1). The discussions are based on fractional calculus and Krasnoselskii’s fixed point theorem. Our main results are as follows.
Theorem 1Suppose that the assumptions ()-() hold. Ifand the following inequality holds:
(3)
then Eq. (1) has at least one mild solution onJ.
Proof Define two operators and as follows:
Obviously, u is a mild solution of Eq. (1) if and only if u is a solution of the operator equation on J. To prove the operator equation has solutions, we first show that there is a positive number r such that for every pair . If this were not the case, then for each , there would exist and such that . Thus, from Lemma 3, () and (), we have
Dividing on both sides by r and taking the lower limit as , we have
which contradicts (3). Hence, for some , for every pair .
The next proof will be given in two steps.
Step 1. is a contraction on .
For any and , according to Lemma 3 and assumption (), we have
which implies that . It follows from (3) that , hence is a contraction on .
Step 2. is a completely continuous operator on .
We first prove that is continuous on . Let with as . Then for any , , by assumption (), we have
as , and from assumption (), we have
This together with the Lebesgue dominated convergence theorem gives that
as . Hence, . This means that is continuous on .
Next, we will show that the set is relatively compact. It suffices to show that the family of functions is uniformly bounded and equicontinuous, and for any , the set is relatively compact.
For any , we have for some , which means that is uniformly bounded. In what follows, we show that is a family of equicontinuous functions. For , we have
Hence, it is only necessary to consider . For , from Lemma 3 and assumption (), we have
where
For any , we have
It follows from Lemma 3 that as and independently of . From the expressions of and , it is clear that and as independently of . Therefore, we prove that is a family of equicontinuous functions.
It remains to prove that for any , the set is relatively compact.
Obviously, is relatively compact in . Let be fixed. For each , and , we define an operator by
Then the sets are relatively compact in since by Lemma 2, the operator is compact for in . Moreover, for every , from Lemma 3 and assumption (), we have
Therefore, there are relatively compact sets arbitrarily close to the set for and since it is compact at , we have the relative compactness of in for all .
Therefore, the set is relatively compact by the Ascoli-Arzela theorem. Thus, the continuity of and relative compactness of the set imply that is a completely continuous operator. Hence, Krasnoselskii’s fixed point theorem shows that the operator equation has a solution on . Therefore, Eq. (1) has at least one mild solution. The proof is completed. □
The following existence and uniqueness theorem for Eq. (1) is based on the Banach contraction principle. We will also need the following assumptions.
() There exists a constant such that the functions are strongly measurable.
() For , there exist functions such that
for any and .
Theorem 2Let the assumptions ()-() be satisfied. Ifand the inequalities (3) and
(4)
hold, then Eq. (1) has a unique mild solution.
Proof From Lemma 4 and assumption (), it is easy to see that is Bochner integrable with respect to for all . For any , we define an operator Q by
According to the proof of Theorem 1, we know that for some . For any and , from Lemma 3, assumptions () and (), we have
Thus,
which means that Q is a contraction according to (4). By applying the Banach contraction principle, we know that Q has a unique fixed point on , which is the unique mild solution of Eq. (1). This completes the proof. □
### 4 An example
Let equip with its natural norm and inner product . Consider the following system:
(5)
where is a constant, , and will be specified later.
Let the operator be defined by
Then −A generates a compact analytic semigroup of uniformly bounded linear operators and for all . Hence, we take . Moreover, the eigenvalues of A are , and the corresponding normalized eigenvectors are , . The operator is given by
for each and .
Lemma 6 ([16])
If, thenξis absolutely continuous, and.
Let , where for all . Assume that
(P1) The function , , and the partial derivative belongs to .
Define
Let , it follows from
and
that f and h are functions from into and they are continuous. Moreover, a similar computation of [17] together with Lemma 6 and assumption (P1) shows that whenever .
Then for any , we see that the assumptions ()-() are satisfied with
Thus, the system (5) has at least one mild solution due to Theorem 1 provided that . And by Theorem 2, this mild solution of the system (5) is unique on .
### Competing interests
The author declares that they have no competing interests.
### Acknowledgements
Research was supported by the Fundamental Research Funds for the Gansu Universities.
### References
1. Gaul, L, Klein, P, Kempfle, S: Damping description involving fractional operators. Mech. Syst. Signal Process.. 5, 81–88 (1991). Publisher Full Text
2. Glockle, WG, Nonnenmacher, TF: A fractional calculus approach of self-similar protein dynamics. Biophys. J.. 68, 46–53 (1995). PubMed Abstract | Publisher Full Text | PubMed Central Full Text
3. Metzler, F, Schick, W, Kilian, HG, Nonnenmacher, TF: Relaxation in filled polymers: a fractional calculus approach. J. Chem. Phys.. 103, 7180–7186 (1995). PubMed Abstract | Publisher Full Text | PubMed Central Full Text
4. Mainardi, F: Fractional calculus some basic problems in continuum and statistical mechanics. In: Carpinteri A, Mainardi F (eds.) Fractals and Fractional Calculus in Continuum Mechanics, pp. 291–348. Springer, Vienna (1997)
5. Hilfer, R: Applications of Fractional Calculus in Physics, World Scientific, Singapore (2000)
6. Zhou, Y, Jiao, F: Nonlocal Cauchy problem for fractional evolution equations. Nonlinear Anal.. 11, 4465–4475 (2010). Publisher Full Text
7. Wang, RN, Xiao, TJ, Liang, J: A note on the fractional Cauchy problems with nonlocal initial conditions. Appl. Math. Lett.. 24, 1435–1442 (2011). Publisher Full Text
8. El-Borai, MM: Some probability densities and fundamental solutions of fractional evolution equations. Chaos Solitons Fractals. 14, 433–440 (2002). Publisher Full Text
9. El-Borai, MM: Exact solutions for some nonlinear fractional parabolic partial differential equations. Appl. Math. Comput.. 206, 150–153 (2008). Publisher Full Text
10. Wang, JR, Zhou, Y: Existence of mild solutions for fractional delay evolution systems. Appl. Math. Comput.. 218, 357–367 (2011). Publisher Full Text
11. Lv, ZW, Liang, J, Xiao, TJ: Solutions to the Cauchy problem for differential equations in Banach spaces with fractional order. Comput. Math. Appl.. 62, 1303–1311 (2011). Publisher Full Text
12. Byszewski, L: Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem. J. Math. Anal. Appl.. 162, 494–505 (1991). Publisher Full Text
13. Byszewski, L, Lakshmikantham, V: Theorems about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Appl. Anal.. 40, 11–19 (1991). Publisher Full Text
14. Pazy, A: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York (1983)
15. Liu, H, Chang, J: Existence for a class of partial differential equations with nonlocal conditions. Nonlinear Anal.. 70, 3076–3083 (2009). Publisher Full Text
16. Travis, CC, Webb, GF: Existence stability and compactness with α-norm for partial functional differential equations. Trans. Am. Math. Soc.. 240, 129–143 (1978)
17. Chang, J, Liu, H: Existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the α-norm. Nonlinear Anal.. 71, 3759–3768 (2009). Publisher Full Text
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2014-07-24 00:20:58
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https://xianblog.wordpress.com/tag/r/
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## occupancy rules
Posted in Kids, R, Statistics with tags , , , , , , , on May 23, 2016 by xi'an
While the last riddle on The Riddler was rather anticlimactic, namely to find the mean of the number Y of empty bins in a uniform multinomial with n bins and m draws, with solution
$\mathbb{E}[Y]=n(1-\frac{1}{n})^m,$
[which still has a link with e in that the fraction of empty bins converges to e⁻¹ when n=m], this led me to some more involved investigation on the distribution of Y. While it can be shown directly that the probability that k bins are non-empty is
${n \choose k}\sum_{i=1}^k (-1)^{k-i}{k \choose i}(i/n)^m$
with an R representation by
miss<-function(n,m){
p=rep(0,n)
for (k in 1:n)
p[k]=choose(n,k)*sum((-1)^((k-1):0)*choose(k,1:k)*(1:k)^m)
return(rev(p)/n^m)}
I wanted to take advantage of the moments of Y, since it writes as a sum of n indicators, counting the number of empty cells. However, the higher moments of Y are not as straightforward as its expectation and I struggled with the representation until I came upon this formula
$\mathbb{E}[Y^k]=\sum_{i=1}^k {k \choose i} i! S(k,i) \left( 1-\frac{i}{n}\right)^m$
where S(k,i) denotes the Stirling number of the second kind… Or i!S(n,i) is the number of surjections from a set of size n to a set of size i. Which leads to the distribution of Y by inverting the moment equations, as in the following R code:
diss<-function(n,m){
A=matrix(0,n,n)
mome=rep(0,n)
A[n,]=rep(1,n)
mome[n]=1
for (k in 1:(n-1)){
A[k,]=(0:(n-1))^k
for (i in 1:k)
mome[k]=mome[k]+factorial(i)*as.integer(Stirling2(n,i))*
(1-(i+1)/n)^m*factorial(k)/factorial(k-i-1)}
return(solve(A,mome))}
that I still checked by raw simulations from the multinomial
zample<-function(n,m,T=1e4){
x=matrix(sample(1:n,m*T,rep=TRUE),nrow=T)
x=sapply(apply(x,1,unique),length)
return(n-x)}
## ABC random forests for Bayesian parameter inference
Posted in Books, Kids, R, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , on May 20, 2016 by xi'an
Before leaving Helsinki, we arXived [from the Air France lounge!] the paper Jean-Michel presented on Monday at ABCruise in Helsinki. This paper summarises the experiments Louis conducted over the past months to assess the great performances of a random forest regression approach to ABC parameter inference. Thus validating in this experimental sense the use of this new approach to conducting ABC for Bayesian inference by random forests. (And not ABC model choice as in the Bioinformatics paper with Pierre Pudlo and others.)
I think the major incentives in exploiting the (still mysterious) tool of random forests [against more traditional ABC approaches like Fearnhead and Prangle (2012) on summary selection] are that (i) forests do not require a preliminary selection of the summary statistics, since an arbitrary number of summaries can be used as input for the random forest, even when including a large number of useless white noise variables; (b) there is no longer a tolerance level involved in the process, since the many trees in the random forest define a natural if rudimentary distance that corresponds to being or not being in the same leaf as the observed vector of summary statistics η(y); (c) the size of the reference table simulated from the prior (predictive) distribution does not need to be as large as for in usual ABC settings and hence this approach leads to significant gains in computing time since the production of the reference table usually is the costly part! To the point that deriving a different forest for each univariate transform of interest is truly a minor drag in the overall computing cost of the approach.
An intriguing point we uncovered through Louis’ experiments is that an unusual version of the variance estimator is preferable to the standard estimator: we indeed exposed better estimation performances when using a weighted version of the out-of-bag residuals (which are computed as the differences between the simulated value of the parameter transforms and their expectation obtained by removing the random trees involving this simulated value). Another intriguing feature [to me] is that the regression weights as proposed by Meinshausen (2006) are obtained as an average of the inverse of the number of terms in the leaf of interest. When estimating the posterior expectation of a transform h(θ) given the observed η(y), this summary statistic η(y) ends up in a given leaf for each tree in the forest and all that matters for computing the weight is the number of points from the reference table ending up in this very leaf. I do find this difficult to explain when confronting the case when many simulated points are in the leaf against the case when a single simulated point makes the leaf. This single point ends up being much more influential that all the points in the other situation… While being an outlier of sorts against the prior simulation. But now that I think more about it (after an expensive Lapin Kulta beer in the Helsinki airport while waiting for a change of tire on our airplane!), it somewhat makes sense that rare simulations that agree with the data should be weighted much more than values that stem from the prior simulations and hence do not translate much of an information brought by the observation. (If this sounds murky, blame the beer.) What I found great about this new approach is that it produces a non-parametric evaluation of the cdf of the quantity of interest h(θ) at no calibration cost or hardly any. (An R package is in the making, to be added to the existing R functions of abcrf we developed for the ABC model choice paper.)
## Using MCMC output to efficiently estimate Bayes factors
Posted in Books, R, Statistics, University life with tags , , , , on May 19, 2016 by xi'an
As I was checking for software to answer a query on X validated about generic Bayes factor derivation, I came across an R software called BayesFactor, which only applies in regression settings and relies on the Savage-Dickey representation of the Bayes factor
$B_{01}=\dfrac{f(y|\theta^0)}{m(y)}=\dfrac{\pi(\theta^0|y)}{\pi(\theta^0)}$
when the null hypothesis writes as θ=θ⁰ (and possibly additional nuisance parameters with [roughly speaking] an independent prior). As we discussed in our paper with Jean-Michel Marin [which got ignored by large!], this representation of the Bayes factor is based on picking a very specific version of the prior, or more exactly of three prior densities. Assuming such versions are selected, I wonder at the performances of this approximation, given that it involves approximating the marginal posterior at θ⁰….
“To ensure that the Bayes factor we compute using the Savage–Dickey ratio is the the ratio of marginal densities that we intend, the condition (…) is easily met by models which specify priors in which the nuisance parameters are independent of the parameters of interest.” Morey et al. (2011)
First, when reading Morey at al. (2011), I realised (a wee bit late!) that Chib’s method is nothing but a version of the Savage-Dickey representation when the marginal posterior can be estimated in a parametric (Rao-Blackwellised) way. However, outside hierarchical models based on conjugate priors such parametric approximations are intractable and non-parametric versions must be invoked instead, which necessarily degrades the quality of the method. A degradation that escalates with the dimension of the parameter θ. In addition, I am somewhat perplexed by the use of a Rao-Blackwell argument in the setting of the Dickey-Savage representation. Indeed this representation assumes that
$\pi_1(\psi|\theta_0)=\pi_0(\psi) \ \ \text{or}\quad \pi_1(\theta_0,\psi)=\pi_1(\theta_0)\pi_0(\psi)$
which means that [the specific version of] the conditional density of θ⁰ given ψ should not depend on the nuisance parameter. But relying on a Rao-Blackwellisation leads to estimate the marginal posterior via full conditionals. Of course, θ given ψ and y may depend on ψ, but still… Morey at al. (2011) advocate the recourse to Chib’s formula as optimal but this obviously requires the full conditional to be available. They acknowledge this point as moot, since it is sufficient from their perspective to specify a conjugate prior. They consider this to be a slight modification of the model (p.377). However, I see the evaluation of an estimated density at a single (I repeat, single!) point as being the direst part of the method as it is clearly more sensitive to approximations that the evaluation of a whole integral, since the later incorporates an averaging effect by definition. Hence, even if this method was truly available for all models, I would be uncertain of its worth when compared with other methods, except the harmonic mean estimator of course!
On the side, Morey at al. (2011) study a simple one-sample t test where they use an improper prior on the nuisance parameter σ, under both models. While the Savage-Dickey representation is correct in this special case, I fail to see why the identity would apply in every case under an improper prior. In particular, independence does not make sense with improper priors. The authors also indicate the possible use of this Bayes factor approximation for encompassing models. At first, I thought this could be most useful in our testing by mixture framework where we define an encompassing model as a mixture. However, I quickly realised that using a Beta Be(a,a) prior on the weight α with a<1 leads to an infinite density value at both zero and one, hence cannot be compatible with a Savage-Dickey representation of the Bayes factor.
## AISTATS 2016 [#1]
Posted in pictures, R, Running, Statistics, Travel, Wines with tags , , , , , , , , , , , , on May 11, 2016 by xi'an
Travelling through Seville, I arrived in Càdiz on Sunday night, along with a massive depression [weather-speaking!]. Walking through the city from the station was nonetheless pleasant as this is an town full of small streets and nice houses. If with less churches than Seville! Richard Samworth gave the first plenary talk of AISTATS 2016 with a presentation on random projections for classification. His classifier is based on an average of a large number of linear random projections of the original data where the projections are chosen as minimising the prediction error over a subset of the components. The performances of this approach seem to be consistently higher than for random forests, which makes it definitely worth investigating further. (A related R package is available.)
The following talks that day covered Bayesian optimisation and probabilistic numerics, with Javier Gonzales introducing glasses for Bayesian optimisation in order to solve its myopia (!)—by which he meant predicting the output of the optimisation over n future steps. And a first mention of the Pima Indians by Daniel Hernandez-Lobato in his talk about EP with stochastic gradient steps towards optimisation. (As well as much larger datasets.) And Mark Girolami bringing quasi-Monte Carlo into control variates. A kernel based ABC by Mijung Park, which uses kernels and maximum mean discrepancy to avoid defining summary statistics, and a version of parallel MCMC by Guillaume Basse. Plus another session on deep learning.
As usual with AISTATS conferences, the central activity of the day was the noon poster session, including speakers discussing their paper, and I had several interesting chats about MCMC related topics, with e.g. one alternative notion of ensemble MCMC [centred on estimating the normalising constant].
We awarded the notable student paper awards before the welcoming cocktail: The winners are Bo DaiNedelina Teneva, and Ye Wang. And this first day ended up with a companionable evening in a most genuine tapa bar, tasting local blood sausage and local blue cheese. (If you do not mind the corrida theme!)
## gap frequencies [& e]
Posted in Kids, R with tags , , , on April 29, 2016 by xi'an
A riddle from The Riddler where brute-force simulation does not pay:
For a given integer N, pick at random without replacement integers between 1 and N by prohibiting consecutive integers until all possible entries are exhausted. What is the frequency of selected integers as N grows to infinity?
A simple implementation of the random experiment is as follows
generope=function(N){
frei=rep(1,N)
hus=0
while (max(frei)==1){
i=sample(rep((1:N)[frei==1],2),1)
frei[i]=frei[i+1]=frei[i-1]=0
hus=hus+1}
return(hus)}
It is however quite slow and does not exploit the recursive feature of the sampling, namely that the first draw breaks the set {1,…,N} into two sets:
generipe=function(N){
if (N<2){ return((N>0))}else{
i=sample(1:N,1)
return(1+generipe(i-2)+generipe(N-i-1))}}
But even this faster solution takes a while to run for large values of N:
frqns=function(N){
space=0
for (t in 1:1e3) space=space+generipe(N)
return(space/(N*1e3))}
as for instance
> microbenchmark(frqns(100),time=10)
Unit: nanoseconds
expr min lq mean median uq max
frqns(100) 178720117 185020903 212212355.77 188710872 205865816 471395620
time 4 8 26.13 32 37 102
Hence this limits the realisation of simulation to, say, N=10⁴. Thinking further about the recursive aspect of the process however leads to a recursion on the frequencies qN, as it is straightforward to prove that
$q_N=\frac{1}{N}+\frac{2}{N^2}\,\sum_{i=1}^{N-2} iq_i$
with q1=1 and q2=1/2. This recursion can be further simplified into
$q_N=\frac{1}{N^2}+\frac{2(N-2)}{N^2}\,q_{N-2}+\frac{(N-1)^2}{N^2}q_{N-1}\qquad(1)$
which allows for a much faster computation
s=seq(1,1e7) #s[n]=n*q[n]
for (n in 3:1e7) s[n]=(1+2*s[n-2]+(n-1)*s[n-1])/n
and a limiting value of 0.4323324… Since storing s does not matter, a sliding update works even better:
a=b=1
for (n in 3:1e8){ c=(1+2*a+(n-1)*b)/n;a=b;b=c}
still producing a final value of 0.4323324, which may mean we have reached some limit in the precision.
As I could not figure out a way to find the limit of the sequence (1) above, I put it on the maths forum of Stack Exchange and very quickly got the answer (obtained by a power series representation) that the limit is (rather amazingly!)
$\dfrac{1 - e^{-2}}{2}$
which is 0.432332358.., hence very close to the numerical value obtained for n=3×10⁸. (Which does not change from n=10⁸, once again for precision reasons.) Now I wonder whether or not an easier derivation of the above is feasible, but we should learn about it in a few hours on The Riddler. [Update: The solution published by The Riddler is exactly that one, using a power series expansion to figure out the limit of the series, unfortunately. I was hoping for a de Montmort trick or sort of…]
## Le Monde puzzle [#960]
Posted in Kids, R with tags , , , , , on April 28, 2016 by xi'an
An arithmetic Le Monde mathematical puzzle:
Given an integer k>1, consider the sequence defined by F(1)=1+1 mod k, F²(1)=F(1)+2 mod k, F³(1)=F²(1)+3 mod k, &tc. [With this notation, F is not necessarily a function.] For which value of k is the sequence the entire {0,1,…,k-1} set?
This leads to an easy brute force resolution, for instance writing the R function
crkl<-function(k) return(unique(cumsum(1:(2*k))%%k))
where 2k is a sufficient substitute for ∞. Then the cases where the successive images of 1 visit the entire set {0,1,…,k-1} are given by
> for (i in 2:550) if (length(crkl(i))==i) print(i)
[1] 2
[1] 4
[1] 8
[1] 16
[1] 32
[1] 64
[1] 128
[1] 256
[1] 512
which suspiciously looks like the result that only the powers of 2 k=2,2²,2³,… lead to a complete exploration of the set {0,1,…,k-1}. Checking a few series in the plane back from Warwick, I quickly found that when k is odd, (1) the sequence is of period k and (2) there is symmetry in the sequence, which means it only takes (k-1)/2 values. For k even, there is a more complicated symmetry, with the sequence being of period 2k, symmetric around its two middle values, and taking the values 1,2,..,1+k(2k+1)/4,..,1+k(k+1)/2. Those values cannot cover the set {0,1,…,k-1} if two are equal, which means an i(i+1)/2 congruent to zero modulo k, hence equal to k. This is clearly impossible when k is a power of 2 because i and i+1 cannot both divide a power of 2. I waited for the published solution as of yesterday’s and the complete argument was to show that when N=2p, the corresponding sequence [for N] is made (modulo p) of the sequence for p plus the same sequence translated by p. The one for N is complete only if the one for p is complete, which by recursion eliminates all cases but the powers of 2…
## Le Monde puzzle [#959]
Posted in Kids, R with tags , , , on April 20, 2016 by xi'an
Another of those arithmetic Le Monde mathematical puzzle:
Find an integer A such that A is the sum of the squares of its four smallest dividers (including1) and an integer B such that B is the sum of the third poser of its four smallest factors. Are there such integers for higher powers?
This begs for a brute force resolution checking the integers until a solution appears. The only exciting part is providing the four smallest factors but a search on Stack overflow led to an existing R function:
FUN <- function(x) {
x <- as.integer(x)
div <- seq_len(abs(x))
return(div[x %% div == 0L])
}
(which uses the 0L representation I was unaware of) and hence my R code:
quest1<-function(n=2){
I=4
stop=TRUE
while ((stop)&(I<1e6)){
I=I+1
dive=FUN(I)
if (length(dive)>3)
stop=(I!=sum(sort(dive)[1:4]^n))
}
return(I)
}
But this code only seems to work for n=2 as produces A=130: it does not return any solution for the next value of n… As shown by the picture below, which solely exhibits a solution for n=2,5, A=17864 (in the second case), there is no solution less than 10⁶ for n=3,4,6,..9. So, unless I missed a point in the question, the solutions for n>2 are larger if they at all exist.
A resolution got published yesterday night in Le Monde and (i) there is indeed no solution for n=3 (!), (ii) there are solutions for n=4 (1,419,874) and n=5 (1,015,690), which are larger than the 10⁶ bound I used in the R code, (iii) there is supposedly no solution for n=5!, when the R code found that 17,864=1⁵+2⁵+4⁵+7⁵… It is far from the first time the solution is wrong or incomplete!
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2016-05-28 13:37:19
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https://www.bionicturtle.com/forum/members/elena77.63481/recent-content
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What's new
Recent content by elena77
1. Delta of Short EUR Call Option
Thank you David, understod.
2. Delta of Short EUR Call Option
Hi David, for Problem 19.10, in your calculation of d1, why don't you include Rf of 12%? I understand the calculation of d1 to be: [LN (S/K)+ {Rf+(Vol^2/2)}*T]/(vol*SQRT(T)) Thank you for your advice.
3. Hull, Chapter 7 , Swaps
Hi there, Would you please reply to the post above? Thank you.
4. Hull, Chapter 7 , Swaps
Hi David, (I moved my initial post in the archive to here) for 7.10 I assume my calculation below misses the loss at the year 3, while final conclusion is the same at circa $0.413 (numbers in$ mio) Floating rate payment: (10+0.4)*exp^(0.078441*0.5) = 9.61558, where 0.078441 is derived from...
5. P1.T2., Stock & Watson Single Regression: Hypothesis Tests and Confidence Intervals
Hi David, I need to understand how p-value is derived. On your study note for tutorial video for the captioned p.12, please explain how we get CDF of 0.9878 for p-value calculation. Similarly, please show calculation for 2-sided p-value in following two slides p.13 (1.34%) and p.14 (4.10%)...
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2021-10-21 06:19:36
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http://ndp.jct.ac.il/tutorials/infitut1/node114.html
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# The algebra of convergent series.
Theorem 9.2.1 Let and be two convergent series. Then the series is convergent and its sum is equal to .
Theorem 9.2.2 Let be a convergent series and . Then the series is convergent and its sum is equal to .
Together these two theorems mean that the set of convergent series of real numbers is a real vector space.
Remark 9.2.3 Adding or deleting terms from a series does not change the convergence/divergence. For a convergent series, it changes the value of the sum.
Example 9.2.4
Noah Dana-Picard 2007-12-28
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2017-06-24 12:13:35
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https://www.aimsciences.org/article/doi/10.3934/proc.2015.0923
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# American Institute of Mathematical Sciences
2015, 2015(special): 923-935. doi: 10.3934/proc.2015.0923
## A functional-analytic technique for the study of analytic solutions of PDEs
1 Department of Civil Engineering, University of Patras, 26500 Patras, Greece 2 Department of Mathematics, University of Patras, 26500 Patras, Greece
Received August 2014 Revised December 2014 Published November 2015
A functional-analytic method is used to study the existence and the uniqueness of bounded, analytic and entire complex solutions of partial differential equations. As a benchmark problem, this method is applied to the nonlinear Benjamin--Bona--Mahony equation and the associated to this, linear equation. The predicted solutions are in power series form and two concrete examples are given for specific initial conditions.
Citation: Eugenia N. Petropoulou, Panayiotis D. Siafarikas. A functional-analytic technique for the study of analytic solutions of PDEs. Conference Publications, 2015, 2015 (special) : 923-935. doi: 10.3934/proc.2015.0923
##### References:
[1] T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems,, Philos. Trans. Roy. Soc. London Ser. A, 272 (1972), 47. Google Scholar [2] G. Caciotta and F. Nicoló, Local and global analytic solutions for a class of characteristic problems of the Einstein vacuum equations in the "double null foliation gauge",, Ann. Henri Poincare, 13 (2012), 1167. Google Scholar [3] G. M. Coclite, F. Gargano and V. Sciacca, Analytic solutions and singularity formation for the Peakon $b$-family equations,, Acta Appl. Math., 122 (2012), 419. Google Scholar [4] C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, in Global Analysis (Proc. Sympos. Pure Math., (1970), 61. Google Scholar [5] L. C. Evans, Partial differential equations,, $2^{nd}$ edition, (2010). Google Scholar [6] N. Hayashi and K. Kato, Global existence of small analytic solutions to Schrödinger equations with quadratic nonlinearity,, Comm. Partial Differential Equations, 22 (1997), 773. Google Scholar [7] A. A. Himonas and G. Petronilho, Analytic well-posedness of periodic gKdV,, J. Differential Equations, 253 (2012), 3101. Google Scholar [8] E. K. Ifantis, Solution of the Schrödinger equation in the Hardy-Lebesgue space,, J. Mathematical Phys., 12 (1971), 1961. Google Scholar [9] E. K. Ifantis, Analytic solutions for nonlinear differential equations,, J. Math. Anal. Appl., 124 (1987), 339. Google Scholar [10] E. K. Ifantis, Global analytic solutions of the radial nonlinear wave equation,, J. Math. Anal. Appl., 124 (1987), 381. Google Scholar [11] J. Kajiwara, Holomorphic solutions of a partial differential equation of mixed type,, Math. Balkanica, 2 (1972), 76. Google Scholar [12] T. Kusano and S. Oharu, Bounded entire solutions of second order semilinear elliptic equations with application to a parabolic initial value problem,, Indiana Univ. Math. J., 34 (1985), 85. Google Scholar [13] E. N. Petropoulou and P. D. Siafarikas, Analytic solutions of some non-linear ordinary differential equations,, Dynam. Systems Appl. 13 (2004), 13 (2004), 283. Google Scholar [14] E. N. Petropoulou and P. D. Siafarikas, Polynomial solutions of linear partial differential equations,, Commun. Pure Appl. Anal. 8 (2009), 8 (2009), 1053. Google Scholar [15] E. N. Petropoulou, P. D. Siafarikas and E. E. Tzirtzilakis, A "discretization" technique for the solution of ODEs,, J. Math. Anal. Appl. 331 (2007), 331 (2007), 279. Google Scholar [16] E. N. Petropoulou, P. D. Siafarikas and E. E. Tzirtzilakis, A "discretization" technique for the solution of ODEs II,, Numer. Funct. Anal. Optim. 30 (2009), 30 (2009), 613. Google Scholar [17] E. N. Petropoulou and E. E. Tzirtzilakis, On the logistic equation in the complex plane,, Numer. Funct. Anal. Optim. 34 (2013), 34 (2013), 770. Google Scholar [18] I. G. Petrovsky, Lecture on partial differential equations., Translated from the Russian by A. Shenitzer, (1957). Google Scholar [19] A. Vourdas, Analytic representations in the unit disc and applications to phase states and squeezing,, Phys. Rev. A 45 (1992), 45 (1992), 1943. Google Scholar [20] G. Zampieri, A sufficient condition for existence of real analytic solutions of P.D.E. with constant coefficients, in open sets of $\mathbbR^{2}$,, Rend. Sem. Mat. Univ. Padova 63 (1980), 63 (1980), 83. Google Scholar [21] G. Zampieri, Analytic solutions of P.D.E.'s., Ann. Univ. Ferrara-Sez. VII-Sc. Mat. XLV (1999), XLV (1999), 365. Google Scholar
show all references
##### References:
[1] T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems,, Philos. Trans. Roy. Soc. London Ser. A, 272 (1972), 47. Google Scholar [2] G. Caciotta and F. Nicoló, Local and global analytic solutions for a class of characteristic problems of the Einstein vacuum equations in the "double null foliation gauge",, Ann. Henri Poincare, 13 (2012), 1167. Google Scholar [3] G. M. Coclite, F. Gargano and V. Sciacca, Analytic solutions and singularity formation for the Peakon $b$-family equations,, Acta Appl. Math., 122 (2012), 419. Google Scholar [4] C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, in Global Analysis (Proc. Sympos. Pure Math., (1970), 61. Google Scholar [5] L. C. Evans, Partial differential equations,, $2^{nd}$ edition, (2010). Google Scholar [6] N. Hayashi and K. Kato, Global existence of small analytic solutions to Schrödinger equations with quadratic nonlinearity,, Comm. Partial Differential Equations, 22 (1997), 773. Google Scholar [7] A. A. Himonas and G. Petronilho, Analytic well-posedness of periodic gKdV,, J. Differential Equations, 253 (2012), 3101. Google Scholar [8] E. K. Ifantis, Solution of the Schrödinger equation in the Hardy-Lebesgue space,, J. Mathematical Phys., 12 (1971), 1961. Google Scholar [9] E. K. Ifantis, Analytic solutions for nonlinear differential equations,, J. Math. Anal. Appl., 124 (1987), 339. Google Scholar [10] E. K. Ifantis, Global analytic solutions of the radial nonlinear wave equation,, J. Math. Anal. Appl., 124 (1987), 381. Google Scholar [11] J. Kajiwara, Holomorphic solutions of a partial differential equation of mixed type,, Math. Balkanica, 2 (1972), 76. Google Scholar [12] T. Kusano and S. Oharu, Bounded entire solutions of second order semilinear elliptic equations with application to a parabolic initial value problem,, Indiana Univ. Math. J., 34 (1985), 85. Google Scholar [13] E. N. Petropoulou and P. D. Siafarikas, Analytic solutions of some non-linear ordinary differential equations,, Dynam. Systems Appl. 13 (2004), 13 (2004), 283. Google Scholar [14] E. N. Petropoulou and P. D. Siafarikas, Polynomial solutions of linear partial differential equations,, Commun. Pure Appl. Anal. 8 (2009), 8 (2009), 1053. Google Scholar [15] E. N. Petropoulou, P. D. Siafarikas and E. E. Tzirtzilakis, A "discretization" technique for the solution of ODEs,, J. Math. Anal. Appl. 331 (2007), 331 (2007), 279. Google Scholar [16] E. N. Petropoulou, P. D. Siafarikas and E. E. Tzirtzilakis, A "discretization" technique for the solution of ODEs II,, Numer. Funct. Anal. Optim. 30 (2009), 30 (2009), 613. Google Scholar [17] E. N. Petropoulou and E. E. Tzirtzilakis, On the logistic equation in the complex plane,, Numer. Funct. Anal. Optim. 34 (2013), 34 (2013), 770. Google Scholar [18] I. G. Petrovsky, Lecture on partial differential equations., Translated from the Russian by A. Shenitzer, (1957). Google Scholar [19] A. Vourdas, Analytic representations in the unit disc and applications to phase states and squeezing,, Phys. Rev. A 45 (1992), 45 (1992), 1943. Google Scholar [20] G. Zampieri, A sufficient condition for existence of real analytic solutions of P.D.E. with constant coefficients, in open sets of $\mathbbR^{2}$,, Rend. Sem. Mat. Univ. Padova 63 (1980), 63 (1980), 83. Google Scholar [21] G. Zampieri, Analytic solutions of P.D.E.'s., Ann. Univ. Ferrara-Sez. VII-Sc. Mat. XLV (1999), XLV (1999), 365. Google Scholar
[1] Hui Yin, Huijiang Zhao. Nonlinear stability of boundary layer solutions for generalized Benjamin-Bona-Mahony-Burgers equation in the half space. Kinetic & Related Models, 2009, 2 (3) : 521-550. doi: 10.3934/krm.2009.2.521 [2] Anne-Sophie de Suzzoni. Continuity of the flow of the Benjamin-Bona-Mahony equation on probability measures. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2905-2920. doi: 10.3934/dcds.2015.35.2905 [3] Milena Stanislavova. On the global attractor for the damped Benjamin-Bona-Mahony equation. Conference Publications, 2005, 2005 (Special) : 824-832. doi: 10.3934/proc.2005.2005.824 [4] Khaled El Dika. Asymptotic stability of solitary waves for the Benjamin-Bona-Mahony equation. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 583-622. doi: 10.3934/dcds.2005.13.583 [5] Hirokazu Ninomiya. Entire solutions and traveling wave solutions of the Allen-Cahn-Nagumo equation. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 2001-2019. doi: 10.3934/dcds.2019084 [6] C. H. Arthur Cheng, John M. Hong, Ying-Chieh Lin, Jiahong Wu, Juan-Ming Yuan. Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 763-779. doi: 10.3934/dcdsb.2016.21.763 [7] Vishal Vasan, Bernard Deconinck. Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3171-3188. doi: 10.3934/dcds.2013.33.3171 [8] Wenxia Chen, Ping Yang, Weiwei Gao, Lixin Tian. The approximate solution for Benjamin-Bona-Mahony equation under slowly varying medium. Communications on Pure & Applied Analysis, 2018, 17 (3) : 823-848. doi: 10.3934/cpaa.2018042 [9] Thierry Horsin, Peter I. Kogut, Olivier Wilk. Optimal $L^2$-control problem in coefficients for a linear elliptic equation. II. Approximation of solutions and optimality conditions. Mathematical Control & Related Fields, 2016, 6 (4) : 595-628. doi: 10.3934/mcrf.2016017 [10] M. S. Bruzón, M. L. Gandarias, J. C. Camacho. Classical and nonclassical symmetries and exact solutions for a generalized Benjamin equation. Conference Publications, 2015, 2015 (special) : 151-158. doi: 10.3934/proc.2015.0151 [11] Mario Pulvirenti, Sergio Simonella, Anton Trushechkin. Microscopic solutions of the Boltzmann-Enskog equation in the series representation. Kinetic & Related Models, 2018, 11 (4) : 911-931. doi: 10.3934/krm.2018036 [12] Christos Sourdis. On the growth of the energy of entire solutions to the vector Allen-Cahn equation. Communications on Pure & Applied Analysis, 2015, 14 (2) : 577-584. doi: 10.3934/cpaa.2015.14.577 [13] Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai, Chao-Jiang Xu, Tong Yang. Bounded solutions of the Boltzmann equation in the whole space. Kinetic & Related Models, 2011, 4 (1) : 17-40. doi: 10.3934/krm.2011.4.17 [14] Okihiro Sawada. Analytic rates of solutions to the Euler equations. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1409-1415. doi: 10.3934/dcdss.2013.6.1409 [15] Christian Pötzsche. Nonautonomous continuation of bounded solutions. Communications on Pure & Applied Analysis, 2011, 10 (3) : 937-961. doi: 10.3934/cpaa.2011.10.937 [16] Jaime Angulo Pava, Carlos Banquet, Márcia Scialom. Stability for the modified and fourth-order Benjamin-Bona-Mahony equations. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 851-871. doi: 10.3934/dcds.2011.30.851 [17] Giuseppina Autuori, Patrizia Pucci. Entire solutions of nonlocal elasticity models for composite materials. Discrete & Continuous Dynamical Systems - S, 2018, 11 (3) : 357-377. doi: 10.3934/dcdss.2018020 [18] Antonio Vitolo. On the growth of positive entire solutions of elliptic PDEs and their gradients. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1335-1346. doi: 10.3934/dcdss.2014.7.1335 [19] Wan-Tong Li, Li Zhang, Guo-Bao Zhang. Invasion entire solutions in a competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1531-1560. doi: 10.3934/dcds.2015.35.1531 [20] Patrizia Pucci, Marco Rigoli. Entire solutions of singular elliptic inequalities on complete manifolds. Discrete & Continuous Dynamical Systems - A, 2008, 20 (1) : 115-137. doi: 10.3934/dcds.2008.20.115
Impact Factor:
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2019-09-23 02:38:51
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https://tex.stackexchange.com/questions/356548/how-can-i-create-the-following-drawing/356594
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How can I create the following drawing?
Can someone help me with this Drawing? i need to add it with Latex to a document and i don't know how to use Latex function properly
LaTeX has a wonderful package specifically for drawing circuits. It's called CircuiTikz (documentation here: https://www.sharelatex.com/blog/2013/09/02/tikz-series-pt4.html).
Your drawing is nothing too complicated for LaTeX standards. Here is the code:
\documentclass[a4paper]{report}
\usepackage{amsmath}
\usepackage{circuitikz}
\begin{document}
\begin{circuitikz} \draw
(0,0) to[battery1] (5,0)
(5,0) to[generic, -*] (5,6)
(5,6) to[generic, -*] (2.5,3)
(5,6) to[generic, -*] (2.5,9)
(2.5,3) to[generic] (2.5, 9)
(2.5,3) to[generic, -*] (0,6)
(2.5,9) to[generic] (0,6)
(0,6) to[ammeter] (0,0)
(1,0) to[short, *-] (1,1.5)
(1,1.5) to[voltmeter] (4,1.5)
(4,1.5) to[short, -*] (4,0)
;
\end{circuitikz}
\end{document}
I hope that my post was helpful. For full documentation see: http://mirror.unl.edu/ctan/graphics/pgf/contrib/circuitikz/doc/circuitikzmanual.pdf.
• Why on Earth would you claim this will not work with other engines? There is absolutely nothing in your code to require XeLaTeX. Nothing whatsoever. I've removed the claim as it only undermines the quality of your answer, which is otherwise good. – cfr Mar 3 '17 at 2:31
• On my system (fully updated) only XeLaTeX worked, so I wrote the answer as such. Of course I might have overlooked some detail that would allow compilation with PDFLaTeX and LuaLaTeX as well. Do you have any knowledge of the latter? I would be grateful. – Gregor Perčič Mar 3 '17 at 9:29
• Worked fine for me with pdfLaTeX. I just compiled your code as was, just to be sure, before editing. – cfr Mar 3 '17 at 22:09
• Can you maybe hypothesize what configuartion my system is faulty and consequently produces the result I have (for me, it compiles only with XeLaTeX)? I'd be very grateful. – Gregor Perčič Mar 4 '17 at 8:57
• Sorry, I have no idea. You don't even say what error you get. Ask a new question with details or ask in chat. – cfr Mar 5 '17 at 4:54
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2019-10-14 01:16:16
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https://wiki.iota.org/smart-contracts/guide/wasm_vm/context
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# Function Call Context
Proxy objects provide generic access capabilities to the data on the host. It is now time to introduce the gateway to the host that allows you to access the functionality that the host sandbox interface provides. We call this gateway the function call context , and it is provided as a predefined parameter to the smart contract function. In fact, you can distinguish two separate flavors of smart contract functions in the IOTA Smart Contracts:
• Func, which allows full mutable access to the smart contract state, and always results in a state update.
• View, which allows only limited, immutable access to the smart contract state, and therefore does not result in a state update. Views can be used to efficiently query the current state of the smart contract.
To support this function type distinction, Func and View functions each receive a separate, different function call context. Only the functionality that is necessary for their implementation can be accessed through their respective contexts, ScFuncContext and ScViewContext. ScViewContext provides a limited, immutable subset of the full functionality provided by ScFuncContext. By having separate context types, compile-time type-checking can be used to enforce their usage constraints.
An important part of setting up a smart contract is defining exactly which Funcs and Views are available and informing the host about them. The host will have to dispatch the function calls to the corresponding smart contract code. To that end, the smart contract Wasm code will expose an externally callable function named on_load that will be called by the host upon initial loading of the smart contract code. The on_load function must provide the host with the list of Funcs and Views, and specific identifiers that can be used to invoke them. It uses a special temporary function context named ScExports. That context can be used to provide the host with a function, type, name, and identifier for each Func and View that can be called in the smart contract.
When the host need to call a smart contract function, it has to do it by invoking a second externally callable function named on_call. The host passes the identifier for the smart contract Func or View that needs to be invoked. The client Wasm code will then use this identifier to set up the corresponding function context and call the function. Note that there are no other parameters necessary because the function can subsequently access any other function-related data through its context object.
Here is a (simplified) example from the dividend example smart contract that showcases some features of WasmLib:
func OnLoad() { exports := wasmlib.NewScExports() exports.AddFunc("divide", funcDivide) exports.AddFunc("init", funcInit) exports.AddFunc("member", funcMember) exports.AddFunc("setOwner", funcSetOwner) exports.AddView("getFactor", viewGetFactor) exports.AddView("getOwner", viewGetOwner)}
The on_load() function first creates the required ScExports context, and then proceeds to define four Funcs named divide, init, member, and setOwner. It does this by calling the add_func() method of the ScExports context. Next it defines two Views named getFactor and getOwner by calling the addView() method of the ScExports context. The second parameter to these methods is the actual smart contract function associated with the name specified. These methods will also automatically assign a unique identifier to the function and then send everything to the host.
In its simplest form this is all that is necessary to initialize a smart contract. To finalize this example, here is what the skeleton function implementations for the above smart contract definition would look like:
func funcDivide(ctx wasmlib.ScFuncContext) { ctx.Log("dividend.funcDivide")}func funcInit(ctx wasmlib.ScFuncContext) { ctx.Log("dividend.funcInit")}func funcMember(ctx wasmlib.ScFuncContext) { ctx.Log("dividend.funcMember")}func funcSetOwner(ctx wasmlib.ScFuncContext) { ctx.Log("dividend.funcSetOwner")}func viewGetFactor(ctx wasmlib.ScViewContext) { ctx.Log("dividend.viewGetFactor")}func viewGetOwner(ctx wasmlib.ScViewContext) { ctx.Log("dividend.viewGetOwner")}
As you can see, each function is provided with a context parameter, which is conventionally named ctx. Notice that the four Funcs are passed an ScFuncContext, whereas the two Views receive an ScViewContext.
This example also showcases an important feature of the contexts: the log() method. This can be used to log human-readable text to the host's log output. Logging text is the only way to add tracing to a smart contract, because it does not have any I/O capabilities other than what the host provides. There is a second logging method, called trace(), that can be used to provide extra debug information to the host's log output. The trace output can be selectively turned on and off at the host.
In the next section we will introduce the schema tool that simplifies smart contract programming a lot.
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2022-05-20 06:50:59
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https://blog.rossry.net/donations-2018/
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Donations 2018
Well, it's been a crazy calendar year in any number of ways...and here at the end of it, I have a few commitments to uphold. I remaincommitted to donating at least 10% of my income to the organizations that I think best make the universe a better place, and to talking about it on this blog. Here are my thoughts at the end of 2018.
(0)
While I've recently been conducting some independent research into investment strategies for effective altruists (results forthcoming), I haven't been particularly active in producing my own independent opinions on the effectiveness or value of organizations. So, as in 2017, my perspective here is primarily a synthesis of a raft of conversations I've had with a (uncredited) gaggle of friends and friends-of-friends.
disclaimers: I've made no particular attempt to be discriminating or fair in these conversations. Some of the friends who have helped me form my opinions here are involved in some capacity in the areas or organizations I'll mention. Some have their own positions on advisory or evaluator boards, or publish their own opinions separately.
Rather than get into the weeds of these conflicts, I'll just advise you to keep your brain engaged throughout. Not all of my reasoning that shapes these opinions was appropriate for this post, and not all of it will be covered here. I've erred towards providing more unexplained information, rather than restricting myself to what I can explain fully here.
I cover logistics (1a), donor lotteries (1b), my general approach to non-lottery donations (1c), the specific charities I’m supporting this year (2a, , and further reading in the form of evaluators’ reports and personal writeups (3).
I'll also drop links to further reading into individual sections, where topical. (In the interest of including more links, I'm linking them without explicit comment in many cases.)
(1a)
Last year, I wrote about donor-advised funds; this year I'm donating a mix of long-term appreciated assets and cash to my DAF, for granting early in 2019. DAFs are a really useful tool for mitigating the end-of-year crunch, and for making it easier to donate things like stocks, mutual funds, and other non-dollar things. One or two organizations aren't supported by Vanguard Charitable (my DAF manager), and I'll donate cash directly.
While deductions are (I think) marginally more valuable to me in tax year 2018 than 2019 due to my part-year residency in New York, I'm not in as much of a rush to donate as I was in 2017, and am setting aside some funds that I ultimately intend to donate, to experiment with both tax-efficient investment-for-altruism and with donating opportunistically during the year. These aren't addressed below.
(1b)
By far the largest single allocation I'm making from my 2018 donation pool is to entering a donor lottery run by the Centre for Effective Altruism. The basic motivation for donor lotteries is, I think, best expressed in this blog post by Ben Hoffman:
Let’s say that your charity budget for this year is $5,000, and your best guess is that it will take about five hours of research to make a satisfactory giving decision. You expect that you’ll be giving to charities for which$5,000 is a small amount, so that they have roughly constant returns to scale with respect to your donation... In particular, for the sake of simplicity, let’s say that you think that the best charity you’re likely to find can add a healthy year to someone’s life for $250, so your donation can buy 20 life-years. Under these circumstances, suppose that someone you trust offers you a bet with a 90% probability of getting nothing, and a 10% probability of getting back ten times what you put in. In this case, if you make a$5,000 bet, your expected giving is 10% * 10 * $5,000 =$5,000, the same as before. And if you expect the same impact per dollar up to $50,000, then if you win, your donation saves$50,000 / $250 = 200 life-years for beneficiaries of this charity. Since you only have a 10% chance of winning, your expected impact is 20 life-years, same as before. But you only need to spend time evaluating charities if you win, so your expected time expenditure is 10% * 5 = 0.5 hours. This is strictly better – you have the same expected impact, for a tenth the expected research time... Of course, if you’re giving away$50,000, you might be motivated to spend more than five hours on this. Let’s say that you think that you can find a charity that’s 10% more effective if you spend ten hours on it. Then in the winning scenario, you’re spending an extra five hours to save an extra 20 lives, not a bad deal. Your expected lives saved is then 22, higher than in the original case, and your expected time allocation is 1 hour, still much less than before. (...)
After all of the thought that I've applied to this problem so far this year, I don't feel like I have much better marginal uses for donations than delegating my decision to evaluators (like GiveWell or ACE) or CEA's EA Funds. At that point, I have little problem squeezing my expected dollars into a few worlds where I can give the matter more thought -- or at worst, donate to selected EA Funds anyway.
I also see positive value in credibly signalling my support for donor lotteries as a mechanism, and in facilitating the existence of donor lotteries themselves, which I expect to improve the expected effectiveness of participants' donations. CEA has more to say about donor lotteries at their main info page.
(1c)
The funds that I'm not directing to my donor-lottery entry I'm allocating along lines broadly similar to 2017 -- in the face of deep uncertainty over how to weigh different kinds of moral and epistemic beliefs, I'm splitting my donation into differently-sized chunks that reflect something of my thinking about on a few at-least-plausible ways of doing good.
I consider this division primarily an exercise in practicing thinking for myself about charitable giving on a variety of margins, not primarily an exercise in aiming to do the absolute most expected good. (That's what the donor-lottery entry is for.) I readily acknowledge that my process here rests on provably-inconsistent heuristics and ad-hoc invented 'principles'. I haven't made extraordinary effort to eradicate either, and I don't expect my current thinking to be the final word so much as a jumping-off point for discussion and reflection going forward.
Like last year, I want to intentionally skew my efforts towards cashing out to "straightforward charity", rather than recursive investments, stochastic gambles, far-future moonshots, and other ungrounded bets with weak feedback loops -- even in cases where I’m not convinced that more direct, or more immediate, interventions are the most effective ways of doing good possible right now. (My intention here is to provide some kind of outside-view backstop against some kinds of decision-making failure modes.)
Practically speaking, I'm directing a substantial minority of my total 2018 donation pool to fighting global poverty and supporting non-human animal welfare, aiming to do good today, unconditionally, in straightforwardly knowable ways. (I'm making these donations outright, rather entering them into a donor lottery.)
I expect to direct any lottery sum towards efforts to make lives better in the far future or 'meta' opportunities to strengthen the community of effective altruists -- and in the face of my present uncertainty of the best way to do so, I'm donating comparatively less to those causes now, and will consider them in depth later if necessary.
But I want to continue a practice of directing some support to organizations who I believe are doing good work, and I'll lay those donations out in the remainder of this post. For the purposes of this post, I'll characterize the size of each donation as 'substantial', 'large', 'medium', and 'small'. These qualifiers are roughly comparable to my uses of the same words in 2017.
(2a)
(global poverty)
Substantial donation to GiveWell (unrestricted funds), fighting global poverty and disease to help humans living today.
My position here is little changed from 2017 (or indeed from 2014); I remain convinced that, among organizations working directly to make life better for humans living today, GiveWell’s top charities are some of the best-researched, highest-impact “sure bets”.
I note that this year, for the first time, GiveWell's list of top charities explicitly distinguishes between programs whose primary benefit is reducing deaths and programs that aim to increase recipients’ incomes and consumption. After reading GiveWell staff members' commentary on their personal donations for giving season 2018, I expect that their internal discussions on the moral tradeoffs between reducing deaths and increasing incomes to be deeper and more thoughtful that my current opinions, and aim to defer to the judgment of GiveWell staff on this moral point, at least for now.
As in the past two years, I feel best making my donation to GiveWell with no restriction on its use, as I trust GiveWell’s discretion to support its own operations where necessary and regrant excess funds to a well-considered balance between opportunities to save lives and opportunities to explicitly better them.
(animal welfare)
Substantial donation to The Humane League, advocating for non-human animal welfare.
I remain particularly uninformed about the landscape of effective animal charities -- though in the past year I have found no compelling evidence against THL or for any other effective animal charity, and I remain impressed by THL on the same grounds I was at the end of 2017.
I asked myself what I could do for <10 minutes that was most likely to change my mind, and I came up with this: I read Animal Charity Evaluators' reviews (1 2 3 4) of their 2018 top four charities, and tried to be generally on the lookout for anything that struck my systems-oriented intuition as particularly positive or negative. In the end, I was most impressed by ACE's view of THL's strengths:
In our view, THL’s most significant advantage is not any single program, but rather their general approach to advocacy. Among animal advocacy organizations, THL makes particularly strong efforts to assess their own programs and to look for and test ways to improve them. Their success in their corporate campaigns, and the publication of their research through Humane League Labs (HLL), has shifted the outlook and programming of several other advocacy organizations toward finding the best ways to advocate for animals.
THL’s organizational structure appears to be strong, with a cohesive and democratic culture promoting positive relationships between THL staff, board members, and volunteers. We think this is especially important for THL because part of the intention of their local offices is to build a grassroots movement, and setting a positive and results-oriented tone for those new to the movement is good for animal advocacy as a whole... (...)
I'm also directing 10% of my total animal-welfare donation to Animal Charity Evaluators, to support their work that helped lead me to my decision. Unlike last year, I'm not able to find a public indication that they have little room for funding in the immediate term, and I want to continue a practice of supporting evaluators I trust (as I did for GiveWell before I began donating unrestricted funds to them instead).
(far future)
Large donation to the Machine Intelligence Research Institute, conducting basic research on intelligence alignment to make better lives for humans in the future.
Small donation to the Future of Humanity Institute, focusing on political challenges arising from transformative AI to make better lives for humans in the future.
I’m far from certain, but my best guess for the most important problem facing us today is lowering the probability that powerful artificial intelligence agents with goals misaligned with human flourishing are developed (or allowed to develop). I want to continue my support of MIRI's contributions to a foundational understanding of intelligence, and of FHI's Governance of AI Program.
I considered an allocation to EA Funds' Far Future Fund, but I value the potential to instead consider the space of far-future donation opportunities first-hand, in the event I'm selected to allocate donor-lottery funds.
A number of friends I talked to mentioned the opportunity for large donors to donate to a major organization aiming to develop General AI systems, with the goal of influencing them favorably towards issues of AI safety and alignment. For donors on my scale, I find this a particularly attractive case for donor lotteries, as donor-lottery winners can build deeper communication channels and better exert influence than can a group of smaller donors.
nb: In mid-2018, I directed a small-for-2017 donation to the Road to AI Safety Excellence, when they were first seeking funding. I'm not supporting them further at this time.
(meta)
Large donation to 80,000 Hours, supporting efforts to grow the effective altruism community.
Medium donation to the Centre for Effective Altruism, providing continuing support to the effective altruism community.
My thinking about organizations in this section, more than any other, relies primarily on first- and second-hand subjective judgments of the track records and principals of the organizations involved.
In general terms, I'm impressed by instances where both of these organizations stepped up to execute an on-reflection-promising approach (that no one else was pursuing) to increasing the impact of aspiring effective altruists, or helping existing members of the community to think better about making the world better. In some cases I have positive subjective opinions about their principals or donors I may be funging donations with; in others I have relatively little. I'm happy to talk about these things more privately, but don't really wish to do so here in public.
nb: I was very excited specifically about CEA's leadership at the end of 2017; after some amount of personnel turnover in the past year, I now have little private information about their leadership in particular, and am primarily weighing their track record -- which I feel warrants the support I'm maintaining.
I expect that if I were to direct more to this 'meta' bucket from my current state of knowledge, I would donate to EA Funds' Effective Altruism Meta Fund, which has in fact donated to both of the above organizations in the past, as well as others that I considered positively but decided not to direct non-lottery donations to.
(2b)
Summary (and direct links to donation pages):
(3)
Charity evaluators’ reports:
Personal writeups, roughly in the order I saw them:
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2019-05-21 01:46:16
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https://math.stackexchange.com/questions/1761955/prove-that-3d-rotation-is-linear
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# Prove that 3d rotation is linear
In a 2d space, a transformation is linear if $f(v+w) = f(v) + f(w)$ and $f(kv) = k*f(v)$, and rotation preserves addition so it is linear. In a 3d space, similar rules apply: $(x, y, z) + (l, j, k) = (x + t, y + j, z + k)$, and $k(x, y, z) = (kx, ky, kz)$.
It follows that applying a given rotation matrix in 3d space
(for example $M = \begin{bmatrix} 1 & 0 & 0 \\ 0 & cos\theta & -sin\theta \\ 0 & sin\theta & cos\theta\end{bmatrix}$ )
should also be linear. The above is just a rotation along the x-axis so it seems trivial. How can I prove that all 3d rotations are linear, given a rotation matrix M?
Edit
How can I prove that all 3d rotations are linear using the definition of linearity, ie using multiplication and addition? Can I use the fact that rotation itself is multiplication, and it preserves addition?
• I think this is probably related to the parallelogram rule for adding vectors – Akiva Weinberger Apr 27 '16 at 23:38
• @AkivaWeinberger I think it is too, just not sure how to show that. – jackwise Apr 27 '16 at 23:42
• IMHO, this question either doesn't make sense or is a tautology. If your rotation is given as a matrix, then since matrix multiplication is linear, the rotation is linear. I think you should pick a definition of rotation that doesn't use matrix at all. e.g. any transform which 1) fix the origin and 2) preserve euclidean distances between any two points and then show that transform has to be a linear one. – achille hui Apr 28 '16 at 3:08
Any rotation is a rotation around some axis. You can write it as a change of basis matrix times a standard rotation matrix (similar to $R_x$, but just being around another non standard axis) in the new basis, then back to the standard basis. So it is just matrix multiplication, and matrix multiplication is linear.
$M$ is a rotation matrix and generates a linear transformation $T$. It operates on vectors $v$ by $T(v)=Mv$. Matrix multiplication is linear, so $T$ is a linear transformation.
• I'm not that great at words & math - could you please give an example? – jackwise Apr 27 '16 at 23:45
• It may be clearer to note that any rotation matrix can be written as a product $M=R_xR_yR_z$. But all we need is that a rotation is a matrix, and that matrix multiplication is linear. – jdods Apr 27 '16 at 23:57
• Is it necessary to change the basis at all? It seems that if the rotation matrix multiplication is linear, that should be enough to begin with. – theREALyumdub Apr 27 '16 at 23:57
• No, but since op knew a standard rotation matrix was linear, I figured it would help since any rotation is rotation around an axis. I.E. just a standard rotation in some basis. – jdods Apr 28 '16 at 0:00
• @jdods I clarified my question, not sure if your answer still applies. – jackwise Apr 28 '16 at 0:30
I think this question has nothing to do with bases and matrix representations. This question is an excellent example of treating linear transformations on their own terms rather than analyzing their component space representations.
A transformation is linear if it doesn't matter if you add two vectors first and then transform the sum or if you transform each vector first and then add together the results + and the same for multiplication by a scalar. Here's a video that explains this: https://www.lem.ma/17
And here's a video that shows that rotations are linear: https://www.lem.ma/gs The video is for rotations in the plane, but there is no difference as far as linearity is concerned.
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2019-09-16 01:57:26
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https://www.pims.math.ca/scientific-event/150311-tsek
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Topology Seminar: Eiko Kin
• Date: 03/11/2015
Speaker(s):
Eiko Kin, Osaka University
Location:
University of British Columbia
Topic:
Pseudo-Anosovs with small dilatations in the hyperelliptic handlebody groups and spherical Hilden groups
Description:
This is a joint work with Susumu Hirose. We consider pseudo-Anosov elements of the mapping class groups on orientable surfaces. We are interested in a numerical invariant of pseudo-Anosovs, called the dilatation. The logarithm of the dilatation of a pseudo-Anosov mapping class is called the entropy. If we fix a surface, then the set of dilatations of pseudo-Anosovs defined on the surface is closed and discrete. In particular we can talk about a minimum of any subset of dilatations defined on the surface in question.
Penner proved that the minimal entropy of pseudo-Anosovs defined on a closed surface of genus g behaves like 1/g. Later Hironaka proved that the minimal entropy of pseudo-Anosovs in the handlebody subgroup on a closed surface of genus $g$ also behaves like 1/g. We prove that the the minimal entropy of the hyperelliptic handlebody sugbroup of genus g has the same asymptotic behavior. (Our examples of pseudo-Anosovs improve the upper bound of the minimal entropy of the handlebody sugbroup given by Hironaka.) To do this, we study the spherical Hilden subgroup of the mapping class group defined on a sphere with 2n punctures, and we construct a sequence of pseudo-Anosovs with small dilatations in the spherical Hilden subgroups.
Other Information:
Location: ESB 4133
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2022-11-29 17:47:59
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https://ee.gateoverflow.in/817/gate-electrical-2017-set-2-question-20
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Let $y^{2}-2y+1=x$ and $\sqrt{x}+y=5$. The value of $x+\sqrt{y}$ equals _________. (Give the answer up to three decimal places).
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2023-02-03 10:49:47
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http://www.chegg.com/homework-help/questions-and-answers/thedrawing-shows-identical-systems-objects-consistsof-small-balls-massesm1-906-kg-m2-418-k-q391779
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## rotational dynamics
Thedrawing below shows two identical systems of objects: each consistsof three small balls of massesm1 = 9.06 kg,m2 = 4.18 kg,and m3 = 7.32 kg, respectively, connected to each other asshown by massless rods. In both systems the axis of rotation isperpendicular to the page, but is located at a different place asshown for each system.
(a)Determine the moment of inertia of each system.
IA = kg·m2
IB = kg·m2
(b) The same force F whose magnitudeis 448 N is applied to the sameball in each system as the drawing shows. Calculate the net torque,magnitude and direction, felt by each system.
A = N·m
B = N·m
(c) Assume the two systems start from rest at the same instant. Asa result of the net torque felt by each system determine theangular speed of each system 10.0 s later.
I have tried this problem 4 times and I amstruggling
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2013-05-19 16:52:01
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https://www.cheenta.com/geometry-of-cauchy-schwarz-inequality/
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# Understand the problem
Cauchy Schwarz Inequality is a powerful tool in Algebra. It was beautiful geometric implications as well. Watch the video and solve the tutorial problems to delve deep into the idea.
# Tutorial Problems!
[/et_pb_text][et_pb_text _builder_version="4.0.6"]1. Look at the expression $\sqrt{x_1^2 + y_1^2} \times \sqrt {x_2^2 + y_2^2} \geq (x_1 x_2 + y_1 y_2 )$ Can you simply square both sides and prove this ? 2. Show that if A, B are any two points in the plane and O is the origin then cosine of the angle AOB is the ratio of $$\frac{\text{dot product of the coordinates}} {\text{product of their distances from origin}}$$[/et_pb_text][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]
# Subscribe to Cheenta's youtube channel
[/et_pb_text][et_pb_code _builder_version="4.0.6" hover_enabled="0"]
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2021-06-15 00:21:44
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https://pos.sissa.it/301/025/
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Volume 301 - 35th International Cosmic Ray Conference (ICRC2017) - Session Solar & Heliospheric. SH-Heliospheric transport and solar modulation
Tracking cosmic-ray spectral variations with neutron monitor time-delay measurements at high cutoff rigidity during 2007-2017
C. Banglieng, D. Ruffolo,* A. Sáiz, P. Evenson, T. Nutaro
*corresponding author
Full text: pdf
Pre-published on: August 16, 2017
Published on: August 03, 2018
Abstract
We present measurements of the leader fraction of neutron monitor counts that did not follow other counts in the same counter tube from the same cosmic ray shower. We use time-delay histograms collected at the Princess Sirindhorn Neutron Monitor at Doi Inthanon, Thailand, which has the world's highest vertical cutoff rigidity for a fixed station (16.8 GV). Changes in the leader fraction are a precise indicator of cosmic ray spectral variations above the cutoff. Our data set from 2007 to 2017 spans a full cycle of solar modulation, including the all-time cosmic ray maximum of 2009 and minimum near the end of 2014, the count rate now having returned to its initial value. The electronics to collect time-delay histograms have been upgraded twice, and we have corrected for such changes to develop a long-term leader fraction dataset. We examine the spectral variation of Galactic cosmic rays above $\sim$17 GV resulting from solar modulation and its solar magnetic polarity dependence.
DOI: https://doi.org/10.22323/1.301.0025
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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2020-12-02 22:46:37
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https://wikimili.com/en/Mollweide_projection
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# Mollweide projection
Last updated
The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.
## Contents
The projection was first published by mathematician and astronomer Karl (or Carl) Brandan Mollweide (1774–1825) of Leipzig in 1805. It was reinvented and popularized in 1857 by Jacques Babinet, who gave it the name homalographic projection. The variation homolographic arose from frequent nineteenth-century usage in star atlases. [1]
## Properties
The Mollweide is a pseudocylindrical projection in which the equator is represented as a straight horizontal line perpendicular to a central meridian one-half its length. The other parallels compress near the poles, while the other meridians are equally spaced at the equator. The meridians at 90 degrees east and west form a perfect circle, and the whole earth is depicted in a proportional 2:1 ellipse. The proportion of the area of the ellipse between any given parallel and the equator is the same as the proportion of the area on the globe between that parallel and the equator, but at the expense of shape distortion, which is significant at the perimeter of the ellipse, although not as severe as in the sinusoidal projection.
Shape distortion may be diminished by using an interrupted version. A sinusoidal interrupted Mollweide projection discards the central meridian in favor of alternating half-meridians which terminate at right angles to the equator. This has the effect of dividing the globe into lobes. In contrast, a parallel interrupted Mollweide projection uses multiple disjoint central meridians, giving the effect of multiple ellipses joined at the equator. More rarely, the projection can be drawn obliquely to shift the areas of distortion to the oceans, allowing the continents to remain truer to form.
The Mollweide, or its properties, has inspired the creation of several other projections, including the Goode's homolosine, van der Grinten and the Boggs eumorphic. [4]
## Mathematical formulation
The projection transforms from latitude and longitude to map coordinates x and y via the following equations: [5]
{\displaystyle {\begin{aligned}x&=R{\frac {2{\sqrt {2}}}{\pi }}\left(\lambda -\lambda _{0}\right)\cos \theta ,\\[5px]y&=R{\sqrt {2}}\sin \theta ,\end{aligned}}}
where θ is an auxiliary angle defined by
${\displaystyle 2\theta +\sin 2\theta =\pi \sin \varphi \qquad (1)}$
and λ is the longitude, λ0 is the central meridian, φ is the latitude, and R is the radius of the globe to be projected. The map has area 4πR2, conforming to the surface area of the generating globe. The x-coordinate has a range of [−2R2, 2R2], and the y-coordinate has a range of [−R2, R2].
Equation (1) may be solved with rapid convergence (but slow near the poles) using Newton–Raphson iteration: [5]
{\displaystyle {\begin{aligned}\theta _{0}&=\varphi ,\\\theta _{n+1}&=\theta _{n}-{\frac {2\theta _{n}+\sin 2\theta _{n}-\pi \sin \varphi }{2+2\cos 2\theta _{n}}}.\end{aligned}}}
If φ = ±π/2, then also θ = ±π/2. In that case the iteration should be bypassed; otherwise, division by zero may result.
There exists a closed-form inverse transformation: [5]
{\displaystyle {\begin{aligned}\varphi &=\arcsin {\frac {2\theta +\sin 2\theta }{\pi }},\\[5px]\lambda &=\lambda _{0}+{\frac {\pi x}{2R{\sqrt {2}}\cos \theta }},\end{aligned}}}
where θ can be found by the relation
${\displaystyle \theta =\arcsin {\frac {y}{R{\sqrt {2}}}}.\,}$
The inverse transformations allow one to find the latitude and longitude corresponding to the map coordinates x and y.
## Related Research Articles
The Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because of its unique property of representing any course of constant bearing as a straight segment. Such a course, known as a rhumb or, mathematically, a loxodrome, is preferred by navigators because the ship can sail in a constant compass direction to reach its destination, eliminating difficult and error-prone course corrections. Linear scale is constant on the Mercator in every direction around any point, thus preserving the angles and the shapes of small objects and fulfilling the conditions of a conformal map projection. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation starts infinitesimally, but accelerates with latitude to become infinite at the poles. So, for example, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system.
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3).
In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north.
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.
The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.
The Bottomley map projection is an equal area map projection defined as:
In cartography, a Tissot's indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.
The van der Grinten projection is a compromise map projection, which means that it is neither equal-area nor conformal. Unlike perspective projections, the van der Grinten projection is an arbitrary geometric construction on the plane. Van der Grinten projects the entire Earth into a circle. It largely preserves the familiar shapes of the Mercator projection while modestly reducing Mercator's distortion. Polar regions are subject to extreme distortion.
The Hammer projection is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide.
The Cassini projection is a map projection described by César-François Cassini de Thury in 1745. It is the transverse aspect of the equirectangular projection, in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Considering the earth as a sphere, the projection is composed of the operations:
In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates. There are two kinds: the regular solid harmonics, which vanish at the origin and the irregular solid harmonics, which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately:
The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. In each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert IV is the Eckert III projection.
The Eckert II projection is an equal-area pseudocylindrical map projection. In the equatorial aspect the network of longitude and latitude lines consists solely of straight lines, and the outer boundary has the distinctive shape of an elongated hexagon. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert II is the Eckert I projection.
The Boggs eumorphic projection is a pseudocylindrical, equal-area map projection used for world maps. Normally it is presented with multiple interruptions. Its equal-area property makes it useful for presenting spatial distribution of phenomena. The projection was developed in 1929 by Samuel Whittemore Boggs (1889–1954) to provide an alternative to the Mercator projection for portraying global areal relationships. Boggs was geographer for the United States Department of State from 1924 until his death. The Boggs eumorphic projection has been used occasionally in textbooks and atlases.
The Equal Earth map projection is an equal-area pseudocylindrical projection for world maps, invented by Bojan Šavrič, Bernhard Jenny, and Tom Patterson in 2018. It is inspired by the widely used Robinson projection, but unlike the Robinson projection, retains the relative size of areas. The projection equations are simple to implement and fast to evaluate.
The Nicolosi globular projection is a map projection invented about the year 1,000 by the Iranian polymath al-Biruni. As a circular representation of a hemisphere, it is called globular because it evokes a globe. It can only display one hemisphere at a time and so normally appears as a "double hemispheric" presentation in world maps. The projection came into use in the Western world starting in 1660, reaching its most common use in the 19th century. As a "compromise" projection, it preserves no particular properties, instead giving a balance of distortions.
The Strebe 1995 projection, Strebe projection, Strebe lenticular equal-area projection, or Strebe equal-area polyconic projection is an equal-area map projection presented by Daniel "daan" Strebe in 1994. Strebe designed the projection to keep all areas proportionally correct in size; to push as much of the inevitable distortion as feasible away from the continental masses and into the Pacific Ocean; to keep a familiar equatorial orientation; and to do all this without slicing up the map.
The Eckert-Greifendorff projection is an equal-area map projection described by Max Eckert-Greifendorff in 1935. Unlike his previous six projections, It is not pseudocylindrical.
## References
1. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 112113, ISBN 0-226-76747-7.
2. Gannon, Megan (December 21, 2012). "New 'Baby Picture' of Universe Unveiled". Space.com . Retrieved December 21, 2012.
3. Bennett, C.L.; Larson, L.; Weiland, J.L.; Jarosk, N.; Hinshaw, N.; Odegard, N.; Smith, K.M.; Hill, R.S.; Gold, B.; Halpern, M.; Komatsu, E.; Nolta, M.R.; Page, L.; Spergel, D.N.; Wollack, E.; Dunkley, J.; Kogut, A.; Limon, M.; Meyer, S.S.; Tucker, G.S.; Wright, E.L. (2013). "Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results". The Astrophysical Journal Supplement Series . 208 (2): 20. arXiv:. Bibcode:2013ApJS..208...20B. doi:10.1088/0067-0049/208/2/20.
4. Map Projections – A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 249252
5. Weisstein, Eric W. "Mollweide Projection". MathWorld .
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2020-06-03 06:42:00
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https://www.komal.hu/verseny/2004-01/inf.e.shtml
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Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up? New to KöMaL?
# Exercises and problems in InformaticsJanuary 2004
I. 67. There are N teams playing a round tournament (2$\displaystyle \le$N $\displaystyle \le$100, with N even). Write your program (i67.pas, ...) that displays a draw for rounds fulfilling the requirements that every team should play in any round, and should meet with any other team exactly once.
See the example for N=4:
Team 1 2 3 4 Round 1 2 1 4 3 Round 2 3 4 1 2 Round 3 4 3 2 1
(10 points)
I. 68. Any binary tree can be represented as a parenthetical expression. For example, (X) corresponds to a tree with one node, while ((X)X(X)) denotes a tree consisting of the root and its left and right child. See further examples.
((X)X) (X(X)) (((X(X))X)X((X)X((X)X(X))))
Write your program (i68.pas, ...) whose input is a parenthetical expression representing a binary tree (containing at least one node), then displays the tree (see the figures). (10 points)
I. 69. Prepare a sheet (i69.xls) so that one can write both into its first and second rows a strictly monotone increasing integer sequence having at most 100 terms. Both sequences will terminate in an empty cell. After the sequences have been entered, a merged sequence should appear in the third row, that is the strictly monotone increasing sequence consisting of the terms of the original ones, but with terms occurring in both of them listed only once. (Solutions using macros are awarded at most half of the score.)
First 1 3 5 7 9 11 13 15 Second 1 4 7 10 13 16 Merged 1 3 4 5 7 9 10 11 13 15 16
(10 points)
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2021-09-26 08:54:40
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https://datascience.stackexchange.com/questions/82915/how-to-convert-dataframe-column-to-rows-in-python
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# How to convert DataFrame column to Rows in Python?
I have the following dataset in df_1 which I want to convert into the format of df_2. In df_2 I have converted the columns of df_1 to rows in df_2 (excluding UserId and Date). I looked up for similar answers but they are providing little complex solutions. Is there a simple way to do this?
df_1
UserId Date -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
87 2011-05-10 18:38:55.030 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
487 2011-11-29 14:46:12.080 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
21 2012-03-02 14:35:06.867 0 1 0 1 2 0 2 2 0 1 2 2 1 3 1
df_2
day | count
-7 0
-7 0
-7 0
-6 0
-6 0
-6 1
-5 0
-5 1
-5 0
. .
. .(Similarly for other columns in between)
. .
6 0
6 0
6 3
7 0
7 0
7 1
Try using pandas melt
dataT = pd.DataFrame({"userID":[1,2,3],"date":["2020-01-01","2019-01-02","2020-08-12"],"-7":[0,1,1],"-6":[1,0,0],"-5":[0,0,0]})
Input:
dataT.melt(value_vars= ["-7","-6","-5"], value_name="count")
Output:
Update
By taking the comment by Benji the code would be:
dataT.melt(id_vars= ["userID","date"], value_name="count")
With output:
• Note that the melt function can also use a "blacklist" of columns, id_vars, where the given answer uses value_vars as a "whitelist". So you could do dataT.melt(id_vars=["userID","date"], value_name="count") to melt all the subsequent columns – Benji Albert Oct 12 '20 at 17:36
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2021-01-17 22:28:52
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https://www.computer.org/portal/web/toh
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# IEEE Transactions on Haptics
Expand your horizons with Colloquium, a monthly survey of abstracts from all CS transactions! Replaces OnlinePlus in January 2017.
## Development and Experimental Validation of a Haptic Compass Based on Asymmetric Torque Stimuli
By Jean-Philippe Choiniere and Clement Gosselin
This paper presents the design, control, and experimental validation of a haptic compass, designed as a guiding device for all environments. The proposed device uses the principle of asymmetric torques. Its design is based on a direct drive motor and a pre-calibrated open-loop control, which allows the generation of stimuli in a wide range of frequencies. User studies are presented and show optimum effectiveness in the frequency range 5-15 $\mathrm{\mathrm{Hz}\;a}$ nd for torques over $40\; \mathrm{m}\mathrm{N}\mathrm{m}$ . The use of a haptic feedback proportional to the angle error is then shown to significantly improve the results. An experimental validation by a group of‘ subjects with the portable device using these stimuli is reported. The results show that all subjects met all route objectives with small lateral deviations (avg. $\mathrm{0.39\;\mathrm{m}}$ ).
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## Access recently published ToH articles
Subscribe to the RSS feed of latest ToH content added to the digital library.
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2017-03-25 12:01:35
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https://askdev.io/questions/788/what-stops-you-from-updating-to-more-recent-operating-system
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# What stops you from updating to more recent operating system variations?
What's the leading the factor you're incapable - or resistant - to update to the most up to date readily available operating system verions?
0
2019-05-04 10:04:08
Source Share
• Current one is still sustained by the supplier
• New one does not collaborate with existing software program (and also I can not get a substitute for the existing software program)
• New one does not collaborate with existing equipment (and also I have no spending plan to upgrade/replace equipment)
• The firm I benefit has actually not yet examined the OS from an useful and also security viewpoint
0
2019-12-03 04:43:05
Source
If not USB assistance - i would certainly still be runing windows NT 4 sp6. Yet given that I relocated to 2000 I get on every new customer os as quickly as it ventures out, simply to see where MS are selecting it. And also just tonns of saved information can stop me for some time, yet except also lengthy.
0
2019-12-03 04:37:57
Source
Time participation and also security, whether speaking about Linux or Windows. With Windows, I have not attempted an upgrade in a long period of time, yet experience has actually educated me to stay clear of the first release of any kind of Windows OS. I constantly wait till SP1 appears, unless I listen to or else from close friends that are very early adopters.
With Linux, I've constantly made use of Red Hat. With Fedora, Red Hat launches have actually come to be extra bleeding side than they made use of to be. As a result of this, I do not hurry to update my Fedora equipments. I wait till a release has actually been out at the very least a couple of weeks and also I read testimonials from very early adopters.
I have no experience with Mac (pertaining to installation and also upgrades), yet with Windows and also with Linux, I locate new launches are usually not fairly all set for prime-time show. I recognize if I made use of a much less bleeding side Linux circulation (such as Debian) after that it would possibly be extra secure to update as quickly as a release appears, yet I'm a hacker ago, and also I such as addressing troubles. (That's one factor I'm on SO and also SF!)
Over I spoke about the security facet. For any kind of OS, it's usually less complicated to re-install as opposed to upgrade. For Linux, I'll usually update one or two times (a year apart) and afterwards do a full reinstall instead of the next upgrade. For Windows, I generally simply change the equipment and also install a new OS on the new equipment. Why ever before re-install Linux? Well, as open resource breakthroughs, some plans are changed or thrown out. When you update, littles flotsam are left, some in /etc and also some in /var and also some in various other areas. On a re - install, every one of that cruft is cleansed away.
That's the moment participation. Doing an upgrade requires time to clean up cruft (in Linux, *. rpmnew and also *. rpmsave, as an example). A complete reinstall requires time, certainly, to make certain that absolutely nothing is shed, every little thing is reconfigured and also re-installed, and more.
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2019-05-11 22:56:32
Source
I make use of Linux at the workplace (Ubuntu 8.10) and also I am really skeptical of updates around the bit/ vehicle driver location or upgrading to new variations (i.e. 9.04) due to the fact that:
• It presently functions
• I can not manage to not be effective for a day+while I re-install my OS
At residence it's a various tale since that's my time ...
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2019-05-09 01:08:08
Source
I made use of to be the sort of individual that would certainly leap to the most up to date OS as quickly as it ran out beta. Yet with the change from XP to Vista, I have actually come to be extra mindful and also traditional. You've all listened to the scary tales concerning straightforward points that damaged. For me it was the capacity to connect to my firm's VPN and also make use of remote desktop computer to reach my job equipment, which by the way, I still can not start.
That experience, paired with the breakthroughs we've seen in virtualization lately (that makes attempting an OS prior to you devote far more sensible), suggests I'll be a lot slower on the uptake of Windows 7.
Brief solution : I obtained burned. Discomfort is a superb educator.
0
2019-05-09 01:03:05
Source
• Inefficiency of the new operating system (as an example Vista)
• Speed of executing usual jobs
• No new attributes which I actually such as.
0
2019-05-09 00:56:54
Source
Stability. We understand the applications work with the OS they're working on, and also any kind of adjustment to the setting can present unplanned effects. Generally the OS is upgraded at the very same time we're intending to release new hardware. We can acquire the hardware, set up the OS, install the software program and also examination, examination, after that examine some even more prior to releasing to the manufacturing setting.
0
2019-05-08 09:12:18
Source
I assume it relies on the regularity the software program is updated. If a new variation appears every 3-6 months, I would certainly be updating systems virtually day-to-day.
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2019-05-08 03:10:12
Source
1. Price
2. As much as windows is worried, prior to the 1st solution pack is generally buggy
3. Time
virtually because order
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2019-05-08 03:05:23
Source
I'm generally eager to update to the most up to date variations of an OS, nonetheless one of the most usual factors I have actually located for individuals not intend to upgrade is either the compatability of old software program, or otherwise intending to find out a new OS.
0
2019-05-08 03:03:59
Source
The existing one simply functions!
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2019-05-08 02:58:08
Source
The problem of re-installing all my applications is the # 1 factor for me. That and also the reality that also after I re-install, there'll most likely be conflicts.
0
2019-05-08 02:55:31
Source
Upgrading the OS on a web server that is organizing great deals of internet sites suggests several several hrs re-installing the websites on the new web server, as well as the downtime and also the ever-present threat of missing out on some undocumented third-party part or solution mounted on the old web server.
Very same holds true on a computer (though even more of the job enters into re-installing applications, and also reconfiguring the setting).
If it ain't damaged, do not repair it.
0
2019-05-08 02:49:22
Source
Having a huge estate of computer systems which all require to be updated with each other. Having numerous Operating Systems or variations of running systems makes complex assistance.
Needing to move great deals of equipments simultaneously is additionally extra difficult and also calls for even more application compatibility examining ahead of time and also customer assistance after.
0
2019-05-08 02:47:09
Source
One Lession that I found out by hand sometimes, I treat it as a regulation : You can NOT update Windows. Formatting/Reinstalling is much faster than "updating" and also managing the concerns. I've obtained attacked by this so usually, despite having apparently straight-forward upgrades like Win2000 => WinXP.
The various other factor is the "Never touch a running system" regulation. If it runs and also there are no security susceptabilities influencing it , do not touch it.
0
2019-05-08 02:39:33
Source
In a great deal of instances, the compatibility of vital software program is not recognized. It might be also worse if the software program was not upgraded given that time.
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2019-05-08 02:32:20
Source
For me, it needs to be downtime & loss of performance.
On the desktop front, despite the fact that I attempt and also maintain my system reasonably "tidy" in regards to what is mounted, it is still set up specifically just how I require it. In the past, I've located it takes 2 or 3 days each year's well worth of information/ applications/ setups to move to a tidy OS install : with information being one of the most time consuming - looking into ratings of tasks from a six various SVN databases simply isn't a fast procedure.
On the web server front, "upgrade" is a little a misnomer : I would certainly never ever before update the whole OS of a web server whilst it was "real-time" : essential spots would certainly be regarding I went (if it ain't damaged, do not repair it). When picking a new web server, it actually relies on the needs, yet others have actually claimed, it's not actually worth the problem of getting on the crest of the wave with a new OS - allow others that can manage to expend troubles experimentation it.
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2019-05-08 02:08:17
Source
I register for the "If it ain't damaged" plan, specifically on web server variations. Needing to go via the discomfort of exercising just how to get every little thing up and also operating in the new variation often tends to maintain me with the variation I presently have.
Just when the new attributes come to be crucial and also called for do I really feel the demand to experience the process once more. And afterwards just when the new crucial attributes surpass the process of exercising just how to get every little thing functioning once more.
0
2019-05-08 00:16:27
Source
I constantly layout/ install. NEVER upgrade. Maintain it wonderful and also tidy. way too many areas crap can get shed or dup 'd.
Yet if u suggest going from older variation to a new variation, it's usually
1. Price
2. Having to re-install every little thing once more.
modify : This is describing Windows OS, not linux, and so on
0
2019-05-08 00:05:43
Source
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2021-05-17 20:15:36
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https://gcseguide.co.uk/maths/trigonometry/sin-cos-tan/
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# Sin, Cos, Tan Graphs
Want to download the Sin, Cos, Tan revision notes in PDF format?
In any right angled triangle, for any angle:
The sine of the angle = the length of the opposite side
the length of the hypotenuse
The cosine of the angle = the length of the adjacent side
the length of the hypotenuse
The tangent of the angle = the length of the opposite side
the length of the adjacent side
The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.
sin = o/h cos = a/h tan = o/a
Often remembered by: soh cah toa
Example:
Find the length of side x in the diagram below:
The angle is 60 degrees. We are given the hypotenuse and need to find the adjacent side. This formula which connects these three is:
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2022-01-26 07:57:38
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https://fykos.org/problems/start?tasktag=astroFyz
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# Search
## astrophysics
### (10 points)6. Series 33. Year - S.
We are sorry. This type of task is not translated to English.
### (3 points)4. Series 33. Year - 1. tchibonaut
Consider an astronaut of weight $M$ remaining still (with respect to a space station) in zero-g state, holding a heavy tool of weight $m$. The distance between the astronaut and the wall of the space station is $l$. Suddenly, he decides to throw the tool against the wall. Find his distance from the wall when the tool hits it.
Karel wanted to set this name for this problem.
### (10 points)4. Series 32. Year - P. V-1 in the space
The interstellar space is not empty but contains an insignificant amount of mass. For simplicity, assume hydrogen only and look up the required density. Could we build a spaceship that would „suck in“ the hydrogen and would use energy from it? How fast/large would the spaceship have to be in order to keep up the thermonuclear fusion only from the acquired hydrogen? What reasonable obstacles in realization should we consider?
crypto-facism → Red Dwarf → drive → thrust → V-1 and the circle closes
### (12 points)1. Series 32. Year - E. hourly
Measure the length of one day. However, there is a limitation: one continuous measurement can't take longer than one hour. For the sake of statistical accuracy, though, do repeat your measurements multiple times.
### (10 points)1. Series 32. Year - P. terrible cold
Some nebulas constituted of a gas from stars, e. g. Bumerang, have lower temperature than the Cosmic Microwave Background (CMB), hence are technically colder than space. How is this possible? Try to determine a condition for a gas ejected by a hot star to cool down below the temperature of the CMB.
Karel wasn't satisfied with the claim that the temperature everywhere in space is at least that of the CMB.
### (9 points)6. Series 31. Year - P. universe expansion compensation
According to the current observations and cosmological models, it seems that our Universe is expanding and the rate of expansion is accelerating. What if that wasn't the case? What if the Universe stayed the same, but the physical laws/constants were changing so that it would seem like the universe is expanding, the way we observe it? Describe as many laws that would need to change.
Karel was intrigued whether one can compensate the expansion of universe.
### (9 points)4. Series 31. Year - P. Voyager II and Voyager I live!
We have a satellite and we want to launch it out of the Solar System. We launch it from Earth's orbit so that after some corrections of the trajectory it gets a velocity which is higher than the escape velocity from the Solar System. What is the probability that the satellite will collide with some cosmic material with higher diameter that $d=1 \mathrm{m}$ before leaving the Solar System.
Karel was wondering why NASA doesn't consider this possibility…
### (3 points)2. Series 31. Year - 2. solar power plant
The solar constant, or more accurately the solar irradiance, is the influx of energy coming from the Sun at the distance where Earth is. It technically doesn't have a constant value, but let's suppose it is approximately $P = 1{,}370\,\mathrm{W\cdot m^{-2}}$. Also, suppose that Earth's orbit is circular and its axis of rotation is tilted with respect to the normal of the orbital plane by $23.5\dg$. What would be the maximum power captured by a solar panel of area $S= 1\,\mathrm{m^2}$ at the summer and winter solstice, if the panel lies flat on the ground in Prague (latitude $50\dg$ N)? Ignore the effects of any obstructions or the atmosphere.
Karel watched Crash Course Astronomy
### (6 points)2. Series 31. Year - 3. observing
What fraction of a spherical planet's surface cannot be seen from the stationary orbit above the planet? (A stationary orbit is one where the satellite stays fixed above a certain point on the planet.) The density of the planet is $\rho$ and its rotation period is $T$.
Filip went through the unseen competition problems.
### (6 points)2. Series 31. Year - 4. nuclear waste no more
Imagine we have a thing (e.g. a nuclear waste container) and we want to get rid of it. We transfer the object to a circular orbit around the Sun at the same distance as Earth, but far enough from Earth to ignore its gravitational influence. Which of these methods of the objects disposal would require the least amount of energy and thus would be the most efficient?
• Throw it into the Sun. Getting it to the solar surface would be sufficient to burn the object.
• Transfer it to a circular orbit in the Asteroid belt (located between the orbits of Mars and Jupiter).
• Get it out of the Solar System completely.
Karel thought about what exactly is SEO and discovered this problem.
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2020-09-19 15:38:05
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http://forum.math.toronto.edu/index.php?topic=1104.msg3880
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### Author Topic: Fourier Transform and IFT table (Read 1103 times)
#### Ruite Xu
• Newbie
• Posts: 4
• Karma: 1
##### Fourier Transform and IFT table
« on: March 20, 2018, 11:02:21 AM »
When I went through application of Fourier transformation in PDE, I found that, for many of them we need to use the convolution theorem, which means we also need to know many IFT (inverse fourier) of some functions such as Gaussian and Exponential, so I want to ask if in test there will be hint tells us some related IFT, or we need to remember them all by ourselves?
#### Victor Ivrii
• Administrator
• Elder Member
• Posts: 2553
• Karma: 0
##### Re: Fourier Transform and IFT table
« Reply #1 on: March 20, 2018, 01:35:56 PM »
I provide either FT or hint
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2020-11-27 11:39:58
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https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/02%3A__Relativity/2.07%3A_Relativistic_Velocity_Transformation
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$$\require{cancel}$$
# 2.7: Relativistic Velocity Transformation
Learning Objectives
By the end of this section, you will be able to:
• Derive the equations consistent with special relativity for transforming velocities in one inertial frame of reference into another.
• Apply the velocity transformation equations to objects moving at relativistic speeds.
• Examine how the combined velocities predicted by the relativistic transformation equations compare with those expected classically.
Remaining in place in a kayak in a fast-moving river takes effort. The river current pulls the kayak along. Trying to paddle against the flow can move the kayak upstream relative to the water, but that only accounts for part of its velocity relative to the shore. The kayak’s motion is an example of how velocities in Newtonian mechanics combine by vector addition. The kayak’s velocity is the vector sum of its velocity relative to the water and the water’s velocity relative to the riverbank. However, the relativistic addition of velocities is quite different.
## Velocity Transformations
Imagine a car traveling at night along a straight road, as in Figure $$\PageIndex{1}$$. The driver sees the light leaving the headlights at speed $$c$$ within the car’s frame of reference. If the Galilean transformation applied to light, then the light from the car’s headlights would approach the pedestrian at a speed $$u = v + c$$, contrary to Einstein’s postulates.
Both the distance traveled and the time of travel are different in the two frames of reference, and they must differ in a way that makes the speed of light the same in all inertial frames. The correct rules for transforming velocities from one frame to another can be obtained from the Lorentz transformation equations.
## Relativistic Transformation of Velocity
Suppose an object P is moving at constant velocity $$u = (u'_x, u'_y, u'_z)$$ as measured in the $$S'$$ frame. The $$S'$$ frame is moving along its x'-axis at velocity $$v$$. In an increment of time dt', the particle is displaced by $$dx'$$ along the x'-axis. Applying the Lorentz transformation equations gives the corresponding increments of time and displacement in the unprimed axes:
\begin{align} dt &= \gamma (dt' + vdx' /c^2) \\[4pt] dx &= \gamma (dx' + vdt') \\[4pt] dy &= dy' \\[4pt] dz &= dz'. \end{align}
The velocity components of the particle seen in the unprimed coordinate system are then
\begin{align} \dfrac{dx}{dt} &= \dfrac{\gamma(dx' + vdt')}{\gamma (dt' + v\,dx'/c^2)} = \dfrac{\dfrac{dx'}{dt'} + v}{1 + \dfrac{v}{c^2} \dfrac{dx'}{dt'}} \\[4pt] \dfrac{dy}{dt} &= \dfrac{dy'}{\gamma (dt' + v\,dx'/c^2)} = \dfrac{\dfrac{dy'}{dt'}}{\gamma \left(1 + \dfrac{v}{c^2} \dfrac{dx'}{dt'}\right)} \\[4pt] \dfrac{dz}{dt} &= \dfrac{dz'}{\gamma (dt' + v\,dx'/c^2)} = \dfrac{\dfrac{dz'}{dt'}}{\gamma \left(1 + \dfrac{v}{c^2} \dfrac{dx'}{dt'}\right)} \end{align}
We thus obtain the equations for the velocity components of the object as seen in frame $$S$$:
$u_x = \left(\dfrac{u'_x + v}{1 + vu'_x/c^2}\right), \, u_y = \left(\dfrac{u'_y/\gamma}{1 + vu'_x/c^2}\right), \, u_z = \left(\dfrac{u'_z/\gamma}{1 + vu'_x/c^2}\right).$
Compare this with how the Galilean transformation of classical mechanics says the velocities transform, by adding simply as vectors:
$u_x = u'_x + u, \, u_y = u'_y, \, u_z = u'_z.$
When the relative velocity of the frames is much smaller than the speed of light, that is, when $$v\gg c,$$ the special relativity velocity addition law reduces to the Galilean velocity law. When the speed $$v$$ of $$S'$$ relative to $$S$$ is comparable to the speed of light, the relativistic velocity addition law gives a much smaller result than the classical (Galilean) velocity addition does.
Example $$\PageIndex{1}$$: Velocity Transformation Equations for Light
Suppose a spaceship heading directly toward Earth at half the speed of light sends a signal to us on a laser-produced beam of light (Figure $$\PageIndex{2}$$). Given that the light leaves the ship at speed $$c$$ as observed from the ship, calculate the speed at which it approaches Earth.
Strategy
Because the light and the spaceship are moving at relativistic speeds, we cannot use simple velocity addition. Instead, we determine the speed at which the light approaches Earth using relativistic velocity addition.
Solution
Identify the knowns: $$v = 0.500c$$; $$u' = c$$.
Identify the unknown: $$u$$.
Express the answer as an equation: $$u = \dfrac{v + u'}{1 + \dfrac{vu'}{c^2}}$$.
Do the calculation:
\begin{align*} u &= \dfrac{v + u'}{1 + \dfrac{vu'}{c^2}} \\[4pt] &= \dfrac{0.500c + c}{1 + \dfrac{(0.500c) (c)}{c^2}} \\[4pt] &= \dfrac{(0.500 + 1)c}{\left(\dfrac{c^2 + 0.500c^2}{c^2}\right)} = c. \end{align*}
Significance
Relativistic velocity addition gives the correct result. Light leaves the ship at speed $$c$$ and approaches Earth at speed $$c$$. The speed of light is independent of the relative motion of source and observer, whether the observer is on the ship or earthbound.
Velocities cannot add to greater than the speed of light, provided that $$v$$ is less than $$c$$ and $$u'$$ does not exceed $$c$$. The following example illustrates that relativistic velocity addition is not as symmetric as classical velocity addition.
Example $$\PageIndex{2}$$: Relativistic Package Delivery
Suppose the spaceship in the previous example approaches Earth at half the speed of light and shoots a canister at a speed of $$0.750c$$ (Figure $$\PageIndex{3}$$).
1. At what velocity does an earthbound observer see the canister if it is shot directly toward Earth?
2. If it is shot directly away from Earth?
Strategy
Because the canister and the spaceship are moving at relativistic speeds, we must determine the speed of the canister by an earthbound observer using relativistic velocity addition instead of simple velocity addition.
Solution for (a)
1. Identify the knowns: $$v = 0.500c$$; $$u' = 0.750c$$.
2. Identify the unknown: $$u$$.
3. Express the answer as an equation: $$u = \dfrac{v + u'}{1 + \dfrac{vu'}{c^2}}$$.
4. Do the calculation: \begin{align*} u &= \dfrac{v + u'}{1 + \dfrac{vu'}{c^2}} \\[4pt] &= \dfrac{0.500c + 0.750c}{1 + \dfrac{(0.500c)(0.750c)}{c^2}} \\[4pt] &= 0.909c. \end{align*}
Solution for (b)
1. Identify the knowns: $$v = 0.500c$$; $$u' = - 0.750c$$.
2. Identify the unknown: $$u$$.
3. Express the answer as an equation: $$u = \dfrac{v + u'}{1 + \dfrac{vu'}{c^2}}$$.
4. Do the calculation: \begin{align*} u &= \dfrac{v + u'}{1 + \dfrac{vu'}{c^2}} \\[4pt] &= \dfrac{0.500c + (-0.750c)}{1 + \dfrac{(0.500c)(-0.750c)}{c^2}} \\[4pt] &=- 0.400c. \end{align*}
Significance
The minus sign indicates a velocity away from Earth (in the opposite direction from $$v$$), which means the canister is heading toward Earth in part (a) and away in part (b), as expected. But relativistic velocities do not add as simply as they do classically. In part (a), the canister does approach Earth faster, but at less than the vector sum of the velocities, which would give $$1.250c$$. In part (b), the canister moves away from Earth at a velocity of −0.400c, which is faster than the −0.250c expected classically. The differences in velocities are not even symmetric: In part (a), an observer on Earth sees the canister and the ship moving apart at a speed of 0.409c, and at a speed of 0.900c in part (b).
Exercise $$\PageIndex{1}$$
Distances along a direction perpendicular to the relative motion of the two frames are the same in both frames. Why then are velocities perpendicular to the x-direction different in the two frames?
Although displacements perpendicular to the relative motion are the same in both frames of reference, the time interval between events differ, and differences in $$dt$$ and $$dt'$$ lead to different velocities seen from the two frames.
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2021-03-01 19:50:13
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https://www.risk.net/comment/7652666/swaps-data-initial-margin-soars-in-q1-2020
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# Swaps data: initial margin soars in Q1 2020
## Model procyclicality drives wide variation in CCP IM hikes through Covid-19 volatility, writes Amir Khwaja of ClarusFT
The first quarter of 2020 was unprecedented in almost every way. Global lockdowns intended to control the Covid-19 pandemic tested market liquidity to the limit as financial markets experienced their widest ride in a decade.
A new set of quarterly CPMI-Iosco quantitative disclosures highlight the impact of whipsawing prices on clearing houses during that turbulent first quarter – and they make for an interesting read.
Larger and more frequent price changes result in higher volatility, which in turn feeds into initial margin (IM) requirements. Models produce higher amounts irrespective of whether they are Span, historical simulation, Monte-Carlo simulation or stress scenario based. That is what the data shows, yet differences in relative increases between products and clearing services are surprising.
Categorising clearing services into interest rate swaps, credit default swaps, and futures and options, we see that IM increased in the quarter for these by 23%, 46% and 66% respectively. Some of this difference reflects varying price volatility observed in each of these products. But the biggest contributor comes down to the procyclicality of the models themselves; so how much the IM increases in times of high volatility and decreases in periods of low volatility.
Comparing different clearing services with the same product class also throws up wide divergence. For interest rate swaps the quarterly changes range from 23% to 61% and for credit default swaps from 44% to 65%. For futures and options, we need to be more careful in drawing conclusions as the constituent clearing services are cross-asset, covering rates, equity, commodities and foreign exchange. While larger differences seem reasonable, a range of 20% to 100% for quarterly IM change exceeds expectation.
The magnitude of these relative differences is a topic that warrants more attention and discussion. Should there be more consistency in assumptions of procyclicality of margin? Is that a desirable goal? Is it possible given the diverse markets, models and the design choices for overall risk management? These are huge topics for future debate and discussion, for today, let’s look at the data and detail.
### Cleared interest rate swaps
Starting with the largest over-the-counter product, interest rate swaps and quarterly trends.
Figure 1 shows:
• Total IM of $271 billion, up$51 billion or 23% in the first quarter from the prior quarter (quarter-on-quarter) and up $90 billion or 50% from a year earlier (year-on-year). • LCH SwapClear with$199 billion IM on March 31, 2020, which is up $28 billion or 16.5% quarter-on-quarter and up$54 billion or 37% year-on-year in dollar terms.
• CME IRS with $40 billion, up 38% quarter-on-quarter and 76% year-on-year. • Eurex IRS with$20 billion, up 61% quarter-on-quarter and 207% year-on-year.
• JSCC IRS with $12 billion, up 45% quarter-on-quarter and 93% year-on-year. The cumulative total for these four clearing services of$271 billion IM on March 31, 2020 is a new record and the size of the jump is unprecedented in recent history. While some of this increase will be driven by a changed risk position from the start of the quarter, the bulk of the increase is likely to be from higher market volatility in driving an increase in the IM model requirement.
The relative quarterly increases vary dramatically – 16.5% at LCH SwapClear, 38% at CME, 45% at JSCC and 61% at Eurex. Unless the increase in risk positions cleared at LCH SwapClear was relatively smaller than at the other CCPs, which is unlikely, this suggests the LCH SwapClear IM model is much less procyclical than the other CCPs. Intuitively we may expect this to be the case as the IM model disclosures tell us that LCH SwapClear uses a 10-year lookback period, CME and JSCC are five years, while Eurex is just three years. However, both CME and Eurex IM Model disclosures also state the use of additional stress periods, while JSCC does not. With this in mind, it is understandable that JSCC’s margin increase would be much larger than LCH’s, which it is. It might also be reasonable to expect CME, Eurex and LCH to be in a similar ballpark, which they are not.
### Cleared credit default swaps
Let’s turn next to credit default swaps, both index and single name.
Figure 2 shows:
• Ice Clear Credit the largest with $50 billion, up$15 billion or 44% quarter-on-quarter and $16 billion or 48% year-on-year. • Ice Clear Europe with$11 billion, up 49% quarter-on-quarter and 67% year-on-year.
• LCH CDSClear with $5 billion, up 65% quarter-on-quarter and 51% year-on-year, in US dollar terms. The cumulative total IM for these three clearing services was$67 billion on March 31, 2020, an increase of 46% from the prior quarter and 51% from a year earlier. Similar to interest rate swaps, the bulk of the IM increase is likely to be from higher market volatility driving an increase in the IM model requirement and credit spreads were particularly very volatile in this period.
### Futures and options
Exchange traded derivatives, namely futures and options show similar increases in initial margin.
Figure 3 shows:
• CME Base the largest with $190 billion, up$82 billion or 75% quarter-on-quarter and $96 billion or 102% year-on-year. • Options Clearing Corporation with$91 billion, up 70% quarter-on-quarter and 112% year-on-year.
• Eurex Clearing with $76 billion, up 108% quarter-on-quarter and 92% year-on-year in US dollar terms. • Ice Clear Europe F&O with$57 billion, up 20% quarter-on-quarter and 22% year-on-year in US dollar terms.
• Ice Clear US F&O with $31 billion, up 64% quarter-on-quarter and 82% year-on-year. • JSCC ETP with$19 billion, up 118% quarter-on-quarter and 120% year-on-year.
• SGX DC, HKEX HKCC, ASX CLF with 21%, 33% and 13% quarter-on-quarter increases.
The cumulative total IM for these clearing services was $487 billion on March 31, 2020, an increase of$195 billion or 66% from the prior quarter. This is a much larger increase than either interest rate swaps and credit default swaps, which were up 23% and 46% respectively.
The relative quarterly changes between the futures and options CCPs are also interesting, ranging from 118% at JSCC ETP to 22% at Ice Clear Europe F&O.
Both of these are probably explained by the sharp increases in IM for futures and options in March, as highlighted in the BIS bulletin covered in my article, procyclical margins in the time of Covid-19, due to the higher procyclical calibration of these IM models as compared with interest rate swaps.
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#### Risk management
###### FCMs to let clients offset swaps and futures margin at Eurex
Banks target Q2 support for client cross-margining following lengthy lobby effort from hedge funds
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2021-01-27 07:27:24
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https://www.hackmath.net/en/math-problem/398
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# Expansion
If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
Correct result:
p = 700 %
#### Solution:
$p = 100\cdot ( 4\cdot 2-1) = 700 \%$
We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
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2020-10-30 15:48:18
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https://mathoverflow.net/questions/167428/v-1-periodic-homotopy-and-principal-bundle-classification
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# $v_1$-periodic homotopy and principal bundle classification
This question came back to my mind while pondering this MO question. The classification of principal bundles is seriously difficult because of our lack of understanding of homotopy groups of compact Lie groups. Although I only understand very little of it, I have seen that the work of Bendersky, Davis, Mahowald, Mimura and others has resulted in the complete computation of $v_1$-periodic homotopy groups of compact Lie groups. Moreover, these seem to describe pretty well the torsion in the homotopy of compact Lie groups in suitably low dimensions. So here are some questions:
1. is it possible to compute the homotopy set $[M,v_1BG]$ where $v_1BG$ should be the $v_1$-periodization of the classifying space $BG$ of a compact Lie group $G$ (i.e. the space whose homotopy are the $v_1$-periodic homotopy groups of $BG$)?
2. what can be said about the relation between the above set and the homotopy set $[M,BG]$ where $M$ is a finite CW-complex? I would expect that this is possible for $M$ of suitably low dimension, but is it possible to quantify "suitably low-dimensional" here?
3. would the above points 1 and 2 allow for improvements in our understanding of classification of principal bundles? For instance, it seems that complete classification of principal $SO(n)$-bundles is possible up to dimensions around 6 or 7. Do we get classification results from $v_1$-periodic homotopy groups on CW-complexes of larger dimension?
I would be grateful for any comments, and I apologize if what I have said above does not capture the meaning of $v_1$-periodic homotopy groups. As I said, I only know very little about these matters.
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2021-06-13 18:11:53
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https://labs.tib.eu/arxiv/?author=Kavli%20Institute%20for%20Cosmology
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• ### Galactic nuclei evolution with spinning black holes: method and implementation(1712.00023)
April 5, 2018 astro-ph.GA, astro-ph.HE
Supermassive black holes at the centre of galactic nuclei mostly grow in mass through gas accretion over cosmic time. This process also modifies the angular momentum (or spin) of black holes, both in magnitude and in orientation. Despite being often neglected in galaxy formation simulations, spin plays a crucial role in modulating accretion power, driving jet feedback, and determining recoil velocity of coalescing black hole binaries. We present a new accretion model for the moving-mesh code {\sc arepo} that incorporates (i) mass accretion through a thin $\alpha$-disc, and (ii) spin evolution through the Bardeen-Petterson effect. We use a diverse suite of idealised simulations to explore the physical connection between spin evolution and larger scale environment. We find that black holes with mass $\lesssim 10^{7}$ M$_{\odot}$ experience quick alignment with the accretion disc. This favours prolonged phases of spin-up, and the spin direction evolves according to the gas inflow on timescales as short as $\lesssim 100$ Myr, which might explain the observed jet direction distribution in Seyfert galaxies. Heavier black holes ($\gtrsim 10^{8}$ M$_{\odot}$) are instead more sensitive to the local gas kinematic. Here we find a wider distribution in spin magnitudes: spin-ups are favoured if gas inflow maintains a preferential direction, and spin-downs occur for nearly isotropic infall, while the spin direction does not change much over short timescales $\sim 100$ Myr. We therefore conclude that supermassive black holes with masses $\gtrsim 5 \times 10^{8}$ M$_{\odot}$ may be the ideal testbed to determine the main mode of black hole fuelling over cosmic time.
• ### One percent determination of the primordial deuterium abundance(1710.11129)
March 26, 2018 nucl-th, astro-ph.CO, astro-ph.GA
We report a reanalysis of a near-pristine absorption system, located at a redshift z_abs=2.52564 toward the quasar Q1243+307, based on the combination of archival and new data obtained with the HIRES echelle spectrograph on the Keck telescope. This absorption system, which has an oxygen abundance [O/H]=-2.769+/-0.028 (~1/600 of the Solar abundance), is among the lowest metallicity systems currently known where a precise measurement of the deuterium abundance is afforded. Our detailed analysis of this system concludes, on the basis of eight D I absorption lines, that the deuterium abundance of this gas cloud is log_10(D/H) = -4.622+/-0.015, which is in very good agreement with the results previously reported by Kirkman et al. (2003), but with an improvement on the precision of this single measurement by a factor of ~3.5. Combining this new estimate with our previous sample of six high precision and homogeneously analyzed D/H measurements, we deduce that the primordial deuterium abundance is log_10(D/H)_P = -4.5974+/-0.0052 or, expressed as a linear quantity, (D/H)_P = (2.527+/-0.030)x10^-5; this value corresponds to a one percent determination of the primordial deuterium abundance. Combining our result with a BBN calculation that uses the latest nuclear physics input, we find that the baryon density derived from BBN agrees to within 2 sigma of the latest results from the Planck CMB data.
• ### Ionized Gas Outflows from the MAGNUM Survey: NGC 1365 and NGC 4945(1801.05448)
Jan. 16, 2018 astro-ph.GA
AGN feedback, acting through strong outflows accelerated in the nuclear region of AGN hosts, is invoked as a key ingredient for galaxy evolution by many models to explain the observed BH-galaxy scaling relations. Recently, some direct observational evidence of radiative mode feedback in action has been finally found in quasars at $z$>1.5. However, it is not possible to study outflows in quasars at those redshifts on small scales ($\lesssim$100 pc), as spatial information is limited by angular resolution. This is instead feasible in nearby active galaxies, which are ideal laboratories to explore outflow structure and properties, as well as the effects of AGN on their host galaxies. In this proceeding we present preliminary results from the MAGNUM survey, which comprises nearby Seyfert galaxies observed with the integral field spectrograph VLT/MUSE. We focus on two sources, NGC 1365 and NGC 4945, that exhibit double conical outflows extending on distances >1 kpc. We disentangle the dominant contributions to ionization of the various gas components observed in the central $\sim$5.3 kpc of NGC 1365. An attempt to infer outflow 3D structure in NGC 4945 is made via simple kinematic modeling, suggesting a hollow cone geometry.
• ### Detection of faint broad emission lines in type 2 AGN: III. On the $M_{BH} - \sigma_\star$ relation of type 2 AGN(1706.06110)
June 19, 2017 astro-ph.GA
Type 2 active galactic nuclei (AGN) represent the majority of the AGN population. However, due to the difficulties in measuring their black hole (BH) masses, it is still unknown whether they follow the same BH mass-host galaxy scaling relations valid for quiescent galaxies and type 1 AGN. Here we present the locus of type 2 AGN having virial BH mass estimates in the $M_{BH}-\sigma_\star$ plane. Our analysis shows that the BH masses of type 2 AGN are $\sim0.9$ dex smaller than type 1 AGN at $\sigma_\star\sim 185$ km s$^{-1}$, regardless of the (early/late) AGN host galaxy morphology. Equivalently, type 2 AGN host galaxies have stellar velocity dispersions $\sim 0.2$ dex higher than type 1 AGN hosts at $M_{BH}\sim10^7$ M$_\odot$.
• ### The primordial deuterium abundance of the most metal-poor damped Lyman-alpha system(1607.03900)
July 13, 2016 nucl-th, astro-ph.CO, astro-ph.GA
We report the discovery and analysis of the most metal-poor damped Lyman-alpha (DLA) system currently known, which also displays the Lyman series absorption lines of neutral deuterium. The average [O/H] abundance of this system is [O/H] = -2.804 +/- 0.015, which includes an absorption component with [O/H] = -3.07 +/- 0.03. Despite the unfortunate blending of many weak D I absorption lines, we report a precise measurement of the deuterium abundance of this system. Using the six highest quality and self-consistently analyzed measures of D/H in DLAs, we report tentative evidence for a subtle decrease of D/H with increasing metallicity. This trend must be confirmed with future high precision D/H measurements spanning a range of metallicity. A weighted mean of these six independent measures provides our best estimate of the primordial abundance of deuterium, 10^5 (D/H)_P = 2.547 +/- 0.033 (log_10 (D/H)_P = -4.5940 +/- 0.0056). We perform a series of detailed Monte Carlo calculations of Big Bang nucleosynthesis (BBN) that incorporate the latest determinations of several key nuclear cross sections, and propagate their associated uncertainty. Combining our measurement of (D/H)_P with these BBN calculations yields an estimate of the cosmic baryon density, 100 Omega_B,0 h^2(BBN) = 2.156 +/- 0.020, if we adopt the most recent theoretical determination of the d(p,gamma)3He reaction rate. This measure of Omega_B,0 h^2 differs by ~2.3 sigma from the Standard Model value estimated from the Planck observations of the cosmic microwave background. Using instead a d(p,gamma)3He reaction rate that is based on the best available experimental cross section data, we estimate 100 Omega_B,0 h^2(BBN) = 2.260 +/- 0.034, which is in somewhat better agreement with the Planck value. Forthcoming measurements of the crucial d(p,gamma)3He cross section may shed further light on this discrepancy.
• The third generation of the Sloan Digital Sky Survey (SDSS-III) took data from 2008 to 2014 using the original SDSS wide-field imager, the original and an upgraded multi-object fiber-fed optical spectrograph, a new near-infrared high-resolution spectrograph, and a novel optical interferometer. All the data from SDSS-III are now made public. In particular, this paper describes Data Release 11 (DR11) including all data acquired through 2013 July, and Data Release 12 (DR12) adding data acquired through 2014 July (including all data included in previous data releases), marking the end of SDSS-III observing. Relative to our previous public release (DR10), DR12 adds one million new spectra of galaxies and quasars from the Baryon Oscillation Spectroscopic Survey (BOSS) over an additional 3000 sq. deg of sky, more than triples the number of H-band spectra of stars as part of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE), and includes repeated accurate radial velocity measurements of 5500 stars from the Multi-Object APO Radial Velocity Exoplanet Large-area Survey (MARVELS). The APOGEE outputs now include measured abundances of 15 different elements for each star. In total, SDSS-III added 2350 sq. deg of ugriz imaging; 155,520 spectra of 138,099 stars as part of the Sloan Exploration of Galactic Understanding and Evolution 2 (SEGUE-2) survey; 2,497,484 BOSS spectra of 1,372,737 galaxies, 294,512 quasars, and 247,216 stars over 9376 sq. deg; 618,080 APOGEE spectra of 156,593 stars; and 197,040 MARVELS spectra of 5,513 stars. Since its first light in 1998, SDSS has imaged over 1/3 of the Celestial sphere in five bands and obtained over five million astronomical spectra.
• ### Precision measures of the primordial abundance of deuterium(1308.3240)
Nov. 27, 2013 hep-ph, nucl-ex, nucl-th, astro-ph.CO
We report the discovery of deuterium absorption in the very metal-poor ([Fe/H] = -2.88) damped Lyman-alpha system at z_abs = 3.06726 toward the QSO SDSS J1358+6522. On the basis of 13 resolved D I absorption lines and the damping wings of the H I Lyman alpha transition, we have obtained a new, precise measure of the primordial abundance of deuterium. Furthermore, to bolster the present statistics of precision D/H measures, we have reanalyzed all of the known deuterium absorption-line systems that satisfy a set of strict criteria. We have adopted a blind analysis strategy (to remove human bias), and developed a software package that is specifically designed for precision D/H abundance measurements. For this reanalyzed sample of systems, we obtain a weighted mean of (D/H)_p = (2.53 +/- 0.04) x 10^-5, corresponding to a Universal baryon density100 Omega_b h^2 = 2.202 +/- 0.046 for the standard model of Big Bang Nucleosynthesis. By combining our measure of (D/H)_p with observations of the cosmic microwave background, we derive the effective number of light fermion species, N_eff = 3.28 +/- 0.28. We therefore rule out the existence of an additional (sterile) neutrino (i.e. N_eff = 4.046) at 99.3 percent confidence (2.7 sigma), provided that N_eff and the baryon-to-photon ratio (eta_10) did not change between BBN and recombination. We also place a strong bound on the neutrino degeneracy parameter, xi_D = +0.05 +/- 0.13 based only on the CMB+(D/H)_p observations. Combining xi_D with the current best literature measure of Y_p, we find |xi| <= +0.062. In future, improved measurements of several key reaction rates, in particular d(p,gamma)3He, and further measures of (D/H)_p with a precision comparable to those considered here, should allow even more stringent limits to be placed on new physics beyond the standard model.
• ### Metals in the IGM approaching the re-ionization epoch: results from X-shooter at the VLT(1306.4604)
Aug. 7, 2013 astro-ph.CO
We present the results of observations taken with the X-shooter spectrograph devoted to the study of quasars at z ~ 6. This paper focuses on the properties of metals at high redshift traced, in particular, by the C IV doublet absorption systems. Six objects were observed with resolutions ~27 and 34 km/s in the visual, and 37.5 and 53.5 km/s in the near infrared. We detected 102 C IV lines in the range: 4.35 < z < 6.2 of which 27 are above z ~ 5. Thanks to the characteristics of resolution and spectral coverage of X-shooter, we could also detect 25 Si IV doublets associated with the C IV at z>5. The column density distribution function of the C IV line sample is observed to evolve in redshift for z>~ 5.3, with respect to the normalization defined by low redshift (1.5 < z <4) C IV lines. This behaviour is reflected in the redshift evolution of the C IV cosmic mass density, Omega_CIV, of lines with column density in the range 13.4 < log N(C IV) < 15, which is consistent with a drop of a factor of ~2 for z>~ 5.3. Considering only the stronger C IV lines (13.8 < log N(CIV) < 15), Omega_CIV gently rises by a factor of ~10 between z ~ 6.2 and z~ 1.5 with a possible flattening toward z ~ 0. The increase is well fitted by a power law: Omega_CIV = (2+-1)x10^{-8} [(1+z)/4]^{-3.1+-0.1}. An insight into the properties of the C IV absorbers and their evolution with redshift is obtained by comparing the observed column densities of associated C IV, Si IV and C II absorptions with the output of a set of CLOUDY photo-ionization models. As already claimed by cosmological simulations, we find that C IV is a good tracer of the metallicity in the low-density intergalacitc medium gas at z ~ 5-6 while at z ~ 3 it arises in gas with over density delta ~100.
• ### A new, precise measurement of the primordial abundance of Deuterium(1205.3785)
July 6, 2012 astro-ph.CO
The metal-poor damped Lyman alpha (DLA) system at z = 3.04984 in the QSO SDSSJ1419+0829 has near-ideal properties for an accurate determination of the primordial abundance of deuterium, (D/H)_p. We have analysed a high-quality spectrum of this object with software specifically designed to deduce the best fitting value of D/H and to assess comprehensively the random and systematic errors affecting this determination. We find (D/H)_DLA = (2.535 +/-0.05) x 10^(-5), which in turn implies Omega_b h^2 = 0.0223 +/- 0.0009, in very good agreement with Omega_b h^2 (CMB) = 0.0222 +/- 0.0004 deduced from the angular power spectrum of the cosmic microwave background. If the value in this DLA is indeed the true (D/H)_p produced by Big-Bang nucleosynthesis (BBN), there may be no need to invoke non-standard physics nor early astration of D to bring together Omega_b h^2 (BBN) and Omega_b h^2 (CMB). The scatter between most of the reported values of (D/H)_p in the literature may be due largely to unaccounted systematic errors and biases. Further progress in this area will require a homogeneous set of data comparable to those reported here and analysed in a self-consistent manner. Such an endeavour, while observationally demanding, has the potential of improving our understanding of BBN physics, including the relevant nuclear reactions, and the subsequent processing of 4He and 7Li through stars.
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2021-01-28 01:28:30
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|
https://puzzling.stackexchange.com/questions/16025/hat-guessing-game-in-vegas
|
# Hat Guessing Game in Vegas
A team of 10 people are going to play a cooperative game. While their eyes are closed, a pit boss will place either a red or green hat on each of their heads, chosen by fair coin flip. They then all open their eyes, and will be able to see the hats on everyone's heads except their own.
The players will then simultaneously bet a number of dollars that the hat they are wearing is green. Specifically, on the pit boss's signal, the players will each call out an integer, which may be positive, negative or zero. Calling a negative number is effectively betting that your hat will be red.
The total winnings of the players is calculated by adding up the bets of people with green hats, and subtracting the bets of people with red hats. The team of players wins if and only if their total winnings are more than zero.
Before the game begins, the players may agree on a strategy, but once the hats are placed, no communication between the players is possible.
What strategy maximizes the players' chances of winning? Why can't they do better?
The players can win with probability
$1- \frac{1}{2^{10}}$
This is optimal because:
Each player's bet has expectation $0$, and therefore, so does the sum of the bets. Therefore, it's not possible to win for every possible setting of hats, so at least of one the $2^{10}$ settings must lose.
A strategy that achieves this is:
The players imagine standing in line in a predetermined order so that each player only sees the hats of the players in front. The front player, who sees nothing, bets \$1 that their hat is green. If it is, the rest of the players see so, and bet nothing, which gives a win. If it's not, the second player bets \$2 that their own hat is green. If it is, the rest of the players know that they are net ahead \$1 and do nothing, and if not, the next player bets \$4 that their hat is green, and so on. Each player is able to simulate what will happen ahead in line, so they all know the correct to make at the same time.
In general, the player who sees $k$ players in front bets $2^k$ dollars that their hat is green only if all hats they see are red, and bets nothing otherwise. If player $k$ is the first in line with a green hat, they win $2^k$, which is enough to offset the $2^k-1$ that the players in front lose for also betting that they have green hats, and nobody behind them bets. The players only lose if everyone has red hats, losing $2^{11}-1$ dollars.
• similar to a Martingale? – smci Nov 5 '16 at 13:27
Surprisingly, the prisoners can win against
every hat sequence except one. If this is possible, then it is obviously optimal: since the average dollars won is always 0, the prisoners can't win all the time.
Here is the strategy:
If you see $n$ red hats, bet $10^{n!}!$ dollars that your hat is green. The point is that this function grows very fast, and anyone wearing green sees 1 more red hat than anyone wearing red. So, if there are any green hats whatsoever, then the total of all bets by people with green hats will be much larger than the total of all bets by people with red hats.
• Good answer, but that seems slightly overkill. Surely $10^n$ would do? – frodoskywalker Jun 5 '15 at 19:42
• Yes, $10^n$ would do. – Lopsy Jun 5 '15 at 20:04
• Damn this right-handed iphone app. Sorry for the downvote. I can fix it after an edit if you do one. – LeppyR64 Jun 5 '15 at 21:13
• @LeppyR64, you have sufficient reputation to make a trivial edit yourself if you wanted to. – James Webster Jun 6 '15 at 8:15
• @LeppyR64, a non-trivial, valid edit might be swapping "prisoner" for "player" to match the question – James Webster Jun 6 '15 at 8:16
You didn't say if the players are allowed to do something between the moment they open their eyes, and the moment they have to place their bid. If, for example, they are allowed to walk around (without talking to each other or communinating in any way!), they can always win.
• At the start, two players stand next to each other
• The other players, one by one, chose their position like this:
• If everybody standing in line has a green hat, stand to the right of them
• If everybody standing in line has a red hat, stand to the left of them
• If there are some red hats and some green hats, there must be an uninterrupted line of green hats to the left, and an uninterrupted line of red hats to the right. Chose your place between the two where the color changes.
• At the end, if there is a red hat to your left, bet a large negative number, since your hat is red as well
• Similarily, if there is a green hat to your right, your hat is green,so bet a large positive number
• If there are only green hats to your left, and only red hats to your right, you don't know the color of your hat; bet a zero (if allowed to), or the smallest number you are allowed to bet. Just reread the instructions, zero is allowed.
• But arranging themselves in this way is communicating! Each player is, by their placement, telling the player before them what color they have. – frodoskywalker Jun 5 '15 at 23:16
• In addition, the starting rules are broken. Start with one player, not two, so they don't accidentally start with a red hat to the right of a green hat. – Oddthinking Jun 6 '15 at 1:18
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2020-10-28 06:09:13
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https://zbmath.org/authors/?q=ai%3Alian.hairong
|
## Lian, Hairong
Compute Distance To:
Author ID: lian.hairong Published as: Lian, Hairong
Documents Indexed: 37 Publications since 2005 Co-Authors: 34 Co-Authors with 36 Joint Publications 2,182 Co-Co-Authors
all top 5
### Co-Authors
0 single-authored 14 Ge, Weigao 5 Zhao, Junfang 4 Agarwal, Ravi P. 4 Pang, Huihui 4 Wang, Peiguang 3 Geng, Fengjie 2 Bai, Zhanbing 2 Wang, Dongli 1 Bai, Dingyong 1 Chen, Yangquan 1 Chu, Baozeng 1 Cui, Zijia 1 Duan, Yu 1 Fang, Xinyu 1 Feng, Hanying 1 Gao, Yue 1 Hua, Dongying 1 Jing, Shiwen 1 Li, Jingwu 1 Li, Mingxia 1 Liu, Changjian 1 O’Regan, Donal 1 Scott, Michael A. 1 Simpson, Robert Napier 1 Sun, Sujing 1 Taus, Matthias 1 Thomas, Derek C. 1 Wang, Haiyan 1 Wang, Youyu 1 Wong, Patricia J. Y. 1 Wu, Yonghong 1 Yan, Gaosheng 1 Yang, Jiazhong 1 Yang, Shu 1 Yu, Xiaozhu 1 Yu, Xin 1 Zhang, Shuai 1 Zhu, Deming
all top 5
### Serials
5 Boundary Value Problems 4 Journal of Mathematical Analysis and Applications 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Computers & Mathematics with Applications 2 Annals of Differential Equations 2 Applied Mathematics Letters 1 Computer Methods in Applied Mechanics and Engineering 1 Applied Mathematics and Computation 1 Zeitschrift für Analysis und ihre Anwendungen 1 Chinese Annals of Mathematics. Series A 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Electronic Journal of Differential Equations (EJDE) 1 Abstract and Applied Analysis 1 Fractional Calculus & Applied Analysis 1 Discrete Dynamics in Nature and Society 1 Analysis (München) 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Advances in Difference Equations 1 Acta Mathematica Sinica. Chinese Series 1 Journal of Nonlinear Science and Applications 1 Journal of Applied Mathematics & Informatics 1 Annals of Applied Mathematics 1 Electronic Research Archive
all top 5
### Fields
32 Ordinary differential equations (34-XX) 13 Operator theory (47-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Difference and functional equations (39-XX) 2 Integral equations (45-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Numerical analysis (65-XX) 1 Partial differential equations (35-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX)
### Citations contained in zbMATH Open
26 Publications have been cited 387 times in 233 Documents Cited by Year
Acoustic isogeometric boundary element analysis. Zbl 1296.65175
Simpson, R. N.; Scott, M. A.; Taus, M.; Thomas, D. C.; Lian, H.
2014
On the existence of blow up solutions for a class of fractional differential equations. Zbl 1312.34007
Bai, Zhanbing; Chen, YangQuan; Lian, Hairong; Sun, Sujing
2014
Triple positive solutions for boundary value problems on infinite intervals. Zbl 1128.34011
Lian, Hairong; Pang, Huihui; Ge, Weigao
2007
Periodic solutions for a second order nonlinear functional differential equation. Zbl 1151.34056
Wang, Youyu; Lian, Hairong; Ge, Weigao
2007
Existence of positive solutions for Sturm-Liouville boundary value problems on the half-line. Zbl 1104.34020
Lian, Hairong; Ge, Weigao
2006
Unbounded upper and lower solutions method for Sturm-Liouville boundary value problem on infinite intervals. Zbl 1167.34320
Lian, Hairong; Wang, Peiguang; Ge, Weigao
2009
Solvability for second-order three-point boundary value problems on a half-line. Zbl 1123.34307
Lian, Hairong; Ge, Weigao
2006
Solvability for second-order three-point boundary value problems at resonance on a half-line. Zbl 1136.34034
Lian, Hairong; Pang, Huihui; Ge, Weigao
2008
Positive solutions for a four-point boundary value problem with the $$p$$-Laplacian. Zbl 1151.34019
Lian, Hairong; Ge, Weigao
2008
Multiple positive solutions for second-order four-point boundary value problem. Zbl 1145.34320
Pang, Huihui; Lian, Hairong; Ge, Weigao
2007
Calculus of variations for a boundary value problem of differential system on the half line. Zbl 1189.34064
Lian, Hairong; Ge, Weigao
2009
Upper and lower solution method for $$n$$th-order BVPs on an infinite interval. Zbl 1308.34035
Lian, Hairong; Zhao, Junfang; Agarwal, Ravi P.
2014
A symmetric solution of a multipoint boundary value problem with one-dimensional $$p$$-Laplacian at resonance. Zbl 1161.34310
Feng, Hanying; Lian, Hairong; Ge, Weigao
2008
Existence of unbounded solutions for a third-order boundary value problem on infinite intervals. Zbl 1254.34045
Lian, Hairong; Zhao, Junfang
2012
On the stability in terms of two measures for perturbed impulsive integro-differential equations. Zbl 1092.45005
Wang, Peiguang; Lian, Hairong
2006
Periodic and subharmonic solutions for a class of second-order $$p$$-Laplacian Hamiltonian systems. Zbl 1320.34065
Lian, Hairong; Wang, Dongli; Bai, Zhanbing; Agarwal, Ravi P.
2014
Bifurcation of limit cycles from a quasi-homogeneous degenerate center. Zbl 1309.34066
Geng, Fengjie; Lian, Hairong
2015
Existence of positive solutions for nonlinear $$m$$-point boundary value problems on time scales. Zbl 1275.34114
Zhao, Junfang; Lian, Hairong; Ge, Weigao
2012
Stability in terms of two measures of impulsive integro-differential equations via variation of the Lyapunov method. Zbl 1096.45010
Wang, Peiguang; Lian, Hairong
2006
Solvability of three-point boundary value problems at resonance with a $$p$$-Laplacian on finite and infinite intervals. Zbl 1261.34025
Lian, Hairong; Wong, Patricia J. Y.; Yang, Shu
2012
Unbounded solutions of second order discrete BVPs on infinite intervals. Zbl 1330.39010
Lian, Hairong; Li, Jingwu; Agarwal, Ravi P.
2016
Multiple unbounded solutions for a boundary value problem on infinite intervals. Zbl 1275.34043
Lian, Hairong; Geng, Fengjie
2011
Global asymptotic stability of high-order delay Hopfield neural networks with time-varying coefficients. Zbl 1106.34050
Wang, Peiguang; Lian, Hairong; Wu, Yonghong
2005
Existence of unbounded solutions to three-point boundary value problems over a semi-infinite interval. Zbl 1274.34087
Lian, Hairong; Cui, Zijia; Zhang, Shuai
2012
Exact multiplicity of solutions for discrete second order Neumann boundary value problems. Zbl 1381.39008
Bai, Dingyong; Lian, Hairong; Wang, Haiyan
2015
Existence of solutions of multi-point boundary value problems on time scales at resonance. Zbl 1347.34037
Zhao, Junfang; Chu, Baozeng; Lian, Hairong
2013
Unbounded solutions of second order discrete BVPs on infinite intervals. Zbl 1330.39010
Lian, Hairong; Li, Jingwu; Agarwal, Ravi P.
2016
Bifurcation of limit cycles from a quasi-homogeneous degenerate center. Zbl 1309.34066
Geng, Fengjie; Lian, Hairong
2015
Exact multiplicity of solutions for discrete second order Neumann boundary value problems. Zbl 1381.39008
Bai, Dingyong; Lian, Hairong; Wang, Haiyan
2015
Acoustic isogeometric boundary element analysis. Zbl 1296.65175
Simpson, R. N.; Scott, M. A.; Taus, M.; Thomas, D. C.; Lian, H.
2014
On the existence of blow up solutions for a class of fractional differential equations. Zbl 1312.34007
Bai, Zhanbing; Chen, YangQuan; Lian, Hairong; Sun, Sujing
2014
Upper and lower solution method for $$n$$th-order BVPs on an infinite interval. Zbl 1308.34035
Lian, Hairong; Zhao, Junfang; Agarwal, Ravi P.
2014
Periodic and subharmonic solutions for a class of second-order $$p$$-Laplacian Hamiltonian systems. Zbl 1320.34065
Lian, Hairong; Wang, Dongli; Bai, Zhanbing; Agarwal, Ravi P.
2014
Existence of solutions of multi-point boundary value problems on time scales at resonance. Zbl 1347.34037
Zhao, Junfang; Chu, Baozeng; Lian, Hairong
2013
Existence of unbounded solutions for a third-order boundary value problem on infinite intervals. Zbl 1254.34045
Lian, Hairong; Zhao, Junfang
2012
Existence of positive solutions for nonlinear $$m$$-point boundary value problems on time scales. Zbl 1275.34114
Zhao, Junfang; Lian, Hairong; Ge, Weigao
2012
Solvability of three-point boundary value problems at resonance with a $$p$$-Laplacian on finite and infinite intervals. Zbl 1261.34025
Lian, Hairong; Wong, Patricia J. Y.; Yang, Shu
2012
Existence of unbounded solutions to three-point boundary value problems over a semi-infinite interval. Zbl 1274.34087
Lian, Hairong; Cui, Zijia; Zhang, Shuai
2012
Multiple unbounded solutions for a boundary value problem on infinite intervals. Zbl 1275.34043
Lian, Hairong; Geng, Fengjie
2011
Unbounded upper and lower solutions method for Sturm-Liouville boundary value problem on infinite intervals. Zbl 1167.34320
Lian, Hairong; Wang, Peiguang; Ge, Weigao
2009
Calculus of variations for a boundary value problem of differential system on the half line. Zbl 1189.34064
Lian, Hairong; Ge, Weigao
2009
Solvability for second-order three-point boundary value problems at resonance on a half-line. Zbl 1136.34034
Lian, Hairong; Pang, Huihui; Ge, Weigao
2008
Positive solutions for a four-point boundary value problem with the $$p$$-Laplacian. Zbl 1151.34019
Lian, Hairong; Ge, Weigao
2008
A symmetric solution of a multipoint boundary value problem with one-dimensional $$p$$-Laplacian at resonance. Zbl 1161.34310
Feng, Hanying; Lian, Hairong; Ge, Weigao
2008
Triple positive solutions for boundary value problems on infinite intervals. Zbl 1128.34011
Lian, Hairong; Pang, Huihui; Ge, Weigao
2007
Periodic solutions for a second order nonlinear functional differential equation. Zbl 1151.34056
Wang, Youyu; Lian, Hairong; Ge, Weigao
2007
Multiple positive solutions for second-order four-point boundary value problem. Zbl 1145.34320
Pang, Huihui; Lian, Hairong; Ge, Weigao
2007
Existence of positive solutions for Sturm-Liouville boundary value problems on the half-line. Zbl 1104.34020
Lian, Hairong; Ge, Weigao
2006
Solvability for second-order three-point boundary value problems on a half-line. Zbl 1123.34307
Lian, Hairong; Ge, Weigao
2006
On the stability in terms of two measures for perturbed impulsive integro-differential equations. Zbl 1092.45005
Wang, Peiguang; Lian, Hairong
2006
Stability in terms of two measures of impulsive integro-differential equations via variation of the Lyapunov method. Zbl 1096.45010
Wang, Peiguang; Lian, Hairong
2006
Global asymptotic stability of high-order delay Hopfield neural networks with time-varying coefficients. Zbl 1106.34050
Wang, Peiguang; Lian, Hairong; Wu, Yonghong
2005
all top 5
### Cited by 332 Authors
11 Ardjouni, Abdelouaheb 11 Liu, Lishan 10 Bai, Zhanbing 10 Djoudi, Ahcene 9 Wong, Patricia J. Y. 8 Cheng, Zhibo 7 Agarwal, Ravi P. 7 Ge, Weigao 7 Liu, Yuji 7 Wu, Yonghong 6 Jiang, Weihua 6 Li, Yongxiang 6 Lian, Hairong 6 O’Regan, Donal 6 Sun, Sujing 5 Hao, Xin’an 5 Liang, Sihua 5 Minhós, Feliz Manuel 5 Ren, Jingli 5 Yu, Changlong 5 Zhang, Jihui 5 Zhao, Junfang 4 Cui, Yujun 4 Guo, Yanping 4 Kim, Chan-Gyun 4 Li, Qiang 4 Shen, Chunfang 4 Wang, Jufang 4 Xu, Jiafa 4 Zhou, Hui 3 Cetin, Erbil 3 Du, Zengji 3 Liu, Bingmei 3 Liu, Wenbin 3 Mansouri, Bouzid 3 Pei, Minghe 3 Wang, Ying 3 Wang, Zhen 3 Yang, Liu 3 Zhao, Zengqin 2 Cabada, Alberto 2 Carrasco, Hugo 2 Chang, Sung Kag 2 Charandabi, Zohreh Zeinalabedini 2 Chen, Haibo 2 Chen, Taiyong 2 Cui, Xiaoxiao 2 de Sousa, Robert 2 Djebali, Smail 2 Dogan, Abdulkadir 2 Geng, Fengjie 2 Han, Zhenlai 2 Iyase, Samuel Azubuike 2 Jeong, Jeongmi 2 Jia, Mei 2 Khemis, Rabah 2 Kosmatov, Nickolai 2 Li, Chun 2 Li, Jianli 2 Li, Junling 2 Lin, Xiaojie 2 Lin, Yingzhen 2 Liu, Feng 2 Liu, Jiang 2 Lu, Junwei 2 Luo, Zhiguo 2 Nieto Roig, Juan Jose 2 Niu, Jing 2 Rezapour, Shahram 2 Su, Xinwei 2 Sun, Bingzhi 2 Sun, Juntao 2 Sun, Qiao 2 Sun, Shurong 2 Sun, Yibing 2 Tatar, Nasser-eddine 2 Tian, Yuansheng 2 Wang, Can 2 Wang, Yilin 2 Wang, Yongqing 2 Wei, Yongfang 2 Wei, Zhongli 2 Xie, Yingkang 2 Yang, Caixia 2 Zhang, Xingqiu 2 Zhao, Yige 1 Afrouzi, Ghasem Alizadeh 1 Agarwal, Praveen 1 Ahmad, Bashir 1 Ahmad, M. Ahmad 1 Akcan, Ummahan 1 Ali, Liaqat 1 Allahverdiev, Bilender Paşaoğlu 1 Alshomrani, Ali Saleh 1 Alwan, Mohamad S. 1 Amir, El Haffaf 1 Aydogan, Seher Melike 1 Benchohra, Mouffak 1 Benmezaï, Abdelhamid 1 Bessioud, Karima ...and 232 more Authors
all top 5
### Cited in 77 Serials
34 Boundary Value Problems 22 Applied Mathematics and Computation 22 Advances in Difference Equations 13 Abstract and Applied Analysis 12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Journal of Applied Mathematics and Computing 6 Computers & Mathematics with Applications 5 Mathematical Methods in the Applied Sciences 5 Journal of Computational and Applied Mathematics 5 Journal of Applied Analysis and Computation 4 Journal of Function Spaces 3 Lithuanian Mathematical Journal 3 Acta Applicandae Mathematicae 3 Turkish Journal of Mathematics 3 Journal of Difference Equations and Applications 3 Journal of Inequalities and Applications 3 Discrete Dynamics in Nature and Society 3 Qualitative Theory of Dynamical Systems 2 Numerical Functional Analysis and Optimization 2 Results in Mathematics 2 Applied Mathematics Letters 2 Journal of Integral Equations and Applications 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Filomat 2 Opuscula Mathematica 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 Fractional Calculus & Applied Analysis 2 Communications in Nonlinear Science and Numerical Simulation 2 Nonlinear Analysis. Real World Applications 2 Nonlinear Analysis. Modelling and Control 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Mediterranean Journal of Mathematics 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 AIMS Mathematics 1 Applicable Analysis 1 Indian Journal of Pure & Applied Mathematics 1 Journal of the Franklin Institute 1 Journal of Mathematical Analysis and Applications 1 Physica A 1 Rocky Mountain Journal of Mathematics 1 Demonstratio Mathematica 1 Journal of Differential Equations 1 Le Matematiche 1 Mathematica Slovaca 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Journal of Symbolic Computation 1 Facta Universitatis. Series Mathematics and Informatics 1 Forum Mathematicum 1 Applications of Mathematics 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 The Journal of Analysis 1 Fractals 1 Buletinul Academiei de Științe a Republicii Moldova. Matematica 1 Complexity 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Differential Equations and Dynamical Systems 1 Honam Mathematical Journal 1 Mathematica Moravica 1 Acta Mathematica Sinica. English Series 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Mathematical Modelling and Analysis 1 Differentsial’nye Uravneniya i Protsessy Upravleniya 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Applied Mathematics 1 Analysis and Applications (Singapore) 1 Cubo 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Journal of Nonlinear Science and Applications 1 Acta Universitatis Sapientiae. Mathematica 1 Journal of Mathematical Extension 1 Arabian Journal of Mathematics 1 Electronic Journal of Mathematical Analysis and Applications EJMAA 1 Mathematics 1 Open Mathematics
all top 5
### Cited in 22 Fields
207 Ordinary differential equations (34-XX) 107 Operator theory (47-XX) 18 Partial differential equations (35-XX) 14 Real functions (26-XX) 8 Difference and functional equations (39-XX) 8 Integral equations (45-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Numerical analysis (65-XX) 5 Biology and other natural sciences (92-XX) 5 Systems theory; control (93-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Computer science (68-XX) 1 Field theory and polynomials (12-XX) 1 Functions of a complex variable (30-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX)
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2022-10-02 04:08:16
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5505217909812927, "perplexity": 9454.852384150397}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337244.17/warc/CC-MAIN-20221002021540-20221002051540-00162.warc.gz"}
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https://cymbeline.ch/2021/09/24/
|
## Copy files with PowerShell Remoting
Recently, at work, I found myself in the situation where I needed to copy some file from my workstation to a jump box. Now of course, on Linux I’d just use `rsync` or `scp`. But our IT doesn’t like provisioning Linux boxes and therefore uses Windows for jump servers too, so no luck here. Luckily, I could convince them to turn on and allow PowerShell Remoting, so with some simple scripts I can still easily copy files over without using SMB and looking at more hassle with IT.
```function Copy-LocalToRemote(
[Parameter(Mandatory = \$true)] \$LocalPath,
[Parameter(Mandatory = \$true)] \$RemotePath,
\$ComputerName = 'my.default.target.host'
) {
Invoke-Command -ComputerName \$ComputerName `
{
param(\$path, \$content)
Set-Content -Path \$path -Value \$content `
-AsByteStream
} `
-ArgumentList \$RemotePath,(
Get-Content \$LocalPath Raw -AsByteStream)
}
function Copy-RemoteToLocal(
[Parameter(Mandatory = \$true)] \$RemotePath,
[Parameter(Mandatory = \$true)] \$LocalPath,
\$ComputerName = 'my.default.source.host'
) {
Invoke-Command -ComputerName \$ComputerName `
{
param(\$path)
Get-Content -Path \$path -Raw -AsByteStream
} `
-ArgumentList \$RemotePath |
Set-Content -Path \$LocalPath -AsByteStream
}
New-Alias -Name 'ltr' -Value 'Copy-LocalToRemote'
New-Alias -Name 'rtl' -Value 'Copy-RemoteToLocal'
```
As you can see, this is quite simple. Obviously, functions above can only copy one file at a time though. Maybe in the future I’ll build something that can copy entire file structures recursively. I also haven’t spent any time looking at how efficient it is to pass streams this way. In fact, I wouldn’t be surprised at all if this would perform poorly for large files. But then again, I’m mostly pushing around scripts and config files, so this works just fine.
|
2021-10-26 16:05:18
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http://www.moravica.ftn.kg.ac.rs/Vol_2/Vol_2.htm
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# Mathematica Moravica, Vol. 2 (1998)
Measure of Noncompactness on Uniform Spaces
Mathematica Moravica, Vol. 2 (1998), 1–8.
Abstract. In this paper we define measure of noncompactness on arbitrary uniform spaces, and give some their properties. We also give one characterization of complete uniform spaces.
Keywords. Measure of noncompactness, uniform space.
Implementation of Multi-Criterion Decision Making Models Recommendation
Mathematica Moravica, Vol. 2 (1998), 9–19.
Abstract. This paper gives some introductory notes on multi-criterion decision making. It addresses to the known division into models of multi-purpose decision making and multi-attribution decision making or multi-criterion analysis, general notion of models, terminology, taxonomy of methods as well as significance of interactive methods and the role of a decision maker in the procedure of solution making. The first out of a set of significant facets of implementation of multi-criterion decision making models is shown further: marginal solutions and their consequences, that is an examination of a possibility of perfect solution of the said model.
Keywords. Multi-criterion optimization, multi-purpose decision making, multi-attribution optimization, multi-criterion analysis, mathematical model, methods, software.
Tauberian Theorems for Generalized Abelian Summability Methods (part of PhD thesis)
Mathematica Moravica, Vol. 2 (1998), 21–66.
Abstract. We introduce and study a significant generalization of Abel's summability method, and their corresponding limiting process. This leads to an analogue to Hardy-Littlewood Tauberian Theorem.The first section includes an introduction to some basic concepts of summability methods and a survey of classical and neoclassical results. In the second section a general summability method is designed and some related Tauberian theorems are established. In the third section higher order of Abel's summability methods are obtained as a special case of a general summability method and the general Littlewood theorem is proved for those summability methods. Finally we give Tauberian theorems corresponding to $(C, m)$-summability methods and present some further convergence theorems.
Keywords. General summability methods, General Tauberian theorem.
The Matuszewska Sequences
Mathematica Moravica, Vol. 2 (1998), 67–74.
Abstract. In this paper we prove a representation theorem for $\Delta RV$-sequences, which we call “Matuszewska sequences”, in the Bojanić-Seneta sense. We also find a connection between the class of $\Delta RV$-sequences and the functional Matuszewska class ERV, and the relations between the sequencial class $\Delta RV$ and the sequencial classes $RVS$ and $\ast RV$.
Keywords. Karamata's theory, sequencial class $\ast RV$, functional Matuszewska class, index funtion.
Theorem of Synthesis for Bisemilattice-valued Fuzzy Sets
Mathematica Moravica, Vol. 2 (1998), 75–83.
Abstract. Bisemilattice-valued fuzzy set ($B$-fuzzy set) is a mapping from a nonempty set to a bisemilattice. A $B$-fuzzy set has two families of level subsets, one for each ordering of the bisemilatÂtice. In this paper, necessary and sufficient conditions under which two families of subsets of a nonempty set are families of level subsets of a $B$-fuzzy set are given.
Keywords. Fuzzy sets, bisemilattices.
Application of an Expanded Min-Max Theorem and Tables of Decision Making for Solving Multi-criterion Conflict Situations
Mathematica Moravica, Vol. 2 (1998), 85–90.
Abstract. This paper proves that it is possible to define optimal strategy for multi-criterion conflict situation using Min-max theorem of Tasković in conjunction with tables of decision making.
Keywords. Multicriteria conflict situation, solving, John von Neumann's minimax principle, Tasković's minimax theorem, Minimax theory.
On the Location of the Zeros of Polynomials
Mathematica Moravica, Vol. 2 (1998), 91–96.
Abstract. In this paper we determine in the complex plane regions containing the zeros of the polynomial $P(z)=z^n+a_1z^{n-1}+a_2z^{n-2}+\cdots+a_{n-1}z+a_n,\qquad n\geq 3.$ We also obtain an expression which represents a upper bound for the moduli of the zeros of $P(z)$.
Keywords. Regions of the zeros, upper bound for the moduli of the zeros, the zeros in the halfplanes.
A Remark Concerning Zeros of One Class of Polynomials
Mathematica Moravica, Vol. 2 (1998), 97–108.
Abstract. In this paper, the distribution of zeros of a class of real polynomials is considered. In some cases the intervals, each one containing one zero, are determined with more accuracy.
Keywords. Distribution of the zeros, intervals of the zeros, zeros of a class of real polynomials.
Some Minimax Theorems on Ordered Sets
Mathematica Moravica, Vol. 2 (1998), 109–120.
Abstract. In this paper we continue the study and considerations of some minimax statements on ordered sets.
Keywords. Minimax theory, Partially ordered sets, Games theory, Saddle points, Transversal points, Borsuk-Ulam theorem, von Neumann's theory, Minimax Inequalities.
Schauder's 54th Problem in Scottish Book
Mathematica Moravica, Vol. 2 (1998), 121–132.
Abstract. The most famous of many problems in nonlinear analysis is Schauder's problem (Scottish Book, Problem 54) of the following form, that if $C$ is a nonempty convex compact subset of a linear topological space does every continuous mapping $f: C\to C$ has a fixed point?
The answer we give in this paper is yes. In this connection this paper proves and extends the Markoff-Kakutani theorem to arbitrary linear topological space as an immediate consequence of the preceding solution of Schauder's problem. During the last twenty years this old conjecture was intensively examined by many mathematians. For set in normed spaces this has been proved by Schauder and for sets in locally convex spaces by Tychonoff.
In this paper we prove that if $C$ is a nonempty convex compact subset of a linear topological space, then every continuous mapping $f: C\to C$ has a fixed point.
On the other hand, in this sense, we extend and connected former results of Brouwer, Schauder, Tychonoff, Markoff, Kakutani, Darbo, Sadovskij, Browder, Krasnoselskij, Ky Fan, Reinermann, Hukuhara, Mazur, Hahn, Ryll-Nardzewski, Day, Riedrich, Jahn, Eisenack-Fenske, Idzik, Kirk, Göhde, Granas, Dugundji, Klee and some others.
Keywords. Fixed point theorems, Brouwer's theorem, Schauder's theorem, Tychonof's theorem, Markoff's theorem, Kakutani's theorem, Sadovskij's theorem, Schauder's Conjecture (Scottish Book, Problem 54).
Transversal Spaces
Mathematica Moravica, Vol. 2 (1998), 133–142.
Abstract. In this paper we formulate a new structure of spaces which we call it transversal (upper or lower) spaces. We introduced the concept of transversal ordered (upper or lower) spaces as a natural extension of Fréchet's, Kurepa's and Menger's spaces.
Keywords. General ecart, distance, general distance, pseudometric, M-metric, Fréchet's and Kurepa's spaces, transversal spaces, Menger's spaces, bisection (upper or lower) functions.
New Geometric Fixed Point Theorems
Mathematica Moravica, Vol. 2 (1998), 143–148.
Abstract. In this paper it is proved the following main result that if $T$ is a self-map on a complete metric space $(X, \rho)$ and if there exists an upper semicontinuous bounded above function $G: X \to \mathbf{R}$ such that $\rho [x,Tx] \leq G(Tx)-G(x)$ for every $x \in X$, then $T$ has a fixed point in $X$. This paper presents and some other results of this type.
Keywords. Fixed point theorems, complete metric spaces, Caristi's theorem, Caristi-Kirk theorem, upper or lower semicontinuous functions.
On Topological n-Groups
Mathematica Moravica, Vol. 2 (1998), 149–159.
Abstract. Let $(Q,A)$ be an $n$-group, $^{-1}$ its inversing operation [:[13,16],1.3], $n \geq 2$, and let $Q$ be equipped with a topology $\mathcal{O}$. Then, in this paper, we say that $Q,A,\mathcal{O}$ is topological $n$-group iff: a) the $n$-ary operation $A$ is continuous in $\mathcal{O}$, and b) the $(n-1)$-ary operation $^{-1}$ is continuous in $\mathcal{O}$. The main result of the paper is the following proposition. Let $(Q,A)$ be an $n$-group, $n \geq 3$, and let $(Q,\{\cdot, \varphi,b\})$ be an arbitrary $nHG$-algebra associated to the $n$-group $(Q,A)$ [:[15],1.5]. Also, $Q$ is equipped with a topology $\mathcal{O}$. Then, $(Q,A,\mathcal{O})$ is a topological $n$-group iff the following statements hold: 1) $(Q,\cdot, \mathcal{O})$ is a topological group [:e.g. [7]], and 2) the unary operation $\varphi$ is continuous in $\mathcal{O}$.
Keywords. $n$-semigroups, $n$-quasigroups, $n$-groups, $\{1,n\}$-neutral operations on $n$-groupoids, inversing operation on $n$-group, $nHG$-algebras, topological groups.
Recurrence Sequences and Norlud-Bernoulli Polynomials
Mathematica Moravica, Vol. 2 (1998), 161–168.
Abstract. The purpose of this paper is to establish some identities containing Norlund-Bernoulli polynomials, which as one application, yield some results of Toscano [8], Kelisky [5] and Zhang and Guo [10] as special cases, as well as other identities involving Bernoulli-Euler and Fibonacci-Lucas or Pell and Pell-Lucas numbers.
Keywords. Recurrence sequence, Norlund-Bernoulli polynomial, Identity.
On $\{1,n\}$-neutral, Inversing and Skew Operations of $n$-Group
Mathematica Moravica, Vol. 2 (1998), 169–173.
Abstract. The skew operation in n-group $(n \geq 3)$ has been introduced in [1]. Using this operation, n-group has been described in [2] as a variety of type $\langle n,1\rangle$. Aim of this note is to connect the skew operation with neutral and inversing operations which have been introduced in [6] and [7].
Keywords. $n$-semigroups, $n$-quasigroups, $n$-groups, $\{1,n\}$-neutral operations on $n$-groupoids, inversing operation on $n$-group, skew operation on $n$-group.
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2018-05-26 04:08:54
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https://socratic.org/questions/how-do-you-find-the-perimeter-of-a-rectangle-in-simplest-radical-form-in-which-t
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# How do you find the perimeter of a rectangle, in simplest radical form, in which the base is sqrt98 and the height is 5sqrt2?
Oct 29, 2016
34
#### Explanation:
$\sqrt{98} = 9.9$
$5 \cdot \sqrt{2} = 7.1$
Since two sides of the rectangle are 9.9 in length,
$2 \cdot 9.9 = 19.8$
Since the other two sides of the rectangle are 7.1 in length,
$2 \cdot 7.1 = 14.2$
Therefore, the total length of the perimeter of the rectangle is,
$19.8 + 14.2 = 34.0$
Oct 29, 2016
The given rectangle has
$b a s e = \sqrt{98} = \sqrt{{7}^{2} \cdot 2} = 7 \sqrt{2}$
and
$h e i g h t = 5 \sqrt{2}$
So
$P e r i m e t e r = 2 \left(b a s e + h e i g h t\right) = 2 \left(7 \sqrt{2} + 5 \sqrt{2}\right) = 2 \cdot 12 \sqrt{2} = 24 \sqrt{2}$
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2019-11-16 01:32:41
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https://matheducators.stackexchange.com/questions/16668/how-can-i-explain-why-numerical-integration-is-easy-but-symbolic-integration-is/16680
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# How can I explain why numerical integration is easy, but symbolic integration is hard?
I'm asking about definite integrals that can effortlessly be found numerically by high schoolers using software. For example,
$$\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \ \mathrm dx$$
This link shows the numerical integration done by software.
This Reddit comment substantiates that the exact solution is knotty, but not why:
The extent of math that this involves (beyond standard integration techniques usually taught in Calc II, just applied on a large scale), is a significant bit of Complex Analysis (the residue theorem, etc.). In general, everything in his derivation should at least be understandable had you taken Calc I-III and Complex Analysis.
How can I explain to someone who is just getting started in calculus why it's so hard to find the exact solution by symbolic integration, when it's so trivial to get a numerical answer using software?
• – Joel Reyes Noche May 28 at 8:16
• I had a hard time understanding the original version of the question, and other people's comments suggest that I wasn't the only one. Only after re-reading it several times and clicking on the links did I realize what the OP was actually asking. I've rewritten the question to try to make it clearer, while hopefully not losing the OP's intent. – Ben Crowell May 30 at 13:15
• I tried plugging this equation into a TI84 calculator (this model is the "standard" the the teachers in my HS use), and I quickly got a 'divide by 0' error. I then adjusted to integrate from -1 to 0 and then 0 to 1 and got a sum of 8.372205547 which is different than the reported result on the linked page, after the 5th digit. Can I assume that the software 'numerical integration' uses a different algorithm between the 2? – JTP - Apologise to Monica May 30 at 22:00
• Just as, for a five year old, learning addition, subtraction, multiplication, division may be incredibly difficult for most, they can easily be trained to use a calculator to "perform" the operations. That doesn't mean they understand how the operations work, just as being able to strictly use CAS for approximating integrals, numerically, doesn't mean students understand what, in fact, integration is. – Namaste May 31 at 17:10
It might be fun to have your students pretend that the only functions they know are sums of monomials $$cx^n$$ where $$n\in{\bf Z}$$, and in particular, play like they know nothing about the function $$f(x)=\ln(x)$$. You see where this is going: we can easily graph $$f(x)=x^n$$ between $$x=1$$ and $$x=2$$ for any $$n$$, and find an antiderivative with the one annoying exception of $$f(x)=x^{-1}$$.
So, what is done in some developments of calculus? We define a new function $$g(x)=\int_{1}^x \frac{1}{t}\, dt$$ precisely so that we can have an antiderivative for the situation where we were previously stuck, and give $$g(x)$$ the special name $$\ln(x).$$
The point is that integration, unlike differentiation, takes one outside the function type of the integrand, e.g., the derivatives of rational functions are rational functions, but their antiderivatives might not be.
Wrap up the lesson with the xkcd comic found here
https://xkcd.com/2117/
When students learn integration, it's usually the first time they've ever encountered a type of mathematical calculation for which there are techniques, but no general algorithm that always succeeds. A good way of explaining why differentiation is rule-based, but integration is not, is to make the analogy with discrete, finite sums.
If you want to evaluate the sum $$f(n)=1+2+3+\ldots+n$$, you can easily find the result for any given $$n$$, but it's harder to find a general formula for $$f(n)$$. OK, so next show the student how to visualize triangles of dots and use geometrical reasoning to find that the answer is $$n(n+1)/2$$.
But you can now demonstrate that going the opposite way is just a straightforward calculation of $$f(n)-f(n-1)$$, with a simplification to show that the result is $$n$$. This rule-based calculation is like a derivative.
So in your example of using software to numerically evaluate a definite integral, what the software is doing is essentially like finding that $$1+2+3=6$$. That's straightforward and rule-based. But that doesn't mean that we can find the general formula $$n(n+1)/2$$ in the same rule-based way.
• Ah man, this is a great insight I was looking for! I always attributed the phenomenon to the arbitrariness of what most are willing to call a 'closed form' (what if erf is a named/special function for you but you don't consider exp simple or important enough to give a name?) or treated it as a byproduct of that system, but differentiation comprises two evaluations (the usual system of writing being biased so as to make $f(x+\delta)$ (or the difference $f(y)-f(x)$) usually 'simplifiable' or analyzable) and discarding terms that are $o(\delta)$, both of which tend to be amenable to – Vandermonde Jun 2 at 15:07
• convenient writing. Whereas (discrete) integration involved adding an indefinite number of terms (or for normal integration, perhaps you can think of a hyperreal number $N$), and it's a miracle when that sum, as a function of $N$, happens to match one that one counts as familiar. Thank you for finding words for the intuition! – Vandermonde Jun 2 at 15:11
You should expect numerical integration to be "easier" [1] than symbolic integration because it is answering a fundamentally weaker question. That is, symbolic integration, if you can do it, gives you an infinitely precise answer. Numerical integration gives you an answer which is approximate, ideally with some bound on the amount of error.
It is like the difference between $$\sqrt{2}$$ and $$1.414 \pm 0.0003$$.
[1]: You might not find numerical integration quite as easy if you were to do it by hand. If you level the playing field and allow the computer for symbolic integration, it can often be pretty easy too.
This reminds me of one of Euler's papers, where he evaluates (not the definite integral, but indefinite integral) $$\int\frac{dz}{(3\pm z^2)\sqrt[3]{1\pm 3z^2}}$$ using an amazing variety of substitutions and other tricks, among other things the formula $$\arctan(x)-\arctan(y) = \arctan\left(\frac{x-y}{1+xy}\right)$$. (In fact, he evaluates it two different ways!)
I think you can feel perfectly free to say that one the greatest mathematicians of all time struggled with various unusual integrals, even of the type which are actually doable with elementary antiderivatives, and then published papers about them. Maybe we don't do that as much today. And that apparently he also thought it wasn't evident which ones are easy and which ones aren't.
But far from being a discouragement, this should be instead freedom for a student. Use creativity, and see what you get! Use all the tricks you have access to now, acquire more later, and keep trying. And these are good thoughts for life; know what you've got, have a growth learning mindset to get more, and persevere.
• We rarely tell students that integration is actually guess-work. We can do the standard integrals now because we have a list of good guesses. – Jessica B May 29 at 6:20
• @JessicaB, it can be taken beyond guesswork. – Peter Taylor May 29 at 7:30
• True. Though note the part of the Wikipedia page connecting this to the undecidable 'does this expression equal zero' problem. In any case, my point was more the discovery than actual integration of any particular integrand. – kcrisman May 30 at 4:27
• @Peter Taylor, the Risch algorithm might “fail” by determining that the anti-derivative is not an elementary function. Then guesswork resumes...perhaps by using elliptic functions, or perhaps the definite integral can be evaluated by contour integration, etc. – user52817 Jun 1 at 18:31
One way of thinking about it (although I'm not sure whether it would be helpful for the student of interest to you):
What are you doing when you 'graph' the function? At each point on the $$x$$-axis, you calculate the value of the function, and plot that on the $$y$$-axis. That is something that can be done at each value. In practice, we start by knowing this is a 'reasonably nice' function (ie mostly continuous), so you can get away with finding the value at finitely many points and either stopping (on a computer screen) or joining the dots (in your head).
Now, what are you doing when you 'integrate' the function? Finding the area under the graph. Well, sort of. Finding the area under the graph can be done. An integral does exist (ignoring issues about measure etc). That's a point students don't always appreciate. There is an integral, and it is some function. The problem is how to write down what that function is. When a student asks 'can I integrate this?' what they really mean is 'can I write the integral of this function in a reasonably nice formula using functions I am familiar with?'
I think phrased that way, it becomes clear why integration is 'harder' than graphing, which should be sufficient explanation for most 17-year-olds.
(Now I've written it out, I can see that this is similar to the point made by user52817 .)
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2019-11-18 07:49:12
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https://itectec.com/ubuntu/ubuntu-any-command-line-calculator-for-ubuntu/
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# Ubuntu – Any command line calculator for Ubuntu
calculatorcommand linesoftware-recommendation
I am looking for a Calculator which can do calculations in the terminal itself without any other extra prefixes and suffixes.
For example: If I typed something like 10000-9000 in the terminal, the answer should come out as 1000.
Once again I am saying, I just need a quick calculator in terminal, without any characters added. I know if I switch to Python, it can do that but I don't want it in such a way.
• ## Bash Arithmetic
Another possible solution is to add a simple function for Bash's builtin arithmetic. Put this in your .bashrc file to try:
=() {
echo "$(($@))"
}
272 (0x110)
$= 16**3 + 16**4 69632 (0x11000) ## Using bc If you want slightly more advanced calculations, you can pipe it to bc like so: =() { local IFS=' ' local calc="${*//p/+}"
calc="${calc//x/*}" bc -l <<<"scale=10;$calc"
}
= 'sqrt(2)' # Returns 1.4142135623
= '4*a(1)' # Returns pi (3.1415926532)
The functions provided by bc are as follows (and can be found from man bc):
sqrt ( expression )
The value of the sqrt function is the square root of the expression.
If the expression is negative, a run time error is generated.
s (x) The sine of x, x is in radians.
c (x) The cosine of x, x is in radians.
a (x) The arctangent of x, arctangent returns radians.
l (x) The natural logarithm of x.
e (x) The exponential function of raising e to the value x.
j (n,x)
The Bessel function of integer order n of x.
It also supports if, for, while and variables like a programming language though if it may be better to write to a file if you wanted that.
Keep in mind that it will substitute p and x in function/variable names. It may be better to just remove the replacements.
## Using gcalccmd
You can also make the function call gcalccmd (from gnome-calculator) like so:
=() {
local IFS=' '
local calc="$*" # Uncomment the below for (p → +) and (x → *) #calc="${calc//p/+}"
#calc="${calc//x/*}" printf '%s\n quit' "$calc" | gcalccmd | sed 's:^> ::g'
}
= 'sqrt(2)' # Returns 1.4142135623
= '4^4' # Returns 256
The available functions seem to be (taken straight from the source code), == denotes equivalent functions:
ln()
sqrt()
abs()
int()
frac()
sin()
cos()
tan()
sin⁻¹() == asin()
cos⁻¹() == acos()
tan⁻¹() == atan()
sinh()
cosh()
tanh()
sinh⁻¹() == asinh()
cosh⁻¹() == acosh()
tanh⁻¹() == atanh()
ones()
twos()
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2021-08-05 13:39:33
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https://math.stackexchange.com/questions/2360138/putnam-understanding-a-proof-that-a-cancellative-semigroup-s-s-t-for-any-s
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# Putnam: Understanding a proof that a cancellative semigroup $S$ s.t. for any $s\in S$ the set of powers of $s$ is finite, is a group.
$$B2.$$ Let $$S$$ be a non-empty set with a binary operation (written like multiplication) such that:
(1) it is associative;
(2) $$ab = ac$$ implies $$b = c$$;
(3) $$ba = ca$$ implies $$b = c$$;
(4) for each element, the set of its powers is finite.
Is $$S$$ necessarily a group?
I understand the solution given:
Let a be any element. We show that for some n > 1 we have an = a. The set of its powers is finite, so for some r > s we have ar = as. If s = 1, we are done. If not, put b = as-1, then b ar-s+1 = b a, so we may cancel to get an = a with n = r - s + 1 > 1. Now put e = an-1. Then we have ea = ae = a.
Now take any b. We have a(eb) = (ae)b = ab, and cancelling gives eb = b. Similarly, (be)a = b(ea) = ba, so be = b. Hence e is an identity.
Also a has an inverse. If n - 1 = 1, then a = e, so a is its own inverse. If n - 1 > 1, then an-2 is its inverse.
Now if b is any other element, we may use the same argument to find another identity f and an element c such that cb = bc = f. But we have e = ef = f, so the identity is unique and c is an inverse for b.
The problem I am having is that they don't mention anything about the closure of such set $$S$$ under the operation.
For example, take $$S = \{1,2,3\}$$ under multiplication. I wouldn't say this is a group because $$2\times3$$ is not in $$S$$ but it fills all the criteria of the problem. What am I misunderstanding about closure? Is it something so obvious they don't even need to mention it in the solution? Thanks.
• The most "compact" definition of a group I've ever seen is a non-empty set $G$ with an associative operation $\times:G^2\to G$ such that for any $a,b\in G$ there is a unique $c\in G$ and a unique $d\in G$ such that $a\times c=b=d\times a.$ – DanielWainfleet Jul 16 '17 at 1:53
• A "binary operation" by definition is closed. Multiplication is not a binary operation on {1,2,3} because it is not closed. – fleablood Jul 16 '17 at 1:56
• @DanielWainfleet This might interest you. Also, a semigroup S is a group if and only if for every $a\in S$ we have $aS=S=Sa$. – Shaun Nov 28 '18 at 23:48
A "binary operation on a set $S$" is a map $S \times S \to S$. Multiplication on $S = \{1,2,3\}$ is a map $S \times S \to \{1,2,3,4,6,9\}$ not $\to S$.
It doesn't make sense to ask whether or not a binary operation is closed. "Closure" comes up when dealing with subalgebras (sub-algebraic structures). That is, we have a binary operation $\mu : S \times S \to S$ and I have some subset $T \subset S$. Then $\mu$ restricts to a map $T \times T \to S$ and the question of closure is whether or not we can restrict the codomain to $T$ as well.
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2020-02-21 10:32:49
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http://bootmath.com/distribution-of-sum-of-n-i-i-d-symmetric-pareto-distributed-random-variables.html
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# Distribution of sum of $n$ i.i.d. symmetric Pareto distributed random variables
Let $X$ be a random variable which follows the symmetric Pareto distribution. For a fix, real parameter set $\alpha > 0$ and $L>0$, its PDF is defined as
$$p_X(x) = \left\{ \begin{array}{ll} \frac{1}{2}\alpha L^\alpha |x|^{-\alpha-1} & |x| \geq L \\ 0 & \mbox{otherwise.} \end{array} \right.$$
If possible, I would like to derive PDF $p_S(x)$, where $S = \sum_{i=1}^n X_i$. Each $X_i$ is i.i.d. according to the PDF given above. I’m particularly interested in the tail distribution $\overline{F}_S(x) = Pr(S > x)$.
My approach is to calculate the $n$-th power of the CF $\varphi_X(\omega)$ and calculate its Fourier transform to obtain $p_S(x)$. However, I’m uncertain if this procedure is valid here. Is it? Do any restrictions emerge inevitably w.r.t. $\alpha$? I observe some “unhandy terms”. Is it possible to obtain $p_S(x)$ analytically and in closed form?
First of all, the CF of a (one sided) Pareto distribution is given by $\varphi_Y(\omega) = \alpha L^\alpha (-i\omega)^\alpha\Gamma(-\alpha, -i\omega L)$. Is the upper incomplete gamma function well defined for a real negative exponent and imaginary integral bounds?
I have
\begin{eqnarray}
\varphi_S(\omega) &=& \frac{1}{2^n}(\varphi_Y(\omega) + \varphi_Y(-\omega))^n\\
&=& \left(\alpha L^\alpha\right)^n|\omega|^{\alpha n}|\Gamma(-\alpha, i\omega L)|^{n} \cos \left( \arg \left( \Gamma(-\alpha, i\omega L)\right)+ \sigma(\omega)\frac{\alpha\pi}{2}\right)\;,
\end{eqnarray}
where $\sigma(\cdot)$ is the signum function.
Alternatively, I have
\begin{eqnarray}
\varphi_S(\omega) &=& \left( \alpha L^\alpha \int\limits_{L}^\infty x^{-\alpha-1} \cos \left(\omega x \right) \,\mathrm{d}x \right)^n.
\end{eqnarray}
Does this help in any way to get $p_S(x)$ or $\overline{F}_S(x)$? How could I proceed?
P.S.: In my case, n is a power of 2. If the inversion has no chance to succeed for a fix $n$, what would be an appropriate approach to investigate $\lim_{n \to \infty} \overline{F}_S(x)$?
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2018-08-17 21:04:43
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http://pjfz.wetourist.it/indefinite-integral-pdf.html
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# Indefinite Integral Pdf
We read this as “the integral of f of x with respect to x” or “the integral of f of x dx. √ Find the indefinite integral and check the result by differentiation. 2: Antiderivatives and Inde nite Integrals De nition. ANSWERS Inde nite integrals: 1. L' = csc2(a;) (la, —. cot1 +C 13. Fundamental Theorem of Calculus (Relationship between definite & indefinite integrals) If and f is continuous, then F is differentiable and. In such case, an indefinite integral is defined, and also written like this: You are going to work with integral of a simple calculation following this simple steps below. tan (sec tan ) 1 x x 5. Unlimited viewing of the article. Exercises - Tough integrals If you want to refer to sections of Survey of integrating methods while working the exercises, you can click here and it will appear in a separate full-size window. The indefinite integral of f(x) is a FUNCTION and answers the question, "What function when differentiated gives f(x)?" Fundamental Theorem of Calculus. • Derivative of a function represent the slope of the curve at any given point, while integral represent the area under the curve. Want to know how to find the indefinite integral (or anti-derivative) of a polynomial? From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. Of course, one way to think of integration is as antidi erentiation. Below is a table of Indefinite Integrals. 1 Indefinite Integrals Integration is a formalization of the process of antidifferentiation. MasterMathMentor. I want to calculate the indefinite integral, but it seems that order of integration in this particular case matters. Dieckmann, Physikalisches Institut der Uni Bonn This table contains hundreds of expressions: indefinite and definite integrals of elliptic integrals, of square roots, arcustangents and a few more exotic functions. At which of these numbers is f continuous from the right, from th Copy the vectors in the figure and use them to draw the following vectors. [PDF] View JH SIR Physical Chemistry notes for class 12 Mar 8, 2020 [PDF] NV SIR 11TH CLASS PHYSICS NOTES for JEE and Boards Feb 27, 2020 [PDF] DOWNLOAD NV SIR PHYSICS NOTES COMPLETE FOR JEE Feb 22, 2020; DISCLAIMER : This website is created solely for Jee aspirants to download pdf, eBooks, study materials for free. Among the wide range of techniques available, most problems can be handled by one or more of the following methods. Let f (x) be a function. We solve this using a specific method. Indefinite Integral Integration of Exponential and Logarithmic Functions Integration of Trigonometric Functions (PDF) Derivatives text problems (PDF) Parabola. Thus, y = x2 + C, where C is arbitrary constant, represents a family of integrals. We read this as "the integral of f of x with respect to x" or "the integral of f of x dx. 2x2 +3x+C 2. The Indefinite Integral 01. Use differentials to approximate the value of the expression. This free calculus worksheet contains problems on antiderivatives and indefinite integration. √ Find the indefinite integral and check the result by differentiation. If F is an antiderivative of f on an interval, then the most general antiderivative of f on that interval is F(x) + C; where C is an arbitrary constant. dx x ∫ x + 3 5 2 5 Evaluate the integral and check your answer by differentiating. AP Calculus Worksheet: Definite and Indefinite Integrals Review 1. A rational function is called proper if the degree of the numerator. •The following example shows this. ©L f2v0 S1z3 U NKYu1tPa 1 TS9o3f Vt7w UazrpeT CL pLbCG. Introduction. The indefinite integral The fundamental theorem of the indefinite integral says that integration (the process of evaluating an indefinite integral) is the reverse of differentiation. Antiderivatives A. Remember: b is the upper limit and a is the. is continuous and decreasing on the interval. Evaluate them and give your answer to two. Download chapter wise important exam questions and answers Assignments of NCERT Integrals, CBSE Class XII Mathematics - Indefinite Integrals. Instead, when we need to talk about the integral of a function as though itself a function, we use the indefinite integral. •The following example shows this. attempts to find another symbolic expression, F , so that diff (F) = f. Thus, when we go through the reverse process of differentiation, we end up. The fundamental theorem of calculus is a simple theorem that has a very intimidating name. We'll call this the definite integral ''f of x' dx', or the definite indefinite integral--I put these limits on, 'a' to 'b'--to denote 'G of b' minus 'G of a' where 'G prime' is any function whose derivative is 'f'. It is based on the following identity between differentials (where u is a function of x): du = u0 dx. The Basics. CBSE Basic Concepts and Assignment/ Sample Questions for Class XII Mathematics - Indefinite Integrals. Students are advised to practice as many problems as possible as only practice can help in achieving perfection in indefinite integrals. Here is a set of practice problems to accompany the Indefinite Integrals section of the Integrals chapter of the notes for Paul Dawkins Calculus I course at Lamar University. integral: [adjective] essential to completeness : constituent. , integrals where one of the limits is one of the values. Table of basic integrals $$\int dx = x + C$$ $$\int x^n dx = \frac{x^{n+1}}{n+1} + C, \quad n\neq 1$$ $$\int \frac{1}{x} dx = \ln |x| + C$$. Say we are given a function of the form, () =, and would like to determine the antiderivative of. NOTE: A definite integral is a number, while an indefinite integral is a family of functions. Currently, we'd have to write something like If f(x) = x2, then what is F(x)?. It is vague and "not definite". Integral is the world's most advanced cloud-based eFX platform combining features for liquidity management, pricing, distribution and risk management. We now address the question of whether we can compute improper integrals, i. Download CBSE Class 12 Indefinite & Definite Integrals Worksheets in pdf covering all important topics with solutions developed as per CBSE and NCERT Syllabus for Chapter Indefinite & Definite Integrals in Class 12. Indefinite integrals. Common-integrals-and-derivatives-pdf. Toppr provides free study materials, last 10 years of question papers, 1000+ hours of video lectures for free. Example: Suppose you must find the definite integral. Evaluating Definite Integrals Evaluate each definite integral. [PDF] Allen chemistry download Feb 10, 2020. 2u3=2 +2u1=2 +C 8. Indefinite Integrals: $24 ?4 J is a definite integral. Q P bAHlklt grMiDghYtisb Rr[evsNeFr[vseodo. Even and odd integrals. The Definite Integrals will be studied in details, in a second volume, to appear soon. A more complete list appears in Appendix B. The word “integral” refers to the definite integral or the indefinite integral. 1 Definition of Indefinite Integrals. The students should read these basic concepts to gain perfection which will help him to get more. In this first volume we cover the Indefinite Integrals. For more about how to use the Integral Calculator, go to "Help" or take a look at the examples. 1 Definisi Integral Tak Tentu (Indefinite Integral. ŸH3 w+7L„w 5. Z ln p x+ x+1 dx 6. Candidates who are pursuing in Class 12 are advised to revise the notes from this post. 1A1 * AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site. pdf Author: jriddle. After the Integral Symbol we put the function we want to find the integral of (called the Integrand). We'll call this the definite integral ''f of x' dx', or the definite indefinite integral--I put these limits on, 'a' to 'b'--to denote 'G of b' minus 'G of a' where 'G prime' is any function whose derivative is 'f'. Evaluate each indefinite integral. The expression f f(x)dx is read as the antiderivative off with respect to x. [PDF] Download premium Mathematics Revision Notes Chapterwise for JEE Main Feb 15, 2020. It is vague and "not definite". By definition, if the derivative of a function f(x) is f'(x), then we say that an indefinite integral of f'(x) with respect to x is f(x). At this point, in this the 624 Sare Sengul and Yasemin Katranci / Procedia - Social and Behavioral Sciences 197 ( 2015 ) 622 – 629 study, results about revealing the meta-cognitive aspects while solving indefinite integral problems are demonstrated. This section covers: Antiderivatives Basic Integration Rules Trigonometric Integration Rules Indefinite Integration Problems Initial Conditions and Particular Solutions Position, Velocity, and Acceleration More Practice WARNING: The techniques in this section only work if the argument of what’s being integrated is just “\$$x\$$”; in other words, “\$$x\$$” is by itself and doesn’t. They are used interchangeably. Calculators are not allowed. Integrals Indefinite integrals Indefinite integral of a function is a primitive (original, antiderivative) of this function. The indefinite integral The fundamental theorem of the indefinite integral says that integration (the process of evaluating an indefinite integral) is the reverse of differentiation. The indefinite integral of f(x) is a FUNCTION and answers the question, "What function when differentiated gives f(x)?" Fundamental Theorem of Calculus. The indefinite integral of a function is just the set of all the primitives of that function. The definite integral link the concept of area to other important concepts such as length, volume, decsity, probability, and other work. {eq}\int t \sec^2 5t dt {/eq} Indefinite Integrals: We have an indefinite integral with the integrand as a linear function and a secant function. The approach is to break this down into the sum of two integrals, I 1 and I 2, and introduce a third integral, I 3, such that I 1 +I 3 and I 2-I 3 are both easy to do, and so the sum of these two integrals is I 1 +I 2, and that's our answer. Most of them are not found in Gradshteyn-Ryzhik. Indefinite Integrals are studied in considerable depth and extent in my e book "Integrals, Vol. They are asked to check their answers using differentiation. Then, � b a f =F(b)−F(a). Through integration we will reverse the process of differentiation. Integral as an anti-derivative. in Mathematics Education. 3 Antiderivatives and Indefinite Integration. RUMUS-RUMUS INTEGRAL KALKULUS II 1. e e ex a a x a alog log log 2. Integral tak tentu dalam bahasa Inggris biasa di kenal dengan nama Indefinite Integral ataupun kadang juga di sebut Antiderivatif yang merupakan suatu bentuk operasi pengintegralan pada suatu fungsi yang menghasilkan suatu fungsi baru. The process of determining an integral of a function is called integration and the function to be integrated is called the integrand. Example: Suppose you must find the definite integral. POWER (POLYNOMIAL) RULE FOR INTEGRATION x NOTE: n must be rational & n cannot equal -1 ndx = PROCEDURE FOR POWER RULE FOR. To denote the indefinite integral of a function f(x) we write: This is read "the indefinite integral of f(x) with respect to x". 1 Indefinite integral: Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Math 1271 Indefinite Integrals 1. At this point, in this the 624 Sare Sengul and Yasemin Katranci / Procedia - Social and Behavioral Sciences 197 ( 2015 ) 622 – 629 study, results about revealing the meta-cognitive aspects while solving indefinite integral problems are demonstrated. This is the currently selected item. Common-integrals-and-derivatives-pdf. Evaluate each indefinite integral. Want to know how to find the indefinite integral (or anti-derivative) of a polynomial? From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. The Basics. Evaluating indefinite integrals for some other functions is also a straightforward calculation. After you have selected all the formulas which you would like to include in cheat sheet, click the "Generate PDF" button. 10) ∫ 54x 12 - 7x 2 dx. Indefinite integrals of Polynomials. ) Review Answers Indefinite Integrals Practice. The two integrals that have dy as the innermost di erential are Z2 0 Zx 0 x 0 ex(y + 2z) dydzdx + 2 0 Z2x x x z x ex(y + 2z. Single Chapter PDF Download$42. The definite integral of f(x) is a NUMBER and represents the area under the curve f(x) from x=a to x=b. Then, the collection of all. Definition of Definite Integral: Area under a curve: J f (x) dx = lim E f Fundamental Theorem of Calculus states: dX = F — F (a) where F is an antiderivative of f. So the integrals should be expressed by Bessel and Struve functions. Create the function. These together constitute the indefinite integral. Using the given limits of integration, nd F(b) F(a). The integral can be computed to give a finite numerical value on any interval properly contained completely within one of these intervals. Find the indefinite integral \int {\left ( {1 + x} \right)\left. 1 : Jul 16, 2012, 9:04 AM: Kevin Parkinson. By Hariom Singh Mar 31, 2017 19:53 IST. This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course. Example 2 Evaluate the following indefinite integral. then there exists for any indefinite integral of / ( ar ) a representation of the form j*f(x)dx=%n(x)+o(^y provided that the obviously necessary condition is satisfied, that / ( x ) be such as to make the integral periodic. 1 1 sin tan 1 sin x x 7. Identify f (u) and u = g(x) and hence find an indefinite integral of the function. CHAPTER-6 INDEFINITE INTEGRAL, INTEGRAL CALCULUS. Indefinite integral problems come in many different types on the AP Calculus Exams. The class 12 RD Sharma solutions will help students develop better skills and help them prepare efficiently for the exams. So, go ahead and check the Important Notes for Class 12 Maths Indefinite Integrals. This is a very simple idea, but we use a very fancy notation. RUMUS-RUMUS INTEGRAL KALKULUS II 1. Powered by Create your own unique website with customizable templates. This means. •The following example shows this. Use the worksheets. Common-integrals-and-derivatives-pdf. Integral [ u v dx ] = u v - Integral [ u v dx ] = I've attached a beautifully formatted PDF. Free Table of Integrals to print on a single sheet side and side. Then type your equation, press ,, and then type X for the variable of integration (if our integral was with respect to dy, this would be Y. i1-2_terminology_and_notation_for_indefinite_integrals. Substitute u back to be left with an expression in terms of x Steps for nding the De nite Integral 1. or a single function (when one or both of the limits of integration are variables). Indefinite integrals. In such case, an indefinite integral is defined, and also written like this: You are going to work with integral of a simple calculation following this simple steps below. Indefinite integral problems come in many different types on the AP Calculus Exams. RD Sharma Class 12 Solutions Chapter 19 Indefinite Integrals Ex 19. Click here for an overview of all the EK's in this course. This is a very simple idea, but we use a very fancy notation. Generally, integrals of the type R xµJ ν(x)dx may be written with Lommel functions, see [8], 10 -74, or [3], III. pdf Author: jriddle. Objective: Use pattern recognition to evaluate an indefinite integral. Thus, y = x2 + C, where C is arbitrary constant, represents a family of integrals. Implicit multiplication (5x = 5*x) is supported. We read this as “the integral of f of x with respect to x” or “the integral of f of x dx. By Hariom Singh Mar 31, 2017 19:53 IST. INTEGRALS 10. site password to open the PDF file. Which one it refers to will be clear from the context. z F xAtlylg KriagXhitys] ArJegspeBrNvgerdv. Vocabulary: The definite integral of ( ) between two limits and is the area under the curve from = to =. 1), we need a set of validated or established basic integrals, called the table of basic integrals. Create the function. Available as prepackaged workflow management solutions for Banks , Margin Brokers , and Asset Managers , Integral allows major market participants to customize their ideal system to meet their. sec 22 x dx 3. Thus L diagonalizes and d E D(g). Sometimes an approximation to a definite integral is. Integrals - Exercises. We begin by briefly discussing integrals of the form Z 2π 0 F(sinat,cosbt)dt. \) A constant factor can be moved across the integral sign:. The notation used to represent all antiderivatives of a function f( x) is the indefinite integral symbol written , where. In the above discussion, we only considered indefinite integrals. Type in any integral to get the solution, steps and graph Generating PDF Feedback. Although definite and indefinite integrals are closely related, there are some key differences to keep in mind. Indefinite Integrals are studied in considerable depth and extent in my e book "Integrals, Vol. A rational function is called proper if the degree of the numerator. Solved Examples of Indefinite Integral 1. Mathematics A function whose derivative is a given function. Indefinite Integral Notation The notation for an anti-derivative or indefinite integral is: if dF dx = f(x), then Z f(x)dx = F(x)+C Here R is called the integral sign, while dx is called the measure and C is called the integration constant. " We will later see how sums and antiderivatives. 212 x dx x 2. Many known indefinite integrals are recorded in integral tables for all to use. In order to compute the indefinite integrals of the form. If any of the integration limits of a definite integral are floating-point numbers (e. INTEGRATION 70 To check, we di ↵erentiate the above expression, so dI dx = d dx 3 2 ln(2x+2)+C = 3 2 · 1 2x+2 ·2, which is correct! This “special case” is an example of a method called substitution, and is not limited to integrals which give you logarithms. (1) Our method is easily adaptable for integrals over a different range, for example between 0 and π or between ±π. 1 Introduction This chapter has several important and challenging goals. The process of finding an antiderivative is called antidifferentiation or. In such case, an indefinite integral is defined, and also written like this: You are going to work with integral of a simple calculation following this simple steps below. It presents the solutions in a very effective and systematic way. Remember: b is the upper limit and a is the. The indefinite integral The fundamental theorem of the indefinite integral says that integration (the process of evaluating an indefinite integral) is the reverse of differentiation. An indefinite integral involving a square root that can be evaluated by first completing a square. x x dx23cos 7. (Let la 24 1b and lbl 18 lb. All MCQs are taken from old papers of IIT-JEE Examination. ©L f2v0 S1z3 U NKYu1tPa 1 TS9o3f Vt7w UazrpeT CL pLbCG. The two integrals that have dy as the innermost di erential are Z2 0 Zx 0 x 0 ex(y + 2z) dydzdx + 2 0 Z2x x x z x ex(y + 2z. 2 ³x dx3 3. The Indefinite Integral (Section 5. Integrals that cannot be expressed using elementary functions can be manipulated symbolically using general functions such as the Meijer G-function. At which of these numbers is f continuous from the right, from th Copy the vectors in the figure and use them to draw the following vectors. (c) An antiderivative of a difference is the difference of the. The Indefinite Integral Remarks • Make careful note here of the difference between a definite integral and an indefinite integral. The definite integral of from to , denoted , is defined to be the signed area between and the axis, from to. Create the function. Look at the formulas and see how this makes sense!. 1 Indefinite Integral Def: The common notation of antiderivative is ∫f(x)dx ∫f(x)dx=F(x) means F'(x)=f(x) Note that the difference between indefinite integral∫f(x)dx and definite integral f(x)dx a b ∫ is that the former is a function whereas the later is a number. CBSE Basic Concepts and Assignment/ Sample Questions for Class XII Mathematics - Indefinite Integrals. In similar way you can obtain expression with product of a. The Substitution Rule 1. After you have selected all the formulas which you would like to include in cheat sheet, click the "Generate PDF" button. Definite Integral Using U-Substitution •When evaluating a definite integral using u-substitution, one has to deal with the limits of integration. Indefinite integrals with exponential and logarithmic functions - from S. The de nite integral gives the cumulative total of many small parts, such as the slivers which add up to the area under a graph. Download CBSE Class 12 Indefinite & Definite Integrals Worksheets in pdf covering all important topics with solutions developed as per CBSE and NCERT Syllabus for Chapter Indefinite & Definite Integrals in Class 12. Diagonalizable indefinite integral quadratic forms hence the same class. Stu Schwartz Indefinite Integration - Homework Stu Schwartz-U. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard. All Chapter 19 - Indefinite Integrals Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Example 2 Evaluate the following indefinite integral. Also get NCERT solutions, books and worksheets for Class 12 Indefinite & Definite Integrals. Jump to navigation Jump to search. 2 3 1 27 x dx x x 11. Let F(x) be a primitive of f(x). We read this as “the integral of f of x with respect to x” or “the integral of f of x dx. Note 1: f x dx is known as an indefinite integral, since its answer is an indefinite, variable answer. Rewrite first if necessary. integral will give us the exact area, so we need to see how we can find this. To evaluate an indefinite integral (one without definite limits), from the home screen press F3 to access the calculus menu, and then navigate to 2: Integrate. pdf from MATH Integrated at James Madison High School. The function of f( x) is called the integrand, and C is reffered to as the constant of integration. Take note that a definite integral is a number, whereas an indefinite integral is a function. The solutions PDF is a major reference guide to help students score well in the Class 12 examination. The resulting integral can be evaluated immediately to give u6 6 + c. A definite integral is either a number (when the limits of integration are constants) or a single function (when one or both of the limits of integration are variables). Example 1. 7) Differentiation - Natural Logs and Exponentials Differentiate each function with respect to x. For example, in Leibniz notation the chain rule is dy dx = dy dt dt dx. 2: Antiderivatives and Inde nite Integrals De nition. This is a way to check the answer to. In other words it is the anti-derivative. Chapter 10 Infinite series, improper integrals, and Taylor series 10. Z 1 z3 3 z2 dz 6. A probability density function f is defined for all x by (a) (b) (c) (d) Rae f(x) = (a and are positive constants) Show that F (x) — is an indefinite integral of f (x), and determine lirnx-*00 F (x) and lim Show that f Lt f (t) dt = F (x), and that F (x) is strictly increasing. For example, f(x) = x2 −3 x4 +3, g(t) = t6 +4t2 −3 7t5 +3t, and h(s) = 5 s3 −4s2 +3s−8 are all rational functions. 5) ∫ x 2 + 3x + 4dx. Students are advised to practice as many problems as possible as only practice can help in achieving perfection in indefinite integrals. LATEST POSTS: [PDF] Download Allen JEE MAINS 2020 Minor and major Test papers with solutions Apr 12, 2020; How to Develop Effective Study Habits Mar 13, 2020 [PDF] View JH SIR Physical Chemistry notes for class 12 Mar 8, 2020 [PDF] NV SIR 11TH CLASS PHYSICS NOTES for JEE and Boards Feb 27, 2020 [PDF] DOWNLOAD NV SIR PHYSICS NOTES COMPLETE FOR JEE Feb 22, 2020. Let f(x) = 2x. Math Formulas: Integrals of Logarithmic Functions List of integrals involving logarithmic functions. Express the sum x x n x i i i n ∆ + ∑ = →∞ 1 * 3 * ( ) 1 lim, on the interval [0, 10], as a definite integral. By assigning dif ferent values to C, we get dif ferent members of the family. The Indefinite Integral Remarks • Make careful note here of the difference between a definite integral and an indefinite integral. What is the difference between Derivative and Integral? • Derivative is the result of the process differentiation, while integral is the result of the process integration. 1 Antiderivatives and Indefinite Integrals. ³ dx x3 1 3. JEE Questions Indefinite Integration: Official, Free, No Login, Fast PDF Download Get top class preparation for JEE/Mains right from your home: get questions, notes, tests, video lectures and more - for all subjects of JEE/Mains. We'll still use this integral sign, but now put that lower and upper bound on this thing. The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. Indefinite Integral Integration of Exponential and Logarithmic Functions Integration of Trigonometric Functions (PDF) Derivatives text problems (PDF) Parabola. 1) ò 10x4dx 2) ò 16x3dx 3) ò-2x-3dx 4) ò-3x-4dx 5) ò 9x 5 4 4 dx 6) ò-25x 2 3 3 dx 7) ò-9 x4 dx 8) ò-3 x2 dx 9) ò 10 3 x2 3 dx 10) ò 25 4 x 4 dx 11) ò 2 (5x8 + 3) x4. Indefinite integral problems come in many different types on the AP Calculus Exams. To get started, try working from the example problem already populated in the box above. The process of finding the indefinite integral is called integration or integrating f(x). Find the indefinite integral. Want to know how to find the indefinite integral (or anti-derivative) of a polynomial? From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. All the immediate integrals. This is the geometrical interpretation of indefinite integral. [x3 +5] dx d 2. There are two popular notations: These are used in slightly different ways best learned by considering examples. The same is true of our current expression: Z x2 −2 √ u du dx dx = Z x2 −2 √ udu. Integral Calculus – Practice Problems for Test #1 Find the differential. 2) Class Work Find the derivative and state a corresponding integration formula. Gn berman maths book pdf. To obtain double/triple/multiple integrals and cyclic integrals you must use amsmath and esint (for cyclic integrals) packages. Use differentials to approximate the value of the expression. Moreover, closed expression for in the usual literature does not seem to be found. Integrals of Even and Odd Functions. Calculators are not allowed. All Chapter 19 - Indefinite Integrals Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Video tutorial on Integral as an antiderivative, indefinite integrals and the constant 'c&' (IB Math, GCSE, A level, AP). A definite integral is either a number (when the limits of integration are constants) or a single function (when one or both of the limits of integration are variables). Indefinite integrals The expression ∫f ()xdx stands for the function which when differentiated gives f(x). Important Corollary: For any function F whose derivative is f (i. It takes students through 16 problems that get progressively more difficult. To get started, try working from the example problem already populated in the box above. Single Chapter PDF Download $42. Choose your answers to the questions and click 'Next' to see the next set of questions. At this point, in this the 624 Sare Sengul and Yasemin Katranci / Procedia - Social and Behavioral Sciences 197 ( 2015 ) 622 – 629 study, results about revealing the meta-cognitive aspects while solving indefinite integral problems are demonstrated. indefinite integral. Integrals of Even and Odd Functions. 1 Indefinite Integral Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard Created Date: 5/9/2016 9:39:46 PM. z F xAtlylg Kr`iagXhitys] ArJegspeBrNvgerdv. Gn berman pdf free download. Some properties of integrals Distance interpretation of the integral. Remember, the definite integral represents the area between the function and the x-axis over the given interval. The curvy symbol is the symbol for the integral. Indefinite Integrals and General Antiderivatives Click to enlarge This PG code shows how to check answers that are indefinite integrals or general antiderivatives. The solutions PDF is a major reference guide to help students score well in the Class 12 examination. Example 2 Evaluate the following indefinite integral. By assigning dif ferent values to C, we get dif ferent members of the family. 2 The Indefinite Integral. 212 x dx x 2. Simplest integration rules. Integration as defined in Section 9. This states that if is continuous on and is its continuous indefinite integral, then. ∫ x4 +3x−9dx. formed as a unit with another part. Meta Description: RD Sharma Solutions for Class 12 Maths Chapter 19 – Indefinite Integrals comprises detailed solutions to all the exercises present in this chapter. dx x x ∫ +2 +2 1 2 9. This proves (ii). If ∂ [email protected][email protected], then the indefinite integral of f[x] is [email protected]=‡[email protected] x, Indefinite integral is just the inverse to derivative. Indefinite Integrals of Polynomials. These two integrals are connected by the so called "Fundamental Theorem of Calculus". Compute F" (x) and show that F has an inflection point xo. Combine multiple words with dashes(-), and seperate tags with spaces. Get Started. CONTINUITY IMPLIES INTEGRABILITY. Also get NCERT solutions, books and worksheets for Class 12 Indefinite & Definite Integrals. Indefinite relative clause definition, a relative clause with an indefinite relative pronoun as subordinating word, as what they said in We heard what they said. dx In Exercises 47—52, evaluate the integral using (a) the given integration limits and (b) the limits obtained by trigonometric substitution. Partially the integrals may be found by MAPLE. For the definite integral , we have two ways to go: 1 Evaluate the indefinite integral which gives 2 Use the above steps describing Integration by Parts directly on the given definite integral. being, containing, or relating to one or more mathematical integers. A rational function is called proper if the degree of the numerator. Remember, the definite integral represents the area between the function and the x-axis over the given interval. Connecting Algebra to Calculus Indefinite Integrals Objective: Find Antiderivatives and use basic integral formulas to find Indefinite Integrals and make connections to Algebra 1 and Algebra 2. At this point, in this the 624 Sare Sengul and Yasemin Katranci / Procedia - Social and Behavioral Sciences 197 ( 2015 ) 622 – 629 study, results about revealing the meta-cognitive aspects while solving indefinite integral problems are demonstrated. If G(x) is any one of the primitives of f(x), then G(x) and F(x) only differ by a constant. Definition of Definite Integral: Area under a curve: J f (x) dx = lim E f Fundamental Theorem of Calculus states: dX = F — F (a) where F is an antiderivative of f. 1) ò 10x4dx 2) ò 16x3dx 3) ò-2x-3dx 4) ò-3x-4dx 5) ò 9x 5 4 4 dx 6) ò-25x 2 3 3 dx 7) ò-9 x4 dx 8) ò-3 x2 dx 9) ò 10 3 x2 3 dx 10) ò 25 4 x 4 dx 11) ò 2 (5x8 + 3) x4. Through the fundamental. For the functions other than sin and cos, there's always either one tan and two secants, or one cot and two cosecants on either side of the formula. (a) a + b (b) a b (c) 12a (d) 3b (e Calculus: Early Transcendentals. (x + 3) √ ( 3 - 4x - x 2 ) - View solution. 2 Integration The indefinite integral of the standard normal PDF is given by T(x) = Z ϕ(x)dx = Z 1 √ 2π ·e−1 2 x2 dx. cot1 +C 13. This is read “The indefinite integral of f(x) with respect to x is F(x) + c". Standards: Algebra 1 2. NOTE: A definite integral is a number, while an indefinite integral is a family of functions. In all of our examples above, the integrals have been indefinite integrals - in other words, integrals without limits of integration (the "a" and "b" in the statement "the integral from a to b"). 1 Problem statement By the fundamental theorem of calculus, to calculate an integral � b a f we need to find a function F satisfying F′ = f. We begin by briefly discussing integrals of the form Z 2π 0 F(sinat,cosbt)dt. Mathematics Learning Centre, University of Sydney 5 Exercises 1. In similar way you can obtain expression with product of a. -1-Evaluate each indefinite integral. This is read "The indefinite integral of f(x) with respect to x is F(x) + c". pdf View Download: 36k: v. 1A - Antiderivatives and Indefinite Integration Objectives: 1. If one or both integration bounds a and b are not numeric, int assumes that a <= b unless you explicitly specify otherwise. Say we are given a function of the form, () =, and would like to determine the antiderivative of. Fungsi ini belum memiliki nilai pasti hingga cara pengintegralan yang menghasilkan fungsi tidak tentu ini. 4-D Integral of Sphere. The number e is often associated with compounded or accelerating growth, as we have seen in earlier sections about the derivative. The Indefinite Integral (Section 5. Press [MENU]→Calculus→Integral to open the Integral command. 1) ò 5x4 (x5 - 5) 3dx; u = x5 - 52) ò 20x3 (5x4 + 2) 5dx; u = 5x4 + 2 3) ò 15x2. Free Integration Worksheet. 3 understand the applications of indefinite integrals in real-life or mathematical contexts Applications of indefinite integrals in some fields such as geometry and physics are required. For example: $\int{2x}\ dx$ is just asking for the anti-derivative of $2x$. Basic Integrals The following are some basic indefinite integrals. It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems. pdf doc Improper Integrals - Recognizing an improper integral and using a value of an integral to find other values. Create the function. 3 Properties of inde nite integral Next we shall prove three properties of the indefinite integrals and use them to integrate some functions. 0 Unported license. the eBook will be available in PDF (PBK) format, which cannot be reflowed. The limit is called the definite integral of f over [a, b]. Selection File type icon File name Description Size Revision Time User; Ċ: Definite Integrals-07152012150440. We adopt the convention that, when a formula for a general indefinite integral is given, it is valid only on an interval. 3) ∫ 5x 9 - 4x 5 + 5x 3 dx. All these integrals differ by a constant. However, it can be expressed in closed form by using the upper incomplete gamma function [9, Equation ]:. Using the given limits of integration, nd F(b) F(a). 2 becomes its integral. The solutions PDF is a major reference guide to help students score well in the Class 12 examination. Indefinite Integrals. If ∫xe xcosxdx = f(x)+c, then f (x) is equal to. To obtain double/triple/multiple integrals and cyclic integrals you must use amsmath and esint (for cyclic integrals) packages. 4 Definition 4. According to the first fundamental theorem of calculus, a definite integral can be evaluated if #f(x)# is continuous on [#a,b#] by:. There are two popular notations: These are used in slightly different ways best learned by considering examples. This is read “The indefinite integral of f(x) with respect to x is F(x) + c". On this page you can read or download rs aggarwal solutions indefinite integral in PDF format. Figure $$\PageIndex{1}$$: Understanding the indefinite integral notation. Indefinite Integrals and General Antiderivatives Click to enlarge This PG code shows how to check answers that are indefinite integrals or general antiderivatives. The connection is give by Evaluation theorem: f(x)dx a b ∫=∫f(x. 2B Improper Integrals. If we need to be specific about the integration variable we will say that we are integrating f(x) with respect to x. ³ dx x3 1 3. Click the blue arrow to compute the integral. It takes students through 16 problems that get progressively more difficult. The process of determining an integral of a function is called integration and the function to be integrated is called the integrand. The reason is because a derivative is only concerned. 6 6 2 2 sin cos sin cos x x x x 6. How to Calculate Indefinite Integrals. Thus, y = x2 + C, where C is arbitrary constant, represents a family of integrals. The process of finding the indefinite integral is called integration or integrating f(x). 3 understand the applications of indefinite integrals in real-life or mathematical contexts Applications of indefinite integrals in some fields such as geometry and physics are required. 201-NYA-05 - Calculus 1 WORKSHEET: INTEGRALS Evaluate the following inde nite integrals: 1. Then type your equation, press ,, and then type X for the variable of integration (if our integral was with respect to dy, this would be Y. notebook February 27, 2018 Objective: Given the rules to find antiderivatives students will be able to find the integral of a given function. notebook 3 February 10, 2020 The expression is read as the antiderivative identify x as the variable of integration. High velocity train [Image source ] A very useful application of calculus is displacement, velocity and acceleration. primitive or anti-derivative is termed as F(x) Integrand is termed as f(x). Fundamental Theorem of Calculus (Relationship between definite & indefinite integrals) If and f is continuous, then F is differentiable and. If F(x) is an integral of f(x) then F(x) + C is also an integral of f(x), where C is any constant. If G(x) is any one of the primitives of f(x), then G(x) and F(x) only differ by a constant. Then we find A and B. Integrals from - to : Even and Odd Functions The integral of any even function taken between the limits - to is twice the integral from 0 to. A template containing four fields is pasted to the entry line. Indefinite integrals of sin(x), cos(x), and eˣ Well once again, we can rewrite it as the sum of integrals. Numerically, it is a limit of Riemann sums: Z b a f(x)dx = lim n!1 Xn i=1 f(x i) x; where we divide the interval x 2[a;b] into n increments of size x = b. Indefinite integrals The expression ∫f ()xdx stands for the function which when differentiated gives f(x). 9 points SCalcET8 122032 Find the magnitude of the resultant force and the angle it makes with the positive x-axis. Fundamental Theorem of Calculus (Relationship between definite & indefinite integrals) If and f is continuous, then F is differentiable and. The terms indefinite integral and antiderivative are synonymous. Thus L diagonalizes and d E D(g). Indefinite Integrals and General Antiderivatives Click to enlarge This PG code shows how to check answers that are indefinite integrals or general antiderivatives. Definition - F is AN antiderivative of f on an interval I if F¢(x) = f (x) for. 1 Problem statement By the fundamental theorem of calculus, to calculate an integral � b a f we need to find a function F satisfying F′ = f. The given interval is partitioned into " n" subintervals that, although not necessary, can be taken to be of equal lengths (Δ x). For the definite integral , we have two ways to go: 1 Evaluate the indefinite integral which gives 2 Use the above steps describing Integration by Parts directly on the given definite integral. Taking the indefinite integral of a continuous function in one variable, just means you are finding the anti-derivative. indefinite integral synonyms, indefinite integral pronunciation, indefinite integral translation, English dictionary definition of indefinite integral. 1 Indefinite Integrals Integration is a formalization of the process of antidifferentiation. Evaluate the indefinite integral. ) Review Answers Indefinite Integrals Practice. 2 If two functions differ by a constant, they have the same derivative. RD Sharma class 12 solutions for the chapter 19 - Indefinite Integrals is given here. indefinite integral synonyms, indefinite integral pronunciation, indefinite integral translation, English dictionary definition of indefinite integral. AP Calculus Worksheet: Indefinite Integrals Evaluate the following integrals. High velocity train [Image source ] A very useful application of calculus is displacement, velocity and acceleration. Through integration we will reverse the process of differentiation. Z 1 1 tan2 x dx 5. It is also worth noting that unlike derivative (we can find derivative of any function), we can't find integral of any function: this means that we can't find integral in terms of functions we know. The basic notions of integral calculus are two closely related notions of the integral, namely the indefinite and the definite integral. If F is an antiderivative of f on an interval, then the most general antiderivative of f on that interval is F(x) + C; where C is an arbitrary constant. For a complete list of Integral functions, please see the list of integrals. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. All Integrals Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. q = integral (fun,xmin,xmax,Name,Value) specifies additional options with one or more Name,Value pair arguments. Use basic integration rules to find antiderivatives. 1, The Indefinite Integral". [g(x) f(x)] = x e–ax2 even odd*even Figure 1. The students should read these basic concepts to gain perfection which will help him to get more. 1 Indefinite integral: Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Integrate with respect to u 6. the Indefinite Integral of x^2lnx dx? need help. pdf doc Improper Integrals - Recognizing an improper integral and using a value of an integral to find other values. The graph tells us which output is associated with a particular input. Mathematics Integrals with exponential function Integrals with logarithmic function. Date: Calculus II Name: Section: Integral Gateway Quiz (sample) ID: Find each indefinite integral. v6 2 3v8=3 8 +C 11. p Worksheet by Kuta Software LLC. THE SUBSTITUTION RULE 16 1. 212 x dx x 2. The indefinite integral of a function ( ) is the family of all functions that are antiderivatives of ( ). Download chapter wise important exam questions and answers Assignments of NCERT Integrals, CBSE Class XII Mathematics - Indefinite Integrals. The indefinite integral of the sum of two functions is equal to the sum of the integrals: 5. pdf doc ; Improper Integrals by Comparison - Using comparison to prove an integral converges/ diverges. Find the indefinite integral \int {\left ( {1 + x} \right)\left. Note 1: f x dx is known as an indefinite integral, since its answer is an indefinite, variable answer. Define indefinite integral. Both of the limits diverge, so the integral diverges. Now, we introduce a notation that was covered in 3. Integration Rules. All these integrals differ by a constant. Math Formulas: Integrals of Logarithmic Functions List of integrals involving logarithmic functions. The table can also be used to find definite integrals using the fundamental theorem of calculus. But these integrals are very similar geometrically. TheÒ#ß_Ñ refore, by the integral test, the series and the integral " (8œ# _ #" _ "8 8 B B. Choose your answers to the questions and click 'Next' to see the next set of questions. p g rM KaLdzeG fw riEtGhK lI 3ncf XiKn8iytZe0 9C5aYlBc Ru1lru 8si. In all of our examples above, the integrals have been indefinite integrals - in other words, integrals without limits of integration (the "a" and "b" in the statement "the integral from a to b"). Z ln p x+ x+1 dx 6. Integrals Indefinite integrals Indefinite integral of a function is a primitive (original, antiderivative) of this function. Elementary integrals All of these follow immediately from the table of derivatives. Integration is like filling a tank from a tap. If G(x) is any one of the primitives of f(x), then G(x) and F(x) only differ by a constant. (c) An antiderivative of a difference is the difference of the. Table of Trig Integrals. Ÿsin5 q„q 6. relating to or concerned with mathematical integration or the results of mathematical integration. Example 1. dx ∫2x+3 1 5. From Wikibooks, open books for an open world < Calculus | Indefinite integralCalculus | Indefinite integral. formed as a unit with another part. Recall (from Derivative as an Instantaneous Rate of Change) that we can find an. Many known indefinite integrals are recorded in integral tables for all to use. of f with respect to x. Hardback$144. Note 2: F x C is known as the general antiderivative, as opposed to an antiderivative. NOTE: A definite integral is a number, while an indefinite integral is a family of functions. ©2005 BE Shapiro Page 3 This document may not be reproduced, posted or published without permission. Z 4 z7 7 z4 +z. Combine multiple words with dashes(-), and seperate tags with spaces. Question: Determine the indefinite integral value. Physics Helpline L K Satapathy Integral Parsial. Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed. Then, � b a f =F(b)−F(a). [g(x) f(x)] = x e–ax2 even odd*even Figure 1. 212 x dx x 2. The given interval is partitioned into " n" subintervals that, although not necessary, can be taken to be of equal lengths (Δ x). Integral Mean Value Theorem. CONTINUITY IMPLIES INTEGRABILITY. Free PDF download of Class 12 Indefinite & Definite Integrals Worksheets with answers will help in scoring more marks in your class tests and school examinations, click links below for worksheets with important questions for Class 12 Indefinite & Definite Integrals chapter wise with solutions. Problem Statement. Let F(x) be a primitive of f(x). ) Review Answers Indefinite Integrals Practice. Similarly, here we offer Theory - Integration. ppt Author: Ilona DiCosmo Created Date: 1/20/2014 6:42:31 PM. (b) Let’s guess that this integral is divergent. CONTINUITY IMPLIES INTEGRABILITY. All the solutions of Indefinite Integrals - Mathematics explained in detail by experts to help students prepare for their CBSE exams. 10) ∫ 54x 12 - 7x 2 dx. Indefinite Integral Notation The notation for an anti-derivative or indefinite integral is: if dF dx = f(x), then Z f(x)dx = F(x)+C Here R is called the integral sign, while dx is called the measure and C is called the integration constant. Using the given limits of integration, nd F(b) F(a). ∫ [f(x)+g(x)]dx = ∫ f(x)dx+ ∫ g(x)dx, i. In case of integrals of the form. Finding Parallel and Perpendicular Lines In Exercises 65 and 66, find an equation of the line passing through t Calculus: An Applied Approach (MindTap Course List) Expanding a Logarithmic Expression In Exercises 5 and 6, use the properties of logarithms to. What is the primary difference between using anti-differentiation when finding a definite versus an indefinite integral? Indefinite integrals don't have defined limits. Next lesson. Because integration reverses differentiation, when we integrate we have to re-introduce the additive constant that is lost when we differentiate. The Table of Integrals, Series, and Products is the major reference source for integrals in the English language. ∫ 6 10 x − x 2 d x Buy Find arrow_forward Calculus: Early Transcendental Fun. Fulton 1 Overview A rational function has the form r(x) = p(x) q(x) where p and q are polynomials. After you have selected all the formulas which you would like to include in cheat sheet, click the "Generate PDF" button. In order to compute the indefinite integrals of the form. The indefinite integral of the difference of two functions is equal to the difference of the integrals: $$\int {\left[ {f\left( x \right) – g\left( x \right)} \right]dx} =$$ $$\int {f\left( x \right)dx} – \int {g\left( x \right)dx}. Therefore, the desired function is f(x)=1 4. This is a very simple idea, but we use a very fancy notation. INDEFINITE INTEGRAL Finding the indefinite integrals Reduction to basic integrals, using the rule ∫ ′ ( ) ⋅f nx ( ) dx = 1. Through the fundamental. 2 PROBLEM SET 7 SOLUTIONS (a) R ln(x) x dx ANSWER: You can do this integral by integration by parts (see below), but its much easier to just substitute u = ln(x), because then du = 1 x dx and the integral just becomes Z udu = u2 2 +C = 1 2 (ln(x))2 +C. 1 Introduction This chapter has several important and challenging goals. dx In Exercises 47—52, evaluate the integral using (a) the given integration limits and (b) the limits obtained by trigonometric substitution. pdf: File Size: 416 kb: File Type: pdf: Download File. The techniques for calculating integrals. Below is a table of Indefinite Integrals. The indefinite integral of the difference of two functions is equal to the difference of the integrals: 6. The process of solving for antideriv. ∫x (1 +x3)dx 8. Integral as an anti-derivative. It is after many integrals that you will start to have a feeling for the right choice. Comparisons With Non-p-Integrals. Verify the statement by showing that the derivative of the right side is equal to the integrand of the. RD Sharma class 12 solutions for the chapter 19 - Indefinite Integrals is given here. For example: $\int{2x}\ dx$ is just asking for the anti-derivative of $2x$. The Substitution Rule 1. Useful for IIT JEE CET PU AP-Maths many other Mathematics High School Exams College courses and examinations. The instructional activity introduces antiderivatives and indefinite integrals to the class along with the notation for integrals. TABLE OF INTEGRALS 1. The interface is specifically optimized for mobile phones and small screens. Indefinite integral, i. 1A1 * AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site. Scribd is the world's largest social reading and publishing site. Integration is the "inverse" of differentiation. Evaluating definite integrals Introduction Definite integrals can be recognised by numbers written to the upper and lower right of the integral sign. Then f(x)dx x c. Suppose that f and g are continuous functions and that Ÿ1 2f HxL „x =-4, Ÿ 1 5f HxL „x =6, Ÿ 1 5gHxL „x =8 Use the properties of definite integrals to find each integral. Nevertheless, it is a good sighter for what’s to follow. If one or both integration bounds a and b are not numeric, int assumes that a <= b unless you explicitly specify otherwise. Save as PDF Page ID 8159 It is important to note that these formulas are presented in terms of indefinite integrals. If you don't see any interesting for you, use our search form on bottom ↓. The solutions PDF is a major reference guide to help students score well in the Class 12 examination. Remark: A definite integral is a number, equal to the value of an infinite sum. INTEGRALS 10. Example 2 Evaluate the following indefinite integral. The main topic is integrals. Fundamental Theorem of Calculus (Relationship between definite & indefinite integrals) If and f is continuous, then F is differentiable and. ANSWER: Let 1u g(x) 5x2 and du g'(x) 10xdx. The term “indefinite integral” is a synonym for antiderivative. Solved Integration Problems Pdf. It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems. Of the four terms, the term most commonly used is integral, short for indefinite integral. Take note that a definite integral is a number, whereas an indefinite integral is a function. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. RD Sharma Class 12 Solutions Chapter 19 Indefinite Integrals Ex 19. Definite vs. Leave these fields blank if you […]. The Indefinite Integral (Section 5. The int command evaluates the indefinite integral by just producing its anti-derivative (without the constant of integration), and does not print the integral symbol. In x In In 2x4 cos In 4x. The Basics. 7) ∫ (x 2 + 2) 2 + (4 - 5x) 2 dx. Area above the x-axis is positive. The indefinite integral of the difference of two functions is equal to the difference of the integrals: \(\int {\left[ {f\left( x \right) – g\left( x \right)} \right]dx} =$$ \(\int {f\left( x \right)dx} – \int {g\left( x \right)dx}. I can find a particular solution of a differential equation using an initial condition. In this case, each integral represents a parabola with its axis along.
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2020-05-25 00:22:59
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https://yourlisten.com/jk3fz4sy
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This particular filter downstairs $a,b)$ near $$\left\frac970705506078364164096, \frac970705507078364164096\right) \approx \left.1238710981,1238710982\right)$$ accordingly the 14 sway produce however caused 8 decimal figures $1\,2\,3\,8\,7\,1\,0\,9\,8$ (furthermore about a 9th, that is each 1 or maybe 2), a productivity associated with higher than $\frac148=1.75$ move per numeral. The rules can be found in suites regarding 10, and you'll cause the latest alined on any purpose, inevitably building the long forgotten put sluggish.
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2017-12-14 23:22:54
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http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=96-219
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96-219 C. Landim and H.-T. Yau
Fluctuation--dissipation equation of asymmetric simple exclusion processes (281K, ps) May 21, 96
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers
Abstract. We consider asymmetric simple exclusion processes on the lattice $\Bbb Z^d$ in dimension $d\ge 3$. We denote by $L$ the generator of the process, $\nabla$ the lattice gradient, $\eta$ the configuration, and $w$ the current of the dynamics associated to the conserved quantity. We prove that the fluctuation--dissipation equation $w = L u + D \nabla \eta$ has a solution for some function $u$ and some constant $D$ identified to be the diffusion coefficient. Intuitively, $Lu$ represents rapid fluctuation and this equation describes a decomposition of the current into fluctuation and gradient of the density field, representing the dissipation.
Files: 96-219.ps
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2019-11-22 04:56:07
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https://www.sanfoundry.com/soil-mechanics-questions-answers-freshers/
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# Soil Mechanics Questions and Answers – Permeability of Stratified Soil Deposits
«
»
This set of Soil Mechanics Questions and Answers for Freshers focuses on “Permeability of Stratified Soil Deposits”.
1. Each layer of stratified soil deposit has its own coefficient of permeability.
a) True
b) False
Explanation: This is true as each layer of the soil in the soil deposit could contain different grain sizes, voids ratio, entrapped and frozen matter, etc.
2. The average coefficient of permeability of whole deposit will depend upon _________
a) direction of flow with respect to bedding plane
b) direction of flow but not with respect to the bedding plane
c) length of the bedding plane
d) width of the bedding plane
Explanation: The average coefficient of permeability does not depend upon the length or the width of the bedding plane but rather depends upon direction of flow with respect to bedding plane.
3. The average permeability parallel to the bedding planes is given by________
a) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}*\frac{1}{2}$$
b) $$k = \frac{1}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
c) $$k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
d) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
Explanation: For flow parallel to the bedding plane,
Total discharge=sum of discharge through the individual layers
q=q1+q2+…+qn
q=kiz=k1 z1+k2 z2+⋯.+kn zn
∴ $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}.$$
Sanfoundry Certification Contest of the Month is Live. 100+ Subjects. Participate Now!
4. The average permeability perpendicular to the bedding planes is given by________
a) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}*\frac{1}{2}$$
b) $$k = \frac{1}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
c) $$k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
d) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
Explanation: For flow perpendicular to the bedding plane,
The head loss through the individual layers is different,
h=h1+h2+….+h3
Since the velocity is given by,
V=ki=kh/L
∴h=vz/k
vz/k=v1z1/k1+ v2z2/k2+….+ vnzn/kn
∴ $$k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
5. A soil deposit has three layers of soil. The permeability of the second layer is twice that of the first layer and the permeability of the third layer is thrice that of the first layer. The thickness of each layer is 5m. What will be its average permeability parallel to the bedding plane?
a) k
b) 2k
c) 3k
d) 4k
Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=2k
K3=3k
And z1=z2=z3=5m
For flow parallel to the bedding plane,
$$K_x=\frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
$$K_x=\frac{5k+10k+15k}{15}$$
∴ Kx=2k.
6. What will be its average permeability perpendicular to the bedding plane if a soil deposit has three layers of soil? The permeability of the second layer is twice that of the first layer and the permeability of the third layer is thrice that of the first layer. The thickness of each layer is 5m.
a) 11k
b) 18k
c) $$\frac{11}{18}k$$
d) $$\frac{18}{11}k$$
Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=2k
K3=3k
And z1=z2=z3=5m
For flow perpendicular to the bedding plane,
$$K_z = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
$$K_z = \frac{15}{\frac{5}{k}+\frac{5}{2k}+\frac{5}{3k}} = \frac{18}{11} k.$$
7. A soil deposit has three layers of soil. The permeability of the second layer is 1/2 that of the first layer and the permeability of the third layer is 1/3 that of the first layer. The thickness of each layer is equal. What will be its average permeability parallel to the bedding plane?
a) 11k
b) 18k
c) $$\frac{11}{18}k$$
d) $$\frac{18}{11}k$$
Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=1/2k
K3=1/3k
And z1=z2=z3=z
For flow parallel to the bedding plane,
$$K_x=\frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
$$K_x=\frac{zk+\frac{zk}{2}+\frac{zk}{3}}{3z}$$
∴ Kx=$$\frac{11}{18}k$$.
8. What will be its average permeability perpendicular to the bedding plane if a soil deposit has three layers of soil? The permeability of the second layer is 1/2 that of the first layer and the permeability of the third layer is 1/3 that of the first layer. The thickness of each layer is equal.
a) k
b) 1/2k
c) 1/3k
d) 1/4k
Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=1/2k
K3=1/3k
And z1=z2=z3=z
For flow perpendicular to the bedding plane,
$$K_z = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
$$K_z = \frac{z}{\frac{z}{k}+\frac{2z}{k}+\frac{3z}{k}}=\frac{1}{2}k.$$
9. The coefficient of permeability of the two soil layers 1 and 2 in soil deposit is 9*10-7 cm/s and 4*10-7 cm/s respectively. The thickness of the layers is equal. The value of average permeability parallel to bedding planes is ________
a) 4.5*10-7 cm/s
b) 5.5*10-7 cm/s
c) 6.5*10-7 cm/s
d) 7.5*10-7 cm/s
Explanation: Given,
K1=9*10-7 cm/s
K2=4*10-7 cm/s
Let the thickness of each layer be z,
Therefore the total thickness is 2z.
For flow parallel to the bedding plane,
$$K_x=\frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
$$K_x=\frac{z*9*10^{-7}+ z*4*10^{-7}}{2z}$$
∴ Kx=6.5*10-7 cm/s.
10. The coefficient of permeability of the two soil layers 1 and 2 in soil deposit is 9*10-7 cm/s and 4*10-7 cm/s respectively. The thickness of the layers is equal. The value of average permeability perpendicular to bedding planes is ________
a) 4.5*10-7 cm/s
b) 5.5*10-7 cm/s
c) 6.5*10-7 cm/s
d) 7.5*10-7 cm/s
Explanation: Given,
K1=9*10-7 cm/s
K2=4*10-7 cm/s
Let the thickness of each layer be z,
Therefore the total thickness is 2z.
For flow perpendicular to the bedding plane,
$$K_z = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
$$K_z = \frac{2z}{\frac{z}{9*10^{-7}}+\frac{z}{4*10^{-7}}}$$
∴ Kz = 5.5*10-7 cm/s.
Sanfoundry Global Education & Learning Series – Soil Mechanics.
To practice all areas of Soil Mechanics for Freshers, here is complete set of 1000+ Multiple Choice Questions and Answers.
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2023-02-03 07:53:12
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https://doc.rasdaman.org/05_geo-services-guide.html
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# 5. Geo Services Guide¶
This guide covers the details of Geo data management in rasdaman. This is supported through a separate component called petascope. Further components are concerned with data ingestion and CRS definition management.
petascope implements the following OGC interface standards:
For this purpose, petascope maintains its additional metadata (such as georeferencing) which is kept in separate relational tables. Note that not all rasdaman raster objects and collections are available through petascope by default, mainly those that have been ingested via WCS-T.
Petascope is implemented as a war file of servlets which give access to coverages (in the OGC sense) stored in rasdaman. Internally, incoming requests requiring coverage evaluation are translated into rasql queries by petascope. These queries are passed on to rasdaman, which constitutes the central workhorse. Results returned from rasdaman are forwarded to the client, finally.
## 5.1. Servlet endpoints¶
Once the petascope servlet is deployed (TODO see installation guide), the following service endpoints are available:
• /rasdaman: context path
• rasdaman/ows: serving OGC Web Services (OWS) like WCS, WCPS, WMS and WCS-T:
• rasdaman/rasql: direct RasQL.
For example, assuming that the service’s IP address is 123.456.789.1 and the service port is 8080, the following request URLs would deliver the Capabilities documents for OGC WMS and WCS, respectively:
http://123.456.789.1:8080/rasdaman/ows?SERVICE=WMS&REQUEST=GetCapabilities&VERSION=1.3.0
http://123.456.789.1:8080/rasdaman/ows?SERVICE=WCS&REQUEST=GetCapabilities&VERSION=2.0.1
## 5.2. The world of coverages¶
### 5.2.1. Offset vectors and coefficients¶
In ISO and OGC specifications, a coverage is defined as a function from a spatial and/or temporal domain to an attribute range. Such domain can represent both vector or raster datasets, including a variety of different topologies like images, point clouds, polygons, triangulated irregular networks, etc. Coverages in the Earth Observation (EO) domain usually tend to model coverages as a geometric grid of points, a.k.a. grid coverages.
Grid coverages are a network of points connected by lines, retaining a gridded structure. Their geometric domain can either be expressed in an analytic form ((geo)rectified grids), or they need non-affine transforms to translate the internal indexed grid to the external (geo) Coordinate Reference System (CRS). Grid coverages inherently have a dimensionality, which is determined by the number of its axis. These axes are not to be confused with the axes of the CRS which defines dimensionality of the tuples of coordinates of each grid point. Indeed the dimensionality of a grid is not necessarily equal to the dimensionality of its CRS (its however surely not greater for geometric constraints): an (oblique?) 2D grid can always be put inside a 3D CRS, for instance.
Petascope currently supports grid topologies whose axes are aligned with the axes of the CRS. Such kind of grids are a subset of GML rectified grids, with the constraint that the offset vectors – the vectors which determine the (fixed) relative geometric distance between grid points along a grid axis – need to be parallel to an axis of the (external) CRS. In such cases, an offset vector can be regarded as resolution of the grid along an axis.
Rectified grids with non-aligned grid axis / offset vectors are not (yet) supported.
======= ALIGNED GRID ======= ===== NON-ALIGNED GRID =====
N ^ ^ 1 N ^ / 1
| | | .
| .-----.-----. | / \.
| | | | | / /\
| .-----.-----. | . / .
| | | | | / \. /
| ^-----.-----. | / /\ /
| v1 | | | GO(N) x- - @ / .
GO(N) x- - @---->.-----.---> 0 | |\. /
| GO| v0 | | \./
CO O____x________________> E CO O____x__\__________> E
GO(E) GO(E) \
0
@ = Grid Origin (GO) O = CRS Origin (CO)
. = grid point E,N = CRS axis labels
0,1 = grid axis labels --> = offset vector (v0,v1)
In addition (starting from version 9.0.0) Petascope supports aligned grids with arbitrary (irregular) spacing between points along one or more (or all) grid axes. This kind of geometry is a subtype of (geo)referenceable grids and can be defined by attaching a set of coefficients (or weights) to an offset vector. The series of coefficients determines how many offset vectors is a grid point geometrically distant from the grid origin, and their cardinality must coincide with the cardinality of the grid points along that axis. Rectified grids (conceivable as a subset of referenceable grids in an Euler diagram) have an inherent series of incremental integer coefficients attached to each offset vector, so that e.g. the third point along axis 0 is computed as [GO + 2\*v0] (indexes start from 0).
A graphical example:
======= IRREGULAR ALIGNED GRID ======= =========== WARPED GRID ===========
N ^ ^ 1 N ^ 1
| | | /
| .------.--.------------. | .-----.----.
| | | | | | / | \
| .------.--.------------. P | .------.-------.
| | | | | | / / /
| ^------.--.------------. | .------.-------.
| v1 | | | | | | | /
GO(N) x- - @----->.--.------------.---> 0 GO(N) x- - @------.-----.-----> 0
| GO| v0 | GO|
CO O____x___________________________> E CO O____x___________________________> E
GO(E)
@ = Grid Origin (GO) O = CRS Origin (CO)
. = grid point (e.g. P) E,N = CRS axis labels
0,1 = grid axis labels --> = offset vector (v0,v1)
In this example, the grid is still aligned with CRS axes E/N, but the spacing is irregular along grid axis 0. We then need to explicitly define a series of 4 coefficients (one for each grid point along 0) that weight their distance to the grid origin (in terms of v0): in our case the weights are c0={0, 1, 1.5, 3.5}. Indeed the point P in the graphical example above – which has internal (rasdaman) grid coordinates {3,2} (origin is {0,0}) – can hence be geometrically expressed as : (GO + c0[3]\*v0 + 2\*v1) = (GO + 3.5\*v0 + 2\*v1).
It is underlined that the irregular spacing must be fixed for each grid line along a certain grid axis. If not so, the referenceable grid becomes warped and the domain needs to be addressed with explicit CRS coordinates for each single grid point (look-up tables).
Note
In petascope only grids whose lines are rectilinear and aligned with a Cartesian CRS are supported. This means: no rotated nor warped (curvilinear) grids.
### 5.2.2. Grid axis labels and CRS axis labels¶
Now that the difference between a grid axis and a CRS axis has been cleared, we address the issue of determining (and customizing) the axis labels a coverage in Petascope.
When importing a coverage, a spatio-temporal CRS needs to be assigned to it, in order to give a meaning to its domain. Composition of CRSs is possible via the OGC SECORE CRS resolver. For instance a time-series of WGS84 images can have the following native CRS:
http://<secore-resolverX-domain>/def/crs-compound?
1=http://<secore-resolverY-domain>/def/crs/EPSG/0/4326&
2=http://<secore-resolverZ-domain>/def/crs/<AUTH>/<VERSION>/<CODE-OF-A-TIME-CRS>
Note: currently gml:CompoundCRS is not supported (#679) so, for example, http://www.opengis.net/def/crs/EPSG/0/7415\ would have to be represented by composing its components using the same format as above i.e.
http://../def/crs-compound?
1=http://www.opengis.net/def/crs/EPSG/0/28992&
2=http://www.opengis.net/def/crs/EPSG/0/5709\
In order to verify the CRS assigned to a coverage offered by Petascope, there are several ways:
1. check the wcs:CoverageSummary/ows:BoundingBox@crs attribute in a WCS GetCapabilities response;
2. check the @srsName attribute in the @{gml:SRSReferenceGroup} attributes group in WCS DescribeCoverage response (gml:domainSet);
3. use the WCPS function crsSet();
It is important to understand that the assigned CRS automatically determines the CRS axis labels (and all other axis semantics like direction and unit of measure), and these are the same labels targeted in the subsets of the WCS and WCPS requests. Such labels correspond to the gml:axisAbbrev elements in the CRS definition (mind that ellipsoidal Coordinate Systems (CS) do not count in case of projected CRSs, which build a further CS on top of it).
This excerpt from the CRS definition of the WGS84 / UTM zone 33N projection shows how the first axis defined by this CRS is the easting, with label E and metres m as Unit of Measure (UoM, see gml:CoordinateSystemAxis@uom link):
<gml:CartesianCS>
[...]
<gml:axis>
<gml:CoordinateSystemAxis gml:id="epsg-axis-1"
uom="http://www.opengis.net/def/uom/EPSG/0/9001">
<gml:descriptionReference
<gml:identifier codeSpace="OGP">
http://www.opengis.net/def/axis/EPSG/0/1</gml:identifier>
<gml:axisAbbrev>E</gml:axisAbbrev>
<gml:axisDirection codeSpace="EPSG">east</gml:axisDirection>
</gml:CoordinateSystemAxis>
</gml:axis>
[...]
</gml:CartesianCS>
Since only aligned grids are supported, we decided to assign the same CRS axes labels to the grid axes. Such labels are listed in the gml:domainSet/gml:axisLabels element of a WCS coverage description, and are not to be confused with the labels of the CRS axes, which are instead listed in the @{gml:SRSReferenceGroup} attributes group, as said.
Indeed, despite the labels of grid and CRS axes will be the same, their order can actually differ. Many geographic CRSs (like the well-known WGS84 /EPSG:4326) define latitudes first, whereas it is GIS practice to always place longitudes in the first place, just like rasdaman does when storing the multidimensional-arrays (marrays).
With regards to this long-standing issue, Petascope strictly keeps the CRS axis order which is defined in its definition when it comes to GML, whereas GIS order (longitude first) is kept for other binary encodings like !GeoTiff or NetCDF, so to keep metadata consistency with common GIS libraries (e.g. GDAL). On the other hand, the order of grid axis labels need to follow the internal grid topology of marrays inside rasdaman.
To make things clearer, an excerpt of the GML domain of our 3D systemtest coverage eobstest (regular time series of EO imagery) is proposed:
The CRS of the coverage is an (ordered) composition of a temporal CRS (linear count of days [d] from the epoch 1950-01-01T00:00:00) and a geospatial CRS where latitude is defined first (the well-known EPSG:4326). This means that every tuple of spatio-temporal coordinates in the coverage’s domain will be a 3D tuple listing the count of days from 1^st^ of January 1950, then latitude degrees then longitude degrees, like shown in the gml:origin/gml:pos element: the origin of the 3D grid is set on 1^st^ of January 1950, 75.5 degrees north and 25 degrees east (with respect to the origin of the cartesian CS defined in EPSG:4326).
Grid coordinates follow instead the internal grid space, which is not aware of any spatio-temporal attribute, and follows the order of axis as they are stored in rasdaman: in the example, it is expressed that the collection is composed of a 6x101x232 marray, having t (time) as first axis, then Long then Lat. The spatio-temporal coordinates are instead expressed following the order of the CRS definition, hence with latitude degrees before longitudes.
A final remark goes to the customization of CRS (and consequently grid) axes labels, which can be particularly needed for temporal CRSs, especially in case of multiple time axis in the same CRS. Concrete CRS definitions are a static XML tree of GML elements defining axis, geographic coordinate systems, datums, and so on. The candidate standard OGC CRS Name-Type Specification offers a new kind of CRS, a parametrized CRS, which can be bound to a concrete definition, a CRS template, and which offers customization of one or more GML elements directly via key-value pairs in the query component of HTTP URL identifying the CRS.
As a practical example, we propose the complete XML definition of the parametrized CRS defining ANSI dates, identified by the URI http://rasdaman.org:8080/def/crs/OGC/0/AnsiDate:
<ParameterizedCRS xmlns:gml="http://www.opengis.net/gml/3.2"
xmlns="http://www.opengis.net/CRS-NTS/1.0"
xmlns:epsg="urn:x-ogp:spec:schema-xsd:EPSG:1.0:dataset"
xmlns:rim="urn:oasis:names:tc:ebxml-regrep:xsd:rim:3.0"
gml:id="param-ansi-date-crs">
<description>Parametrized temporal CRS of days elapsed
from 1-Jan-1601 (00h00 UTC).</description>
<gml:identifier codeSpace="http://www.ietf.org/rfc/rfc3986">
http://rasdaman.org:8080/def/crs/OGC/0/AnsiDate</gml:identifier>
<parameters>
<parameter name="axis-label">
<value>"ansi"</value>
<target>//gml:CoordinateSystemAxis/gml:axisAbbrev</target>
</parameter>
</parameters>
<targetCRS
</ParameterizedCRS>
This single-parameter definition allow the customization of the concrete CRS template OGC:.AnsiDate-template (identified by http://rasdaman.org:8080/def/crs/OGC/0/.AnsiDate-template) on its unique axis label (crsnts:parameter/crsnts:target), via a parameter labeled axis-label, and default value ansi.
This way, when we assign this parameterized CRS to a coverage, we can either leave the default ansi label to the time axis, or change it to some other value by setting the parameter in the URL query:
• default ansi axis label: http://rasdaman.org:8080/def/crs/OGC/0/AnsiDate
• custom ansi_date axis label: http://rasdaman.org:8080/def/crs/OGC/0/AnsiDate?axis-label="ansi_date"
### 5.2.3. Coverage Implementation Schema (CIS 1.0 and CIS 1.1) in petascope¶
CIS specifies the OGC coverage model by establishing a concrete, interoperable, conformance-testable coverage structure regardless of their data format encoding down to the level of single “pixels” or “voxels”.
Coverages can be encoded in any suitable format (such as GML, JSON, GeoTIFF, or netCDF). Coverages are independent from service definitions and, therefore, can be accessed through a variety of OGC services types, such as the Web Coverage Service (WCS) Standard.
Since rasdaman version 9.7+, besides CIS 1.0 for WCS version 2.0.1, petascope supports CIS 1.1 for WCS version 2.1.0 with these conformance classes:
• Class coverage.
• Class grid-regular (in CIS 1.0: GridCoverage and RectifiedGridCoverage coverage types).
• Class grid-irregular (only supports CIS::IrregularAxis, in CIS 1.0: ReferenceableGridCoverage coverage type).
• Class gml-coverage: For WCS version 2.1.0 only, petascope allows to transform CIS 1.0 coverage types to CIS 1.1 in GML format by new non-standard extra parameter in the request outputType=GeneralGridCoverage, see here for more information.
• Class other-format-coverage.
• Class multipart-coverage.
### 5.2.4. Subsets in Petascope¶
We will describe how subsets (trims and slices) are treated by Petascope. Before this you will have to understand how the topology of a grid coverage is interpreted with regards to its origin, its bounding-box and the assumptions on the sample spaces of the points. Some practical examples will be proposed.
#### 5.2.4.1. Geometric interpretation of a coverage¶
This section will focus on how the topology of a grid coverage is stored and how Petascope interprets it. When it comes to the so-called domainSet of a coverage (hereby also called domain, topology or geometry), Petascope follows pretty much the GML model for rectified grids: the grid origin and one offset vector per grid axis are enough to deduce the full domainSet of such (regular) grids. When it comes to referenceable grids, the domainSet still is kept in a compact vectorial form by adding weighting coefficients to one or more offset vectors.
As by GML standard <http://www.opengeospatial.org/standards/gml>_ a grid is a “network composed of two or more sets of curves in which the members of each set intersect the members of the other sets in an algorithmic way”. The intersections of the curves are represented by points: a point is 0D and is defined by a single coordinate tuple.
A first question arises on where to put the grid origin. The GML and GMLCOV standards say that the mapping from the domain to the range (feature space, payload, values) of a coverage is specified through a function, formally a gml:coverageFunction. From the GML standard: “If the gml:coverageFunction property is omitted for a gridded coverage (including rectified gridded coverages) the gml:startPoint is considered to be the value of the gml:low property in the gml:Grid geometry, and the gml:sequenceRule is assumed to be linear and the gml:axisOrder property is assumed to be +1 +2”.
In the image, it is assumed that the first grid axis (+1) is the horizontal axis, while the second (+2) is the vertical axis; the grid starting point is the full diamond. Rasdaman uses its own grid function when listing cell values, linearly spanning the outer dimensions first, then proceeding to the innermost ones. To make it clearer, this means column-major order.
In order to have a coeherent GML output, a mapping coverage function is then declared. This can look like this in a 3D hypothetical response:
<gml:coverageFunction>
<gml:GridFunction>
<gml:sequenceRule axisOrder="+3 +2 +1">Linear</gml:sequenceRule>
<gml:startPoint>0 0 0</gml:startPoint>
</gml:GridFunction>
</gml:coverageFunction>
Coming back to the origin question on where to put the origin of our grid coverages, we have to make it coincide to what the starting value represents in rasdaman, the marray origin. As often done in GIS applications, the origin of an image is set to be its upper-left corner: this finally means that the origin of our rectified and referenceable grid coverages shall be there too in order to provide a coherent GML/GMLCOV coverage. Note that placing the origin in the upper-left corner of an image means that the offset vector along the northing axis will point South, hence will have negative norm (in case the direction of the CRS axis points North!).
When it comes to further dimensions (a third elevation axis, time, etc.), the position of the origin depends on the way data has been ingested. Taking the example of a time series, if the marray origin (which we can denote as [0:0:__:0], though it is more precisely described as [dom.lo[0]:dom.lo[1]:__:dom.lo[n]) is the earliest moment in time, then the grid origin will be the earliest moment in the series too, and the offset vector in time will point to the future (positive norm); in the other case, the origin will be the latest time in the series, and its vector will point to the past (negative norm).
To summarize, in any case the grid origin must point to the marray origin. This is important in order to properly implement our linear sequence rule.
A second question arises on how to treat coverage points: are they points or are they areas? The formal ISO term for the area of a point is sample space. We will refer to it as well as footprint or area. The GML standard provides guidance on the way to interpret a coverage: “When a grid point is used to represent a sample space (e.g. image pixel), the grid point represents the center of the sample space (see ISO 19123:2005, 8.2.2)”.
In spite of this, there is no formal way to describe GML-wise the footprint of the points of a grid. Our current policy applies distinct choices separately for each grid axis, in the following way:
• regular axis: when a grid axis has equal spacing between each of its points, then it is assumed that the sample space of the points is equal to this spacing (resolution) and that the grid points are in the middle of this interval.
• irregular axis: when a grid axis has an uneven spacing between its points, then there is no (currently implemented) way to either express or deduce its sample space, hence 0D points are assumed here (no footprint).
It is important to note that sample spaces are meaningful when areas are legal in the Coordinate Reference System (CRS): this is not the case for Index CRSs, where the allowed values are integrals only. Even on regular axes, points in an Index CRSs can only be points, and hence will have 0D footprint. Such policy is translated in practice to a point-is-pixel-center interpretation of regular rectified images.
The following art explains it visually:
KEY
# = grid origin o = pixel corners
+ = grid points @ = upper-left corner of BBOX
{v_0,v_1} = offset vectors
|======== GRID COVERAGE MODEL =========| |===== GRID COVERAGE + FOOTPRINTS =====|
{UL}
v_0 @-------o-------o-------o-------o--- -
--------> | | | | |
. #-------+-------+-------+--- - | # | + | + | + |
v_1 | | | | | | | | | |
| | | | . o-------o-------o-------o-------o-- -
V | | | . | | | | .
+-------+-------+--- - | + | + | + | .
| | | | | | |
| | . o-------o-------o-------o-- -
| | . | | | .
+-------+--- - | + | + . .
| | | | .
| . o-------o--- -
| . | .
+--- - . + .
. .
.
|======================================| |======================================|
The left-side grid is the GML coverage model for a regular grid: it is a network of (rectilinear) curves, whose intersections determine the grid points ‘+’. The description of this model is what petascopedb knows about the grid.
The right-hand grid is instead how Petascope inteprets the information in petascopedb, and hence is the coverage that is seen by the enduser. You can see that, being this a regular grid, sample spaces (pixels) are added in the perception of the coverage, causing an extension of the bbox (gml:boundedBy) of half-pixel on all sides. The width of the pixel is assumed to be equal to the (regular) spacing of the grid points, hence each pixel is of size |v_0| x |v_1|, being * the norm operator.
As a final example, imagine that we take this regular 2D pattern and we build a stack of such images on irregular levels of altitude:
KEY
# = grid origin X = ticks of the CRS height axis
+ = grid points O = origin of the CRS height axis
{v_0,v_2} = offset vectors
O-------X--------X----------------------------X----------X-----X-----------> height
|
| ---> v_2
| . #________+____________________________+__________+_____+
| v_0 | | | | | |
| V +________+____________________________+__________+_____+
| | | | | |
| +________+____________________________+__________+_____+
| | | | | |
| +________+____________________________+__________+_____+
| | | | | |
V . . . . .
easting
In petascopedb we will need to add an other axis to the coverage topology, assigning a vector ‘v_2’ to it (we support gmlrgrid:ReferenceableGridByVectors only, hence each axis of any kind of grid will have a vector). Weighting coefficients will then determine the height of each new z-level of the cube: such heights are encoded as distance from the grid origin ‘#’ normalized by the offset vector v_2. Please note that the vector of northings v_1 is not visible due to the 2D perspective: the image is showing the XZ plane.
Regarding the sample spaces, while petascope will still assume the points are pixels on the XY plane (eastings/northings), it will instead assume 0D footprint along Z, that is along height: this means that the extent of the cube along height will exactly fit to the lowest and highest layers, and that input Z slices will have to select the exact value of an existing layer.
The latter would not hold on regular axes: this is because input subsets are targeting the sample spaces, and not just the grid points, but this is covered more deeply in the following section.
#### 5.2.4.2. Input and output subsettings¶
This section will cover two different facets of the interpretation and usage of subsets: how they are formalized by Petascope and how they are adjusted. Trimming subsets ‘lo,hi’ are mainly covered here: slices do not pose many interpretative discussions.
A first point is whether an interval (a trim operation) should be (half) open or closed. Formally speaking, this determines whether the extremes of the subset should or shouldn’t be considered part of it: (lo,hi) is an open interval, [lo.hi) is a (right) open interval, and [lo,hi] is a closed interval. Requirement 38 of the WCS Core standard (OGC 09-110r4) specifies that a /subset/ is a closed interval.
A subsequent question is whether to apply the subsets on the coverage points or on their footprints. While the WCS standard does not provide recommendations, we decided to target the sample spaces, being it a much more intuitive behavior for users who might ignore the internal representation of an image and do not want to lose that “half-pixel” that would inevitably get lost if footprints were to be ignored.
We also consider here “right-open sample spaces”, so the borders of the footprints are not all part of the footprint itself: this means that two adjacent footprints will not share the border, which will instead belong to the greater point (so typically on the right side in the CRS space). A slice exactly on that border will then pick the right-hand “greater” point only. Border-points instead always include the external borders of the footprint: slices right on the native BBOX of the whole coverage will pick the border points and will not return an exception.
Clarified this, the last point is how coverage bounds are set before shipping, with respect to the input subsets. That means whether our service should return the request bounding box or the minimal bounding box.
Following the (strong) encouragement in the WCS standard itself (requirement 38 WCS Core), Petascope will fit the input subsets to the extents of sample spaces (e.g. to the pixel areas), thus returning the minimal bounding box. This means that the input bbox will usually be extended to the next footprint border. This is also a consequence of our decision to apply subsets on footprints: a value which lies inside a pixel will always select the associated grid point, even if the position of the grid point is actually outside of the subset interval.
#### 5.2.4.3. Examples¶
In this section we will examine the intepretation of subsets by petascope by taking different subsets on a single dimension of 2D coverage. To appreciate the effect of sample spaces, we will first assume regular spacing on the axis, and then irregular 0D-footprints.
Test coverage information:
--------------------
mean_summer_airtemp (EPSG:4326)
Size is 886, 711
Pixel Size = (0.050000000000000,-0.050000000000000)
Upper Left ( 111.9750000, -8.9750000)
Lower Left ( 111.9750000, -44.5250000)
Upper Right ( 156.2750000, -8.9750000)
Lower Right ( 156.2750000, -44.5250000)
From this geo-information we deduce that the grid origin,
which has to be set in the upper-left corner of the image,
in the centre of the pixel are, will be:
origin(mean_summer_airtemp) = [ (111.975 + 0.025) , (-8.975 - 0.025) ]
= [ 112.000 , -9.000 ]
Regular axis: *point-is-area*
KEY
o = grid point
| = footprint border
[=s=] = subset
[ = subset.lo
] = subset.hi
_______________________________________________________________________
112.000 112.050 112.100 112.150 112.200
Long: |----o----|----o----|----o----|----o----|----o----|-- -- -
cell0 cell1 cell2 cell3 cell4
[s1]
[== s2 ===]
[== s3 ==]
[==== s4 ====]
[== s5 ==]
_______________________________________________________________________
s1: [112.000, 112.020]
s2: [112.025, 112.075]
s3: [112.025, 112.070]
s4: [112.010, 112.070]
s5: [111.950, 112.000]
Applying these subsets to mean_summer_airtemp will produce the following responses:
| GRID POINTS INCLUDED | OUTPUT BOUNDING-BOX(Long)
-----+----------------------+----------------------------
s1 | cell0 | [ 111.975, 112.025 ]
s2 | cell1, cell2 | [ 112.025, 112.125 ]
s3 | cell1 | [ 112.025, 112.075 ]
s4 | cell0, cell1 | [ 111.975, 112.075 ]
s5 | cell0 | [ 111.9
Irregular axis: *point-is-point*
KEY
o = grid point
[=s=] = subset
[ = subset.lo
] = subset.hi
_______________________________________________________________________
112.000 112.075 112.110 112.230
Long: o-------------o--------o-----------------o--- -- -
cell0 cell1 cell2 cell3
[s1]
[== s2 ===]
[== s3 ==]
[======= s4 =======]
[== s5 ==]
_______________________________________________________________________
s1: [112.000, 112.020]
s2: [112.010, 112.065]
s3: [112.040, 112.090]
s4: [111.970, 112.090]
s5: [111.920, 112.000]
Applying these subsets to mean_summer_airtemp will produce the following responses (please note tickets #681 and #682):
| GRID POINTS INCLUDED | OUTPUT BOUNDING-BOX(Long)
-----+----------------------+----------------------------
s1 | cell0 | [ 112.000, 112.000 ]
s2 | --- (WCSException) | [ --- ]
s3 | cell1 | [ 112.075, 112.075 ]
s4 | cell0, cell1 | [ 112.000, 112.075 ]
s5 | cell0 | [ 112.000, 112.000 ]
### 5.2.5. CRS management¶
Petascope relies on a [SecoreUserGuide SECORE] Coordinate Reference System (CRS) resolver that can provide proper metadata on, indeed, coverage’s native CRSs. One could either [SecoreDevGuide deploy] a local SECORE instance, or use the official OGC SECORE resolver (http://www.opengis.net/def/crs/). CRS resources are identified then by HTTP URIs, following the related OGC policy document of 2011, based on the White Paper ‘OGC Identifiers - the case for http URIs’. These HTTP URIs must resolve to GML resources that describe the CRS, such as http://rasdaman.org:8080/def/crs/EPSG/0/27700 that themselves contain only resolvable HTTP URIs pointing to additional definitions within the CRS; so for example http://www.epsg-registry.org/export.htm?gml=urn:ogc:def:crs:EPSG::27700 is not allowed because, though it is a resolvable HTTP URI pointing at a GML resource that describes the CRS, internally it uses URNs which SECORE is unable to resolve.
## 5.3. OGC Web Services¶
### 5.3.1. WCS¶
“The OpenGIS Web Coverage Service Interface Standard (WCS) defines a standard interface and operations that enables interoperable access to geospatial coverages.” (WCS standards)
Metadata regarding the range (feature space) of a coverage "myCoverage" is a fundamental part of a GMLCOV coverage model. Responses to WCS DescribeCoverage and GetCoverage will show such information in the gmlcov:rangeType element, encoded as fields of the OGC SWE data model. For instance, the range type of a test coverage mr, associated with the primitive quantity with unsigned char values is the following:
<gmlcov:rangeType>
<swe:DataRecord>
<swe:field name="value">
<swe:Quantity definition="http://www.opengis.net/def/dataType/OGC/0/unsignedByte">
<swe:label>unsigned char</swe:label>
<swe:description>primitive</swe:description>
<swe:uom code="10^0"/>
<swe:constraint>
<swe:AllowedValues>
<swe:interval>0 255</swe:interval>
</swe:AllowedValues>
</swe:constraint>
</swe:Quantity>
</swe:field>
</swe:DataRecord>
</gmlcov:rangeType>
The set of standard rasdaman data types, materializes the base types defined in the ODMG standard, which is converted to SWE Quantity elements’ defintion attributes by table below:
Table 5.1 rasdaman base types to Quantity’s definition types
rasdaman types size Quantity’s definition types
boolean 8 bit unsignedByte
octet 8 bit signedByte
char 8 bit unsignedByte
short 16 bit signedShort
unsigned short / ushort 16 bit unsignedShort
long 32 bit signedInt
unsigned long / ulong 32 bit unsignedInt
float 32 bit float32
double 64 bit float64
complex 64 bit cfloat32
complexd 128 bit cfloat64
Note that a quantity can be associated with multiple allowed intervals, as by SWE specifications.
Declarations of NIL values are also possible: one or more values representing not available data or which have special meanings can be declared along with related reasons, which are expressed via URIs (see http://www.opengis.net/def/nil/OGC/0/ for official NIL resources provided by OGC).
You can use http://yourserver/rasdaman/ows as service endpoints to which to send WCS requests, e.g.
http://yourserver/rasdaman/ows?service=WCS&version=2.0.1&request=GetCapabilities
See example queries in the WCS systemtest which send KVP (key value pairs) GET request and XML POST request to Petascope.
### 5.3.2. WCPS¶
“The OpenGIS Web Coverage Service Interface Standard (WCS) defines a protocol-independent language for the extraction, processing, and analysis of multi-dimensional gridded coverages representing sensor, image, or statistics data. Services implementing this language provide access to original or derived sets of geospatial coverage information, in forms that are useful for client-side rendering, input into scientific models, and other client applications. Further information about WPCS can be found at the WCPS Service page of the OGC Network. (http://www.opengeospatial.org/standards/wcps)
The WCPS language is independent from any particular request and response encoding, allowing embedding of WCPS into different target service frameworks like WCS and WPS. The following documents are relevant for WCPS; they can be downloaded from www.opengeospatial.org/standards/wcps:
• OGC 08-068r2: The protocol-independent (“abstract”) syntax definition; this is the core document. Document type: IS (Interface Standard.
• OGC 08-059r3: This document defines the embedding of WCPS into WCS by specifying a concrete protocol which adds an optional ProcessCoverages request type to WCS. Document type: IS (Interface Standard).
• OGC 09-045: This draft document defines the embedding of WCPS into WPS as an application profile by specifying a concrete subtype of the Execute request type.
There are a online demo and online tutorial; see also the WCPS manual and tutorial.
The petascope implementation supports both Abstract (example) and XML syntaxes (example). For guidelines on how to safely build and troubleshoot WCPS query with Petascope, see this topic in the mailing-list.
The standard for WCPS GET request is
http://yourserver/rasdaman/ows?service=WCS&version=2.0.1
&request=ProcessCoverage&query=YOUR\_WCPS\_QUERY
You can use http://your.server/rasdaman/ows/wcps as a shortcut service endpoint to which to send WCPS requests. This is not an OGC standard for WCPS but is kept for testing purpose for WCPS queries. The following form is equivalent to the previous one:
http://yourserver/rasdaman/ows/wcps?query=YOUR\_WCPS\_QUERY
### 5.3.3. WMS¶
“The OpenGIS Web Map Service Interface Standard (WMS) provides a simple HTTP interface for requesting geo-registered map images from one or more distributed geospatial databases. A WMS request defines the geographic layer(s) and area of interest to be processed. The response to the request is one or more geo-registered map images (returned as JPEG, PNG, etc) that can be displayed in a browser application. The interface also supports the ability to specify whether the returned images should be transparent so that layers from multiple servers can be combined or not.”
Petascope supports WMS 1.3.0. Some resources:
The WMS 1.3 is self-administered by all intents and purposes, the database schema is created automatically and updates each time the Petascope servlet starts if necessary. The only input needed from the administrator is the service information which should be filled in $RMANHOME/etc/wms_service.properties before the servlet is started. #### 5.3.3.2. Layer creating & removal¶ Layers can be easily created from existing coverages in WCS. This has several advantages: • Creating the layer is extremely simple and can be done by both humans and machines. • The possibilities of inserting data into WCS are quite advanced (see wiki:WCSTImportGuide). • Data is not duplicated among the services offered by Petascope. There are 2 ways of publising a new WMS layer from an imported geo-referenced coverage: • By setting: wms_import in the ingredients file when importing wcst_import. • By sending HTTP InsertWCSLayer request manually to petascope. Possible WMS requests: • The InsertWCSLayer request will create a new layer from an existing coverage without an associated WMS layer served by the web coverage service offered by petascope. Example: http://example.org/rasdaman/ows?service=WMS&version=1.3.0 &request=InsertWCSLayer&wcsCoverageId=MyCoverage • To update an existing WMS layer from an existing coverage with an associated WMS layer use UpdateWCSLayer request. Example: http://example.org/rasdaman/ows?service=WMS&version=1.3.0 &request=UpdateWCSLayer&wcsCoverageId=MyCoverage • To remove a layer, just delete associated coverage. Example: http://example.org/rasdaman/ows?service=WCS&version=2.0.1 &request=DeleteCoverage&coverageId=MyCoverage #### 5.3.3.3. Transparent nodata value¶ By adding a parameter transparent=true to WMS requests, the returned image will have NoData Value=0 in the bands’ metadata, so the WMS client will consider all the pixels with 0 value as transparent. E.g: http://localhost:8080/rasdaman/ows?service=WMS&version=1.3.0 &request=GetMap&layers=waxlake1 &bbox=618887,3228196,690885,%203300195.0 &crs=EPSG:32615&width=600&height=600&format=image/png &TRANSPARENT=TRUE #### 5.3.3.4. Interpolation value¶ Since v9.8, when output CRS is different from the native CRS in a GetMap request, the WMS service will reproject the result to the requested output CRS. The interpolation / resampling algorithm used during the reprojection can be controlled with a non-standard parameter interpolation=<method> added to the GetMap request. Valid values for <method> are documented in the rasql project() function, cf. Geographic projection; by default, nearest-neighbour is used (near). Example request that changes the default interpolation method: http://localhost:8080/rasdaman/ows?service=WMS &version=1.3.0 &request=GetMap &layers=test_wms_3857 &bbox=-44.525,111.976,-8.978,156.274 &crs=EPSG:4326 &width=60 &height=60 &Styles= &format=image/png &interpolation=bilinear #### 5.3.3.5. Style creation¶ Styles can be created for layers using rasql and WCPS query fragments. This allows users to define several visualization options for the same dataset in a flexible way. Examples of such options would be color classification, NDVI detection etc. The following HTTP request will create a style with the name, abstract and layer provided in the KVP parameters below Note For Tomcat version 7+ it requires the query (WCPS/rasql fragment) to be encoded correctly. Please use this website http://meyerweb.com/eric/tools/dencoder/ to encode your query first: • WCPS query fragment example (since rasdaman 9.5): http://localhost:8080/rasdaman/ows? service=WMS& version=1.3.0& request=InsertStyle& name=wcpsQueryFragment& layer=test_wms_4326& abstract=This style marks the areas where fires are in progress with the color red& wcpsQueryFragment=switch case$c > 1000 return {red: 107; green:17; blue:68}
default return {red: 150; green:103; blue:14})
The variable $c will be replaced by a layer name when sending a GetMap request containing this layer's style. • Rasql query fragment examples: http://example.org/rasdaman/ows?service=WMS&version=1.3.0&request=InsertStyle &name=FireMarkup &layer=dessert_area &abstract=This style marks the areas where fires are in progress with the color red &rasqlTransformFragment=case$Iterator when ($Iterator + 2) > 200 then {255, 0, 0} else {0, 255, 0} end The variable $Iterator will be replaced with the actual name of the rasdaman collection and the whole fragment will be integrated inside the regular GetMap request.
• Since v9.8.1, it is possible to use multiple layers in a style definition. Besides the iterators $c in WCPS query fragments and $Iterator in rasql query fragments, which always refer to the current layer, other layers can be referenced by name using an iterator of the form $LAYER_NAME in the style expression. Example: create a WCPS query fragment style referencing 2 layers ($c refers to layer sentinel2_B4 which defines the style):
http://localhost:8080/rasdaman/ows?
service=WMS&
version=1.3.0&
request=InsertStyle&
name=BandsCombined&
layer=sentinel2_B4&
abstract=This style needs 2 layers&
wcpsQueryFragment=$c +$sentinel2_B8
Then, in any GetMap request using this style, the result will be obtained from the combination of the 2 layers: sentinel2_B4 and sentinel2_B8:
http://localhost:8080/rasdaman/ows?
service=WMS&
version=1.3.0&
request=GetMap&
layers=sentinel2_B4&
bbox=-44.975,111.975,-8.975,155.975&width=800&height=600&crs=EPSG:4326&
format=image/png&transparent=true&
styles=BandsCombined
• Since v10.0, a WMS style supports ColorTable definition which allows to colorize the result of WMS GetMap request when the style is requested. A style can contain either one or both query fragment and Color Table definitions. The InsertStyle request supports two new non-standard extra parameters colorTableType (valid values: ColorMap, GDAL and SLD) and colorTableDefintion containing corresponding definition, example:
http://localhost:8080/rasdaman/ows?
service=WMS&
version=1.3.0&
request=InsertStyle&
name=test&
layer=test_wms_4326&
abstract=This style marks the areas where fires are in progress with the color red&
wcpsQueryFragment=switch case c > 1000 return {red: 107; green:17; blue:68} default return {red: 150; green:103; blue:14})& colorTableType=ColorMap& colorTableDefinition={"type": "intervals", "colorTable": { "0": [0, 0, 255, 0], "100": [125, 125, 125, 255], "255": [255, 0, 0, 255] } } Below the supported color table definitions for each color table type are explained: • Rasdaman ColorMap: check Coloring Arrays for more details. The color table definition must be a JSON object, for example: { "type": "intervals", "colorTable": { "0": [0, 0, 255, 0], "100": [125, 125, 125, 255], "255": [255, 0, 0, 255] } } • GDAL ColorPalette: check encode for more details. The color table definition must be a JSON object and contains 256 color arrays in colorTable array, example: { "colorTable": [ [255,0,0,255], [216,31,30,255], [216,31,30,255], ..., [43,131,186,255] ] } • WMS Styled Layer Descriptor (SLD): The color table definition must be valid XML and contains ColorMap element. Check Coloring Arrays for details about the supported types (ramp (default), values, intervals), example ColorMap with type="values": <?xml version="1.0" encoding="UTF-8"?> <StyledLayerDescriptor xmlns="http://www.opengis.net/sld" xmlns:gml="http://www.opengis.net/gml" xmlns:sld="http://www.opengis.net/sld" xmlns:ogc="http://www.opengis.net/ogc" version="1.0.0"> <UserLayer> <sld:LayerFeatureConstraints> <sld:FeatureTypeConstraint/> </sld:LayerFeatureConstraints> <sld:UserStyle> <sld:Name>sqi_fig5_crop1</sld:Name> <sld:FeatureTypeStyle> <sld:Rule> <sld:RasterSymbolizer> </sld:ChannelSelection> <sld:ColorMap type="values"> <ColorMapEntry color="#0000FF" quantity="150" /> <ColorMapEntry color="#FFFF00" quantity="200" /> <ColorMapEntry color="#FF0000" quantity="250" /> </sld:ColorMap> </sld:RasterSymbolizer> </sld:Rule> </sld:FeatureTypeStyle> </sld:UserStyle> </UserLayer> </StyledLayerDescriptor> Removal To remove a particular style you can use a DeleteStyle request. Note that this is a non-standard extension of WMS 1.3. http://example.org/rasdaman/ows?service=WMS&version=1.3.0 &request=DeleteStyle&layer=dessert_area&style=FireMarkup #### 5.3.3.6. 3D+ coverage as WMS layer¶ Petascope allows to import a 3D+ coverage as a WMS layer. The user can specify "wms_import": true in the ingredients file when importing data with wcst_import.sh for 3D+ coverage with regular_time_series, irregular_time_series and general_coverage recipes. For example you find an irregular_time_series 3D coverage from 2D geotiff files use case. Once the data coverage is ingested, the user can send GetMap requests on non-geo-referenced axes according to the OGC WMS 1.3.0 standard. The table below shows the subset parameters for different axis types: Axis Type Subset parameter Time time=… Elevation elevation=… Other dim_AxisName=… (e.g dim_pressure=…) According to the WMS 1.3.0 specification, the subset for non-geo-referenced axes can have these formats: • Specific value (value1): time=‘2012-01-01T00:01:20Z, dim_pressure=20,… • Range values (min/max): time=‘2012-01-01T00:01:20Z’/‘2013-01-01T00:01:20Z, dim_pressure=20/30,… • Multiple values (value1,value2,value3,…): time=‘2012-01-01T00:01:20Z, ‘2013-01-01T00:01:20Z, dim_pressure=20,30,60,100,… • Multiple range values (min1/max1,min2/max2,…): dim_pressure=20/30,40/60,… Note A GetMap request is always 2D, so if a non-geo-referenced axis is omitted from the request it will be considered as a slice on the upper bound of this axis (e.g. in a time-series it will return the slice for the latest date). GetMap request examples: * Multiple values on time, dim_pressure axes of 4d coverage. #### 5.3.3.7. Testing the WMS¶ You can test the service using your favorite WMS client or directly through a GetMap request like the following: http://example.org/rasdaman/ows?service=WMS&version=1.3.0&request=GetMap &layers=MyLayer &bbox=618885.0,3228195.0,690885.0,3300195.0 &crs=EPSG:32615 &width=600 &height=600 &format=image/png #### 5.3.3.8. Errors and Workarounds¶ Cannot load new WMS layer in QGIS In this case, the problem is due to QGIS caching the WMS GetCapabilities from the last request so the new layer does not exist (see here for clear caching solution: http://osgeo-org.1560.x6.nabble.com/WMS-provider-Cannot-calculate-extent-td5250516.html) ### 5.3.4. WCS-T¶ The WCS Transaction extension (WCS-T) defines a standard way of inserting, deleting and updating coverages via a set of web requests. This guide describes the request types that WCS-T introduces and shows the steps necessary to import coverage data into a rasdaman server, data which is then available in the server’s WCS offerings. Supported coverage data format Currently, WCS-T supports coverages in GML format for importing. The metadata of the coverage is thus explicitly specified, while the raw cell values can be stored either explicitly in the GML body, or in an external file linked in the GML body, as shown in the examples below. The format of the file storing the cell values must be one supported by the GDAL library (http://www.gdal.org/formats_list.html), such as TIFF / GeoTIFF, JPEG, JPEG2000, PNG etc. Note Besides the standard HTTP GET requests, petascope supports key-value parameters which are sent as HTTP POST requests to Insert/Update coverages. #### 5.3.4.1. Inserting coverages¶ Inserting a new coverage into the server’s WCS offerings is done using the InsertCoverage request. Standard parameters: Request Parameter Value Description Required service WCS Yes version 2.0.1 or later Yes request InsertCoverage Yes inputCoverageRef a valid url. Url pointing to the GML coverage to be inserted. One of inputCoverageRef or inputCoverage is required inputCoverage a coverage in GML format The coverage to be inserted, in GML format. One of inputCoverageRef or inputCoverage is required useId new or existing Indicates wheter to use the coverage id from the coverage body, or tells the server to generate a new one. No Vendor specific parameters: Request Parameter Value Description Required pixelDataType any GDAL supported data type (e.g: Float32) or concatenated data types by commas, (e.g: Float32,Int32,Float32). In cases where cell values are given in the GML body, the datatype can be indicated through this parameter. If omitted, it defaults to Byte. No tiling same as rasdaman tiling clause wiki:Tiling Indicates the tiling of the array holding the cell values. No The response of a successful coverage request is the coverage id of the newly inserted coverage. Examples The following example shows how to insert the coverage available at: http://schemas.opengis.net/gmlcov/1.0/examples/exampleRectifiedGridCoverage-1.xml. The tuple list is given in the GML body. http://localhost:8080/rasdaman/ows?service=WCS&version=2.0.1&request=InsertCoverage &coverageRef=http://schemas.opengis.net/gmlcov/1.0/examples/exampleRectifiedGridCoverage-1.xml The following example shows how to insert a coverage stored on the server on which rasdaman runs. The cell values are stored in a TIFF file (attachment:myCov.gml), the coverage id is generated by the server and aligned tiling is used for the array storing the cell values. http://localhost:8080/rasdaman/ows?service=WCS&version=2.0.1&request=InsertCoverage &coverageRef=file:///etc/data/myCov.gml&useId=new&tiling=aligned [0:500, 0:500] Coming soon: the same operation, but via a POST XML request to http://localhost:8080/rasdaman/ows: <?xml version="1.0" encoding="UTF-8"?> <wcs:InsertCoverage xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:wcs="http://www.opengis.net/wcs/2.0" xmlns:gml="http://www.opengis.net/gml/3.2" xsi:schemaLocation="http://schemas.opengis.net/wcs/2.0 ../wcsAll.xsd" service="WCS" version="2.0.1"> <wcs:coverage>here goes the contents of myCov.gml</wcs:coverage> <wcs:useId> new </wcs:useId> </wcs:InsertCoverage> #### 5.3.4.2. Deleting coverages¶ To delete a coverage (along with the corresponding rasdaman collection), use the standard DeleteCoverage WCS-T request. For example, the coverage ‘test_mr’ can be deleted with a request as following: http://yourserver/rasdaman/ows?service=WCS&version=2.0.1 &request=DeleteCoverage&coverageId=test_mr Deleting coverages is also possible from the WS-client frontend available at http://yourserver/rasdaman/ows (WCS > DeleteCoverage tab). #### 5.3.4.3. Non-standard requests¶ WMS The following requests are used to create/delete downscaled coverages. Internally they are used for efficient zooming in/out in WMS, and downscaling when using the scale() function in WCPS or scaling extension in WCS. • InsertScaleLevel: create a downscaled collection for a specific coverage and given level; e.g. to create a downscaled coverage of test_world_map_scale_levels that is 4x smaller: http://localhost:8082/rasdaman/ows?service=WCS&version=2.0.1 &request=InsertScaleLevel &coverageId=test_world_map_scale_levels &level=4 • DeleteScaleLevel: delete an existing downscaled coverage at a given level; e.g. to delete downscaled level 4 of coverage test_world_map_scale_levels: http://localhost:8082/rasdaman/ows?service=WCS&version=2.0.1 &request=DeleteScaleLevel &coverageId=test_world_map_scale_levels &level=4 wcst_import can send InsertScaleLevel requests automatically when importing data with it with scale_levels option in the ingredients file, more details here. ## 5.4. Non-standard functionality¶ ### 5.4.1. Update coverage’s metadata from WSClient¶ Since v9.8, coverage’s metadata can be updated from WSClient by selecting a text file (mime type: text/xml | application/json | text/plain) containing new metadata and upload it to petascope. Then, petascope will read the content of the text file and update corresponding coverage’s metadata. Note This feature only exists in WSClient: OGC WCS > Describe Coverage tab when one is already logged in with petascope admin user in Admin tab. The endpoint for this feature in petascope is http://your-server/rasdaman/ows/UpdateCoverageMetadata which requires “multipart/form-data” POST requests. The request should contain 2 parts: the first part is coverageId to update, the second part is a path to a text file to be uploaded to server. ### 5.4.2. Transform CIS 1.0 coverages to CIS 1.1 coverages in petascope¶ Since rasdaman v9.7, WCS and WCPS services in Petascope allows to transform a coverage imported in CIS 1.0 to CIS 1.1 with output in application/gml+xml format and a new non-standard parameter outputType=GeneralGridCoverage. Note This feature only valids for WCS version 2.1.0 and WCPS. #### 5.4.2.1. WCS¶ When requesting with WCS version 2.1.0 with DescribeCoverage/GetCoverage requests, one can transform coverage imported in CIS 1.0 to CIS 1.1 by adding extra request parameter outputType=GeneralGridCoverage as example below: http://localhost:8080/rasdaman/ows?service=WCS&version=2.1.0 &request=DescribeCoverage &coverageId=test_mean_summer_airtemp &outputType=GeneralGridCoverage http://localhost:8080/rasdaman/ows?service=WCS&version=2.1.0 &request=GetCoverage &coverageId=test_mean_summer_airtemp &output=application/gml+xml &outputType=GeneralGridCoverage #### 5.4.2.2. WCPS¶ For WCPS requests, the same can be achieved using the extra parameter outputType=GeneralGridCoverage in encode() with application/gml+xml. Example: for c in (test_irr_cube_2) return encode(c, "application/gml+xml", "{\"outputType\":\"GeneralGridCoverage\"}") ### 5.4.3. Clipping in petascope¶ WCS and WCPS services in Petascope support the WKT format for clipping with MultiPolygon (2D), Polygon (2D) and LineString (1D+). The result of MultiPolygon and Polygon is always a 2D coverage, and LineString results in a 1D coverage. Petascope also supports curtain and corridor clippings by Polygon and Linestring on 3D+ coverages by Polygon (2D) and Linestring (1D). The result of curtain clipping has same dimensionality as the input coverage and the result of corridor clipping is always a 3D coverage with the first axis being the trackline of the corridor by convention. Below you find the documentation for WCS and WCPS with a few simple examples; an interactive demo is available here. #### 5.4.3.1. WCS¶ Clipping can be done by adding a &clip= parameter to the request. If the subsettingCRS parameter is specified then this CRS applies to the clipping WKT as well, otherwise it is assumed that the WKT is in the native coverage CRS. Examples • Polygon clipping on coverage with nativeCRS EPSG:4326. http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_wms_4326& clip=POLYGON((55.8 -96.6, 15.0 -17.3))& format=image/png • Polygon clipping with coordinates in EPSG:3857 (from subsettingCRS parameter) on coverage with nativeCRS EPSG:4326. http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_wms_4326& clip=POLYGON((13589894.568 -2015496.69612, 15086830.0246 -1780682.3822))& subsettingCrs=http://opengis.net/def/crs/EPSG/0/3857& format=image/png • Linestring clipping on a 3D coverage (axes: X, Y, ansidate). http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_irr_cube_2& clip=LineStringZ(75042.7273594 5094865.55794 "2008-01-01T02:01:20.000Z", 705042.727359 5454865.55794 "2008-01-08T00:02:58.000Z")& format=text/csv • Multipolygon clipping on 2D coverage http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_mean_summer_airtemp& clip=Multipolygon( ((-23.189600 118.432617, -27.458321 117.421875, -30.020354 126.562500, -24.295789 125.244141)), ((-27.380304 137.768555, -30.967012 147.700195, -25.491629 151.259766, -18.050561 142.075195)) )& format=image/png • Curtain clipping by a Linestring on 3D coverage http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_eobstest& clip=CURTAIN( projection(Lat, Long), linestring(25 41, 30 41, 30 45, 30 42) )& format=text/csv • Curtain clipping by a Polygon on 3D coverage http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_eobstest& clip=CURTAIN(projection(Lat, Long), Polygon((25 40, 30 40, 30 45, 30 42)))& format=text/csv • Corridor clipping by a Linestring on 3D coverage http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_irr_cube_2& clip=corridor( projection(E, N), LineString(75042.7273594 5094865.55794 "2008-01-01T02:01:20.000Z", 75042.7273594 5194865.55794 "2008-01-01T02:01:20.000Z"), LineString(75042.7273594 5094865.55794, 75042.7273594 5094865.55794, 85042.7273594 5194865.55794, 95042.7273594 5194865.55794) )& format=application/gml+xml • Corridor clipping by a Polygon on 3D coverage http://localhost:8080/rasdaman/ows& service=WCS& version=2.0.1& request=GetCoverage& coverageId=test_eobstest& clip=corridor( projection(Lat, Long), LineString(26 41 "1950-01-01", 28 41 "1950-01-02"), Polygon((25 40, 30 40, 30 45, 25 45)), discrete )& format=application/gml+xml #### 5.4.3.2. WCPS¶ A special function that works similarly as in the case of WCS is provided with the following signature: clip( coverageExpression, wkt [, subsettingCrs ] ) where • coverageExpression is some coverage variable like cov or an expression that results in a coverage like cos(cov+10) • wkt is a valid WKT construct, e.g. POLYGON((...)), LineString(...) • subsettingCrs is an optional parameter to specify the CRS for the coordinates in wkt (e.g “http://opengis.net/def/crs/EPSG/0/4326”). Examples • Polygon clipping with coordinates in EPSG:4326 on coverage with nativeCRS EPSG:3857. for c in (test_wms_3857) return encode( clip(c, POLYGON(( -17.8115 122.0801, -15.7923 135.5273, -24.8466 151.5234, -19.9733 137.4609, -33.1376 151.8750, -22.0245 135.6152, -37.5097 145.3711, -24.4471 133.0664, -34.7416 135.8789, -25.7207 130.6934, -31.8029 130.6934, -26.5855 128.7598, -32.6949 125.5078, -26.3525 126.5625, -35.0300 118.2129, -25.8790 124.2773, -30.6757 115.4004, -24.2870 122.3438, -27.1374 114.0820, -23.2413 120.5859, -22.3501 114.7852, -21.4531 118.5645 )), "http://opengis.net/def/crs/EPSG/0/4326" ) , "png") • Linestring clipping on 3D coverage (axes: X, Y, datetime). for c in (test_irr_cube_2) return encode( clip(c, LineStringZ(75042.7273594 5094865.55794 "2008-01-01T02:01:20.000Z", 705042.727359 5454865.55794 "2008-01-08T00:02:58.000Z")) , "csv") • Linestring clipping on 2D coverage with coordinates (axes: X, Y). for c in (test_mean_summer_airtemp) return encode( clip(c, LineString(-29.3822 120.2783, -19.5184 144.4043)) with coordinates , "csv") In this case the geo coordinates of the values on the linestring will be included as well in the result. The first band of the result will hold the X coordinate, second band the Y coordinate, and the remaining bands the original cell values. Example output for the above query: "-28.975 119.975 90","-28.975 120.475 84","-28.475 120.975 80", ... • Multipolygon clipping on 2D coverage. for c in (test_mean_summer_airtemp) return encode( clip(c, Multipolygon( (( -20.4270 131.6931, -28.4204 124.1895, -27.9944 139.4604, -26.3919 129.0015 )), (( -20.4270 131.6931, -19.9527 142.4268, -27.9944 139.4604, -21.8819 140.5151 )) ) ) , "png") • Curtain clipping by a Linestring on 3D coverage for c in (test_eobstest) return encode( clip(c, CURTAIN(projection(Lat, Long), linestring(25 40, 30 40, 30 45, 30 42) ) ), "csv") • Curtain clipping by a Polygon on 3D coverage for c in (test_eobstest) return encode( clip(c, CURTAIN(projection(Lat, Long), Polygon((25 40, 30 40, 30 45, 30 42)) ) ), "csv") • Corridor clipping by a Linestring on 3D coverage for c in (test_irr_cube_2) return encode( clip( c, corridor( projection(E, N), LineString(75042.7273594 5094865.55794 "2008-01-01T02:01:20.000Z", 75042.7273594 5194865.55794 "2008-01-01T02:01:20.000Z"), Linestring(75042.7273594 5094865.55794, 75042.7273594 5094865.55794, 85042.7273594 5194865.55794, 95042.7273594 5194865.55794) ) ) , "gml") • Corridor clipping by a Polygon on 3D coverage (geo CRS: EPSG:4326) with input geo coordinates in EPSG:3857. for c in (test_eobstest) return encode( clip( c, corridor( projection(Lat, Long), LineString(4566099.12252 2999080.94347 "1950-01-01", 4566099.12252 3248973.78965 "1950-01-02"), Polygon((4452779.63173 2875744.62435, 4452779.63173 3503549.8435, 5009377.0857 3503549.8435, 5009377.0857 2875744.62435)) ), "http://localhost:8080/def/crs/EPSG/0/3857" ) , "gml") ### 5.4.4. Auto-ratio for scaling X or Y axis in WCPS¶ Since v9.8, the scale function in WCPS allows to specify the target extent of only one of the spatial X/Y axes (e.g. only Long). In this case, the extent of the other axis will be automatically determined to preserve the original ratio between the two spatial axes. For example in the request below, petascope will automatically set the extent of Lat to a value that preserves the ratio in the output result: for c in (test_mean_summer_airtemp) return encode(scale( c, { Long:"CRS:1"(0:160) } ), "png" ) ### 5.4.5. Extract domain interval from domain()/imageCrsdomain() in WCPS¶ Since v9.8, one can extract domain interval (lowerBound:upperBound or an individual bound) from result of domain and imagerCrsdomain operators on a specific coverage’s axis. The syntax is operator(.lo|.hi)? with (.lo or .hi) returns the lower bound or upper bound of this interval. Example, coverage test_eobstest has 3 dimensions. By standard, imageCrsdomain(c) returns (0:5,0:29,0:39). With this extended feature, imageCrsdomain(c,Long) returns 0:39 and imageCrsdomain(c,Long).hi returns 39. Also, the third argument (CRS URI) in domain() operator changed to optional. If this argument is not specified, domain() will use CRS URI of the selected axis (second argument) instead. ### 5.4.6. Resample a projected output in WMS request¶ By adding optional interpolation parameter in GetMap request, see details. ### 5.4.7. LET clause in WCPS¶ Since v10.0, an optional LET clause is supported in WCPS queries. It allows binding alias variables to valid WCPS query sub-expressions, and subsequently make use of the variables in the RETURN clause instead of repeating the aliased sub-expressions. The syntax is FOR CLAUSE LETvariable1 := coverageExpression,
$variable2 := coverageExpression, ... RETURN CLAUSE For example for$c in (test_mr)
let $a :=$c[i(0:50), j(0:40)],
$b := avg($c) * 2
return encode(scale($c, { imageCrsdomain($a) }) + $b, "png") Note, there is a special case for shorthand subset expression. The variable in LET clause can have this syntax LET$variable1 := [dimensionalIntervalList]
And a shorthand subset expression can use this variable directly with this syntax
coverageVariable[$variable1] For example for$c in (test_mr)
let $a := [i(20), j(40)],$b := 10
return encode($c[$a] + $b, "json") ## 5.5. Data import¶ Raster data (tiff, netCDF, grib, …) can be imported in petascope through its WCS-T standard implementation. For convenience rasdaman provides the wcst_import.sh tool, which hides the complexity of building WCS-T requests for data import. Internally, WCS-T ingests the coverage geo-information into petascopedb, while the raster data is ingested into rasdaman. Building large timeseries/datacubes, mosaics, etc. and keeping them up-to-date as new data becomes available is supported even for complex data formats and file/directory organizations. The systemtest contains many examples for importing different types of data. Following is a detailed documentation on how to setup an ingredients file for your dataset. ### 5.5.1. Introduction¶ The wcst_import.sh tool introduces two concepts: Recipe - A recipe is a class implementing the BaseRecipe that based on a set of parameters (ingredients) can import a set of files into WCS forming a well defined coverage (image, regular timeseries, irregular timeseries etc); Ingredients - An ingredients file is a JSON file containing a set of parameters that define how the recipe should behave (e.g. the WCS endpoint, the coverage name, etc.) To execute an ingredients file in order to import some data: $ wcst_import.sh path/to/my_ingredients.json
Alternatively, wcst_import.sh tool can be started as a daemon as follows:
$wcst_import.sh path/to/my_ingredients.json --daemon start or as a daemon that is “watching” for new data at some interval (in seconds): $ wcst_import.sh path/to/my_ingredients.json --watch <interval>
For further informations regarding wcst_import.sh commands and usage:
$wcst_import.sh --help The workflow behind is depicted approximately on Figure 5.1. Figure 5.1 Ingestion process with wcst_import.sh An ingredients file with all possible options can be found here; in the same directory you will find several examples for different recipes. ### 5.5.2. Recipes¶ As of now, these recipes are provided: For each one of these there is an ingredients example under the ingredients/ directory, together with an example for the available parameters Further on each recipe type is described in turn. #### 5.5.2.1. Common options¶ Some options are commonly applicable to all recipes. config section • service_url - The endpoint of the WCS service with the WCS-T extension enabled • mock - Print WCS-T requests but do not execute anything if set to true. Set to false by default. • automated - Set to true to avoid any interaction during the ingestion process. Useful in production environments for automated deployment for example. By default it is false, i.e. user confirmation is needed to execute the ingestion. • blocking (since v9.8) - Set to false to analyze and import each file separately (non-blocking mode). By default blocking is set to true, i.e. wcst_import will analyze all input files first to create corresponding coverage descriptions, and only then import them. The advantage of non-blocking mode is that the analyzing and importing happens incrementally (in blocking mode the analyzing step can take a long time, e.g. days, before the import can even begin). Note When importing in non-blocking import mode for coverages with irregular axes, it will only rely on sorted files by filenames and it can fail if these axes’ coefficients are collected from input files’ metadata (e.g: DateTime value in TIFF’s tag or GRIB metadata) as they might not be consecutive. wcst_import will not analyze all files to collect metadata to be sorted by DateTime as in default blocking import mode. • default_null_values - This parameter adds default null values for bands that do not have a null value provided by the file itself. The value for this parameter should be an array containing the desired null value either as a closed interval low:high or single values. E.g. for a coverage with 3 bands "default_null_values": [ "9995:9999", "-9, -10, -87", 3.14 ], Note, if set this parameter will override the null/nodata values present in the input files. • tmp_directory - Temporary directory in which gml and data files are created; should be readable and writable by rasdaman, petascope and current user. By default this is /tmp. • crs_resolver - The crs resolver to use for generating WCS-T request. By default it is determined from the petascope.properties setting. • url_root - In case the files are exposed via a web-server and not locally, you can specify the root file url here; the default value is "file://". • skip - Set to true to ignore files that failed to import; by default it is false, i.e. the ingestion is terminated when a file fails to import. • retry - Set to true to retry a failed request. The number of retries is either 5, or the value of setting retries if specified. This is set to false by default. • retries - Control how many times to retry a failed WCS-T request; set to 5 by default. • retry_sleep - Set number of seconds to wait before retrying after an error; a floating-point number can also be specified for sub-second precision. Default values is 1. • track_files - Set to true to allow files to be tracked in order to avoid reimporting already imported files. This setting is enabled by default. • resumer_dir_path - The directory in which to store the track file. By default it will be stored next to the ingredients file. • slice_restriction - Limit the slices that are imported to the ones that fit in a specified bounding box. Each subset in the bounding box should be of form { "low": 0, "high": <max> }, where low/high are given in the axis format. Example: "slice_restriction": [ { "low": 0, "high": 36000 }, { "low": 0, "high": 18000 }, { "low": "2012-02-09", "high": "2012-12-09", "type": "date" } ] • description_max_no_slices - maximum number of slices (files) to show for preview before starting the actual ingestion. • subset_correction (deprecated since rasdaman v9.6) - In some cases the resolution is small enough to affect the precision of the transformation from domain coordinates to grid coordinates. To allow for corrections that will make the import possible, set this parameter to true. • insitu - Set to true to register files in-situ, rather than ingest them in rasdaman. Note: only applicable to rasdaman enterprise. recipes/options section • import_order - Allow to sort the input files (ascending (default) or descending).Currently, it sorts by datetime which allows to import coverage from the first date or the recent date. Example: "import_order": "descending" • tiling - Specifies the tile structure to be created for the coverage in rasdaman. You can set arbitrary tile sizes for the tiling option only if the tile name is ALIGNED. Example: "tiling": "ALIGNED [0:0, 0:1023, 0:1023] TILE SIZE 5000000" For more information on tiling please check the Storage Layout Language • wms_import - If set to true, after importing data to coverage, it will also create a WMS layer from the imported coverage and populate metadata for this layer. After that, this layer will be available from WMS GetCapabilties request. Example: "wms_import": true • scale_levels - Enable the WMS pyramids feature. Level must be positive number and greater than 1. Syntax: "scale_levels": [ 1.5, 2, 4, ... ] hooks section Since v9.8, wcst_import allows to run bash commands before/after ingestion by adding optional hooks configuration in an ingredient file. There are 2 types of ingestion hooks: • before_ingestion: run bash commands before analyzing input file(s) (e.g: using gdalwarp to reproject input file(s) from EPSG:3857 CRS to EPSG:4326 CRS and import projected EPSG:4326 input file(s)) to a coverage. • after_ingestion: run bash commands after importing input file(s) to coverage (e.g: clean all projected file(s) from gdalwarp command above). When importing mode is set to non-blocking ("blocking": false), wcst_import will run before/after hook(s) for the file which is being used to update coverage, while the default blocking importing mode will run before/after hook(s) for all input files before/after they are updated to a coverage. Parameters are explained below. "hooks": [ { // Describe what this ingestion hook does "description": "reproject input files.", // Run bash command before importing file(s) to coverage "when": "before_ingestion", // Bash command which should be run for each input file "cmd": "gdalwarp -t_srs EPSG:4326 -tr 0.02 0.02 -overwrite \"${file:path}\" \"${file:path}.projected\"", // If set to *true*, when a bash command line returns any error, wcst_import terminates immediately. // **NOTE:** only valid for before hook. "abort_on_error": true, // wcst_import will consider the specified path(s) as the actual file(s) // to be ingested after running the hook, rather than the original file. // This is an array of paths where globbing is allowed (same as the "input":"paths" option). // **NOTE:** only valid for before hook. "replace_path": ["${file:path}.projected"]
},
{
// Describe what this ingestion hook does
"description": "Remove projected files.",
// Run bash command after importing file(s) to coverage
"when": "after_ingestion",
// Bash command which should be run for each imported file(s)
"cmd": "rm -rf \"${file:path}.projected\"" }, // more before and after hooks if needed ... ] Example: Import GDAL subdatasets The example ingredients below contains a pre-hook which replaces the collected file path into a GDAL subdataset form; in this particular case, with the GDAL driver for NetCDF a single variable from the collected NetCDF files is imported. "slicer": { "type": "gdal", ... }, "hooks": [ { "description": "Demonstrate import 1 variable for netCDF with subdataset", "when": "before_ingestion", "cmd": "", "abort_on_error": true, // GDAL netCDF subdataset variable file path "replace_path": ["NETCDF:${file:path}:area"]
}
]
#### 5.5.2.2. Mosaic map¶
Well suited for importing a tiled map, not necessarily continuous; it will place all input files given under a single coverage and deal with their position in space. Parameters are explained below.
{
"config": {
// The endpoint of the WCS service with the WCS-T extension enabled
"service_url": "http://localhost:8080/rasdaman/ows",
// If set to true, it will print the WCS-T requests and will not
// execute them. To actually execute them set it to false.
"mock": true,
// If set to true, the process will not require any user confirmation.
// This is useful for production environments when deployment is automated.
"automated": false
},
"input": {
// The name of the coverage; if the coverage already exists,
// it will be updated with the new files
"coverage_id": "MyCoverage",
// Absolute or relative (to the ingredients file) path or regex that
// would work with the ls command. Multiple paths separated by commas
// can be specified.
"paths": [ "/var/data/*" ]
},
"recipe": {
// The name of the recipe
"name": "map_mosaic",
"options": {
// The tiling to be applied in rasdaman
"tiling": "ALIGNED [0:511, 0:511]"
}
}
}
#### 5.5.2.3. Regular timeseries¶
Well suited for importing multiple 2-D slices created at regular intervals of time (e.g sensor data, satelite imagery etc) as 3-D cube with the third axis being a temporal one. Parameters are explained below
{
"config": {
// The endpoint of the WCS service with the WCS-T extension enabled
"service_url": "http://localhost:8080/rasdaman/ows",
// If set to true, it will print the WCS-T requests and will not
// execute them. To actually execute them set it to false.
"mock": true,
// If set to true, the process will not require any user confirmation.
// This is useful for production environments when deployment is automated.
"automated": false
},
"input": {
// The name of the coverage; if the coverage already exists,
// it will be updated with the new files
"coverage_id": "MyCoverage",
// Absolute or relative (to the ingredients file) path or regex that
// would work with the ls command. Multiple paths separated by commas
// can be specified.
"paths": [ "/var/data/*" ]
},
"recipe": {
// The name of the recipe
"name": "time_series_regular",
"options": {
// Starting date for the first spatial slice
"time_start": "2012-12-02T20:12:02",
// Format of the time provided above: auto to try to guess it,
// otherwise use any combination of YYYY:MM:DD HH:mm:ss
"time_format": "auto",
// Distance between each slice in time, granularity seconds to days
"time_step": "2 days 10 minutes 3 seconds",
// CRS to be used for the time axis
"time_crs": "http://localhost:8080/def/crs/OGC/0/AnsiDate",
// The tiling to be applied in rasdaman
"tiling": "ALIGNED [0:1000, 0:1000, 0:2]"
}
}
}
#### 5.5.2.4. Irregular timeseries¶
Well suited for importing multiple 2-D slices created at irregular intervals of time into a 3-D cube with the third axis being a temporal one. There are two types of time parameters in “options”, one needs to be choosed according to the particular use case:
{
"config": {
// The endpoint of the WCS service with the WCS-T extension enabled
"service_url": "http://localhost:8080/rasdaman/ows",
// If set to true, it will print the WCS-T requests and will not
// execute them. To actually execute them set it to false.
"mock": true,
// If set to true, the process will not require any user confirmation.
// This is useful for production environments when deployment is automated.
"automated": false
},
"input": {
// The name of the coverage; if the coverage already exists,
// it will be updated with the new files
"coverage_id": "MyCoverage",
// Absolute or relative (to the ingredients file) path or regex that
// would work with the ls command. Multiple paths separated by commas
// can be specified.
"paths": [ "/var/data/*" ]
},
"recipe": {
// The name of the recipe
"name": "time_series_irregular",
"options": {
// Information about the time parameter, two options (pick one!)
// 1. Get the date for the slice from a tag that can be read by GDAL
"time_parameter": {
// The name of such a tag
"tag_name": "TIFFTAG_DATETIME"
},
// The format of the datetime value in the tag
"datetime_format": "YYYY:MM:DD HH:mm:ss"
},
// 2. Extract the date/time from the file name
"time_parameter" :{
"filename": {
// The regex has to contain groups of tokens, separated by parentheses.
"regex": "(.*)_(.*)_(.+?)_(.*)",
// Which regex group to use for retrieving the time value
"group": "2"
},
}
// CRS to be used for the time axis
"time_crs": "http://localhost:8080/def/crs/OGC/0/AnsiDate",
// The tiling to be applied in rasdaman
"tiling": "ALIGNED [0:1000, 0:1000, 0:2]"
}
}
}
#### 5.5.2.5. General coverage¶
The general recipe aims to be a highly flexible recipe that can handle any kind of data files (be it 2D, 3D or n-D) and model them in coverages of any dimensionality. It does that by allowing users to define their own coverage models with any number of bands and axes and fill the necesary coverage information through the so called ingredient sentences inside the ingredients.
##### 5.5.2.5.1. Ingredient Sentences¶
An ingredient expression can be of multiple types:
• Numeric - e.g. 2, 4.5
• Strings - e.g. 'Some information'
• Functions - e.g. datetime('2012-01-01', 'YYYY-mm-dd')
• Expressions - allows a user to collect information from inside the ingested file using a specific driver. An expression is of form ${driverName:driverOperation} - e.g. ${gdal:minX}, ${netcdf:variable:time:min. You can find all the possible expressions here. • Any valid python expression - You can combine the types below into a python expression; this allows you to do mathematical operations, some string parsing etc. - e.g. ${gdal:minX} + 1/2 * ${gdal:resolutionX} or datetime(${netcdf:variable:time:min} * 24 * 3600)
##### 5.5.2.5.2. Parameters¶
Using the ingredient sentences we can define any coverage model directly in the options of the ingredients file. Each coverage model contains a
• global - specifies fields which should be saved (e.g. the licence, the creator etc) once for the whole coverage. Example:
"global": {
"Title": "'Drought code'"
},
• local - specifies fields which are fetched from each input file to be stored in coverage’s metadata. Then, when subsetting output coverage, only associated local metadata will be added to the result. Example:
"local": {
"LocalMetadataKey": "${netcdf:metadata:LOCAL_METADATA}" } • colorPaletteTable - specifies the path to a Color Palette Table (.cpt) file which can be used internally when encoding coverage to PNG to colorize result. Example: "colorPaletteTable": "PATH/TO/color_palette_table.cpt" Since v10, general recipe with slicer gdal reads colorPaletteTable automatically if the first input file (TIFF format with Color Table (RGB with 256 entries)) contains this metadata when colorPaletteTable is set to auto or not specified in the ingredients file. If colorPaletteTable is set to empty, this metadata is ignored when creating coverage’s global metadata. • slicer - specifies the driver (netcdf, gdal or grib) to use to read from the data files and for each axis from the CRS how to obtain the bounds and resolution corresponding to each file. Note “type”: “gdal” is used for TIFF, PNG, and other 2D formats. An example for the netCDF format can be found here and for PNG here. Here’s an example ingredient file for grib data: "recipe": { "name": "general_coverage", "options": { // Provide the coverage description and the method of building it "coverage": { // The coverage has 4 axes by combining 3 CRSes (Lat, Long, ansi, ensemble) "crs": "EPSG/0/4326@OGC/0/AnsiDate@OGC/0/Index1D?axis-label=\"ensemble\"", // specify metadata in json format "metadata": { "type": "json", "global": { // We will save the following fields from the input file // for the whole coverage "MarsType": "'${grib:marsType}'",
"Experiment": "'${grib:experimentVersionNumber}'" }, // or automatically import metadata, netcdf/gdal only (!) "global": "auto" "local": { // and the following field for each file that will compose the final coverage "level": "${grib:level}"
}
},
// specify the "driver" for reading each file
"slicer": {
// Use the grib driver, which gives access to grib and file expressions.
"type": "grib",
// The pixels in grib are considered to be 0D in the middle of the cell,
// as opposed to e.g. GeoTiff, which considers pixels to be intervals
"pixelIsPoint": true,
// Define the bands to create from the files (1 band in this case)
"bands": [
{
"name": "temp2m",
"definition": "The temperature at 2 meters.",
"description": "We measure temperature at 2 meters using sensors and
then we process the values using a sophisticated algorithm.",
"nilReason": "The nil value represents an error in the sensor."
"uomCode": "${grib:unitsOfFirstFixedSurface}", "nilValue": "-99999" } ], "axes": { // For each axis specify how to extract the spatio-temporal position // of each file that we ingest "Latitude": { // E.g. to determine at which Latitude the nth file will be positioned, // we will evaluate the given expression on the file "min": "${grib:latitudeOfLastGridPointInDegrees} +
(${grib:jDirectionIncrementInDegrees} if bool(${grib:jScansPositively})
else -${grib:jDirectionIncrementInDegrees})", "max": "${grib:latitudeOfFirstGridPointInDegrees}",
"resolution": "${grib:jDirectionIncrementInDegrees} if bool(${grib:jScansPositively})
else -${grib:jDirectionIncrementInDegrees}", // This optional configuration is added since version 9.8. // The crs order specifies the order of the CRS axis in coverage // that will be created and allows to change standard abbreviation for axis label // from EPSG database to a different name (e.g: "Lat" -> "Latitude"). "crsOrder": 0 // The grid order specifies the order of the axis in the raster // that will be created "gridOrder": 3 }, "Long": { "min": "${grib:longitudeOfFirstGridPointInDegrees}",
"max": "${grib:longitudeOfLastGridPointInDegrees} + (-${grib:iDirectionIncrementInDegrees}
if bool(${grib:iScansNegatively}) else${grib:iDirectionIncrementInDegrees})",
"resolution": "-${grib:iDirectionIncrementInDegrees} if bool(${grib:iScansNegatively})
else ${grib:iDirectionIncrementInDegrees}", "crsOrder": 1 "gridOrder": 2 }, "ansi": { "min": "grib_datetime(${grib:dataDate}, ${grib:dataTime})", "resolution": "1.0 / 4.0", "type": "ansidate", "crsOrder": 2, "gridOrder": 1, // In case and axis does not natively belong to a file (e.g. as time), // then this property must set to false; by default it is true otherwise. "dataBound": false }, "ensemble": { "min": "${grib:localDefinitionNumber}",
"resolution": 1,
"crsOrder": 3,
"gridOrder": 0
}
}
},
"tiling": "REGULAR [0:0, 0:20, 0:1023, 0:1023]"
}
}
##### 5.5.2.5.3. Possible Expressions¶
Each driver allows various expressions to extract information from input files. We will mark with capital letters, things that vary in the expression. E.g. ${gdal:metadata:YOUR_FIELD} means that you can replace YOUR_FIELD with any valid gdal metadata tag (e.g. a TIFFTAG_DATETIME) Netcdf Take a look at this NetCDF example for a general recipe ingredient file that uses many netcdf expressions. Type Description Examples Metadata information ${netcdf:metadata:YOUR_METADATA_FIELD} ${netcdf:metadata:title} Variable information ${netcdf:variable:VARIABLE_NAME:MODIFIER} where VARIABLE_NAME can be any variable in the file and MODIFIER can be one of: first|last|max|min; Any extra modifiers will return the corresponding metadata field on the given variable ${netcdf:variable:time:min} ${netcdf:variable:t:units}
Dimension information ${netcdf:dimension:DIMENSION_NAME} where DIMENSION_NAME can be any dimension in the file. This will return the value on the selected dimension. ${netcdf:dimension:time}
GDAL
For TIFF, PNG, JPEG, and other 2D data formats we use GDAL. Take a look at this GDAL example for a general recipe ingredient file that uses many GDAL expressions.
Type Description Examples
Metadata information ${gdal:metadata:METADATA_FIELD}${gdal:metadata:TIFFTAG_NAME}
Geo Bounds ${gdal:BOUND_NAME} where BOUND_NAME can be one of the minX|maxX|minY|maxY ${gdal:minX}
Geo Resolution ${gdal:RESOLUTION_NAME} where RESOLUTION_NAME can be one of the resolutionX|resolutionY ${gdal:resolutionX}
Origin ${gdal:ORIGIN_NAME} where ORIGIN_NAME can be one of the originX|originY ${gdal:originY}
GRIB
Take a look at this GRIB example for a general recipe ingredient file that uses many grib expressions.
Type Description Examples
GRIB Key ${grib:KEY} where KEY can be any of the keys contained in the GRIB file ${grib:experimentVersionNumber}
File
Type Description Examples
File Information ${file:PROPERTY} where property can be one of path|name|dir_path|original_path|original_dir_path original_* allows to get the original input file’s path/directory (used only when using pre-hook with replace_path to replace original input file paths with customized file paths). ${file:path}
Special Functions
A couple of special functions are available to deal with some more complicated cases:
Function Name Description Examples
grib_datetime(date,time) This function helps to deal with the usual grib date and time format. It returns back a datetime string in ISO format. grib_datetime(${grib:dataDate},${grib:dataTime})
datetime(date, format) This function helps to deal with strange date time formats. It returns back a datetime string in ISO format. datetime("20120101:1200", "YYYYMMDD:HHmm")
regex_extract(input, regex, group) This function extracts information from a string using regex; input is the string you parse, regex is the regular expression, group is the regex group you want to select datetime(regex_extract('${file:name}', '(.*)_(.*)_(.*)_(\\d\\d\\d\\d-\\d\\d) (.*)', 4), 'YYYY-MM') replace(input, old, new) Replaces all occurrences of a substring with another substring in the input string replace('${file:path}','.tiff', '.xml')
Band’s unit of measurement (uom) code for netCDF and GRIB recipes
• In netCDF recipes you can add uom for each band by referencing the metadata key of the specific variable. For example, for variable LAI:
"uomCode": "${netcdf:variable:LAI:units}" • In GRIB recipes adding uom for bands is same as for netCDF, except that a GRIB expression is used to fetch this information from metadata in the GRIB file. Example: "bands": [ { "name": "Temperature_isobaric", "identifier": "Temperature_isobaric", "description": "Bands description", "nilReason": "Nil value represents missing values.", "nilValue": 9999, "uomCode": "${grib:unitsOfFirstFixedSurface}"
}
]
Beside the global metadata of a coverage, you can add local metadata for each file which is a part of the whole coverage (e.g a 3D time-series coverage mosaiced from 2D GeoTiff files).
In ingredient file of general recipe, under the metadata section add a “local” object with keys and values extracted by using format type expression. Example of extracting an attribute from a netCDF input file:
"metadata": {
"type": "xml",
"global": {
...
},
"local": {
"LocalMetadataKey": "${netcdf:metadata:LOCAL_METADATA}" } } Afterwards, each file’s envelope (geo domain) and its local metadata will be added to the coverage metadata under <slice>...</slice> element if coverage metadata is imported in XML format. Example of a coverage containing local metadata in XML from 2 netCDF files: <slices> <!--- Begin Local Metadata from netCDF file 1 --> <slice> <boundedBy> <Envelope> <axisLabels>Lat Long ansi forecast</axisLabels> <srsDimension>4</srsDimension> <lowerCorner>34.4396675 29.6015625 "2017-01-10T00:00:00+00:00" 0</lowerCorner> <upperCorner>34.7208095 29.8828125 "2017-01-10T00:00:00+00:00" 0</upperCorner> </Envelope> </boundedBy> <LocalMetadataKey>FROM FILE 1</LocalMetadataKey> <fileReferenceHistory> /tmp/wcs_local_metadata_netcdf_in_xml/20170110_0_ecfire_fwi_dc.nc </fileReferenceHistory> </slice> <!--- End Local Metadata from netCDF file 1 --> <!--- Begin Local Metadata from netCDF file 2 --> <slice> <boundedBy> <Envelope> <axisLabels>Lat Long ansi forecast</axisLabels> <srsDimension>4</srsDimension> <lowerCorner>34.4396675 29.6015625 "2017-02-10T00:00:00+00:00" 3</lowerCorner> <upperCorner>34.7208095 29.8828125 "2017-02-10T00:00:00+00:00" 3</upperCorner> </Envelope> </boundedBy> <LocalMetadataKey>FROM FILE 2</LocalMetadataKey> <fileReferenceHistory> /tmp/wcs_local_metadata_netcdf_in_xml/20170210_3_ecfire_fwi_dc.nc </fileReferenceHistory> </slice> <!--- End Local Metadata from netCDF file 2 --> </slices> Since v10.0, local metadata for input files can be fetched from corresponding external text files using the optional metadata_file setting. For example: "local": { "local_metadata_key": "${gdal:metadata:local_metadata_key}",
// The metadata from the external XML file will be created
// as a child element of this root element
"root_element": "INSPIRE",
// Path to the external XML file corresponding to
// the importing input file
"path": "replace('${file:path}', '.tiff', '.xml')" } } When subsetting a coverage which contains local metadata section from input files (via WC(P)S requests), if the geo domains of subsetted coverage intersect with some input files’ envelopes, only local metadata of these files will be added to the output coverage metadata. For example: a GetCoverage request with a trim such that crs axis subsets are within netCDF file 1: http://localhost:8080/rasdaman/ows?service=WCS&version=2.0.1 &request=GetCoverage &subset=ansi("2017-01-10T00:00:00+00:00") &subset=Lat(34.4396675,34.4396675) &subset=Long(29.6015625,29.6015625) &subset=forecast(0) The coverage’s metadata result will contain only local metadata from netCDF file 1: <slices> <!--- Begin Local Metadata from netCDF file 1 --> <slice> <boundedBy> <Envelope> <axisLabels>Lat Long ansi forecast</axisLabels> <srsDimension>4</srsDimension> <lowerCorner>34.4396675 29.6015625 "2017-01-10T00:00:00+00:00" 0</lowerCorner> <upperCorner>34.7208095 29.8828125 "2017-01-10T00:00:00+00:00" 0</upperCorner> </Envelope> </boundedBy> <LocalMetadataKey>FROM FILE 1</LocalMetadataKey> <fileReferenceHistory> /tmp/wcs_local_metadata_netcdf_in_xml/20170110_0_ecfire_fwi_dc.nc </fileReferenceHistory> </slice> <!--- End Local Metadata from netCDF file 1 --> <slices> Customized axis labels in coverage This feature is available since rasdaman version 9.8 for general recipe. Before, axis labels for a coverage must match axis abbreviations in CRS’s GML definition when they are configured in the ingredient file under section "slicer"/"axes". With this new feature, one can set an arbitrary name for each axis label by adding optional configuration "crsOrder" for each axis accordingly the position index which starts from 0 of axis in coverage’s CRS. For example with below configuration, coverage will be created with 3 customized axes MyDateTimeAxis, MyLatAxis and MyLongAxis based on coverage’s CRS (AnsiDate (1 DateTime axis) and EPSG:4326 (Lat and Long axes)): "axes": { "MyDateTimeAxis": { // Match DateTime axis in AnsiDate CRS "crsOrder": 0, ... }, "MyLongAxis": { // Match Long axis in EPSG:4326 "crsOder": 2, ... }, "MyLatAxis": { // Match Lat axis in EPSG:4326 "crsOder": 1, ... } } Group several coverage slices into a group Since v9.8+, wcst_import allows to group input files on irregular axes (with "dataBound": false) by optional sliceGroupSize: value (positive integer). E.g: "time": { "min": "datetime(regex_extract('${file:name}', '(.*)\\.(.*)',1), 'YYYYMMDD')",
"gridOrder": 0,
"type": "ansidate",
"irregular": true,
"sliceGroupSize": 7,
"dataBound": false
}
If each input slice corresponds to index X, and one wants to have slice groups of size N, then the index would be translated with this option as follows:
X - (X % N)
Typical use case is importing 3D coverage from 2D satellite imageries where time axis is irregular and its values are fetched from input files by regex expression. Then, all input files which belong to 1 time window (e.g: "sliceGroupSize": 7 (7 days in AnsiDate CRS) will have the same value which is the first date of this week).
Band and dimension metadata in netCDF
Metadata can be individually specified for each band and axis in the ingredient file. This metadata is automatically added to the result output when encoding to netCDF. Example:
"metadata": {
"type": "xml",
"global": {
"description": "'3-band data.'",
"resolution": "'1'"
},
"bands": {
"red": {
},
"green": {
},
"blue": {
}
},
"axes": {
"i": {
},
"j": {
}
}
}
Since v9.7, for this metadata can be automatically derived from the input netCDF files.
• If "bands" is set to "auto" or does not exist under "metadata" in the ingredient file, all user-specified bands will have metadata which is fetched directly from the netCDF file.
• Otherwise, the user could specify metadata explicitly by a dictionary of keys/values. Metadata for 1 band is collected automatically if: 1) band is not added. 2) band is set to "auto".
• If "axes" is set to "auto" or does not exist under "metadata" in the ingredient file, all user-specified axes will have metadata which is fetched directly from the netCDF file. The axis label for variable is detected from the min or max value of CRS axis configuration under "slicer/axes" section. For example:
"slicer": {
...
"axes": {
"Long": {
# 'lon' is variable name in netCDF file for CRS axis 'Long'.
"min": "${netcdf:variable:lon:min}" ... } } } • Otherwise, the user could specify metadata explicitly by a dictionary of keys/values. Metadata for 1 axis is collected automatically if: 1) axis is not added. 2) axis is set to "auto". 3) axis is set with ${netcdf:variable:DimensionName:metadata}.
#### 5.5.2.6. Import from external WCS¶
Allows to import a coverage from a remote petascope endpoint into the local petascope. Parameters are explained below.
{
"config": {
"service_url": "http://localhost:8080/rasdaman/ows",
"default_crs": "http://localhost:8080/def/crs/EPSG/0/4326",
"automated": true
},
"input": {
"coverage_id": "test_wcs_extract"
},
"recipe": {
// name of recipe
"name": "wcs_extract",
"options": {
// remote coverage id in remote petascope
"coverage_id": "test_time3d",
// remote petascope endpoint
"wcs_endpoint" : "http://localhost:8080/rasdaman/ows",
// the partitioning scheme as a list of the maximum number of pixels on each
// axis dimension e.g. [500, 500, 1] will split the 3-D coverage in 2-D slices
// of 500 by 500.
"partitioning_scheme" : [0, 0, 500],
// The tiling to be applied in rasdaman
"tiling": "ALIGNED [0:2000, 0:2000]"
}
}
}
#### 5.5.2.7. Import Sentinel 1 data¶
This is a convenience recipe for importing Sentinel 1 data in particular; currently only GRD/SLC product types are supported, and only geo-referenced tiff files. Below is an example:
{
"config": {
"service_url": "http://localhost:8080/rasdaman/ows",
"automated": true,
"track_files": false
},
"input": {
"coverage_id": "S1_GRD_${modebeam}_${polarisation}",
// (e.g: a geo-referenced tiff file to CRS: EPSG:4326, mode beam IW,
// singler polarisation VH:
// s1a-iw-grd-vh-20190226t171654-20190326t171719-026512-02f856-002.tiff)
"paths": [ "*.tiff" ],
// If not specified, default product is "GRD"
"product": "SLC"
"modebeams": ["EW", "IW"],
"polarisations": ["HH", "HV", "VV", "VH"]
},
"recipe": {
"name": "sentinel1",
"options": {
"coverage": {
"type": "xml",
"global": {
"Title": "'Sentinel-1 GRD data served by rasdaman'"
}
}
},
"tiling": "ALIGNED [0:0, 0:1999, 0:1999] TILE SIZE 32000000",
"wms_import": true
}
}
}
The recipe extends general_coverage so the "recipe" section has the same structure. However, a lot of information is automatically filled in by the recipe now, so the ingredients file is much simpler as the example above shows.
The other obvious difference is that the "coverage_id" is templated with several variables enclosed in ${ and } which are automatically replaced to generate the actual coverage name during import: • modebeam - the mode beam of input files, e.g. IW/EW. • polarisation - single polarisation of input files, e.g: HH/HV/VV/VH If the files collected by "paths" are varying in any of these parameters, the corresponding variables must appear somewhere in the "coverage_id" (as for each combination a separate coverage will be constructed). Otherwise, the ingestion will either fail or result in invalid coverages. E.g. if all data’s mode beam is IW, but still different polarisations, the "coverage_id" could be "MyCoverage_${polarisation}";
In addition, the data to be ingested can be optionall filtered with the following options in the "input" section:
• modebeams - specify a subset of mode beams to ingest from the data, e.g. only the IW mode beam; if not specified, data of all supported mode beams will be ingested.
• polarisations - specify a subset of polarisations to ingest, e.g. only the HH polarisation; if not specified, data of all supported polarisations will be ingested.
Limitations:
• Only GRD/SLC products are supported.
• Data must be geo-referenced.
• Filenames are assumed to be of the format: s1[ab]-(.*?)-grd(.?)-(.*?)-(.*?)-(.*?)-(.*?)-(.*?)-(.*?).tiff or s1[ab]-(.*?)-slc(.?)-(.*?)-(.*?)-(.*?)-(.*?)-(.*?)-(.*?).tiff.
#### 5.5.2.8. Import Sentinel 2 data¶
This is a convenience recipe for importing Sentinel 2 data in particular. It relies on support for Sentinel 2 in more recent GDAL versions. Importing zipped Sentinel 2 is also possible and automatically handled.
Below is an example:
{
"config": {
"service_url": "http://localhost:8080/rasdaman/ows",
"automated": true
},
"input": {
"coverage_id": "S2_${crsCode}_${resolution}_${level}", "paths": [ "S2*.zip" ], // Optional filtering settings "resolutions": ["10m", "20m", "60m", "TCI"], "levels": ["L1C", "L2A"], "crss": ["32757"] // remove or leave empty to ingest any CRS }, "recipe": { "name": "sentinel2", "options": { "coverage": { "metadata": { "type": "xml", "global": { "Title": "'Sentinel-2 data served by rasdaman'" } } }, "tiling": "ALIGNED [0:0, 0:1999, 0:1999] TILE SIZE 32000000", "wms_import": true } } } The recipe extends general_coverage so the "recipe" section has the same structure. However, a lot of information is automatically filled in by the recipe now, so the ingredients file is much simpler as the example above shows. The other obvious difference is that the "coverage_id" is templated with several variables enclosed in ${ and } which are automatically replaced to generate the actual coverage name during import:
• crsCode - the CRS EPSG code of the imported files, e.g. 32757 for WGS 84 / UTM zone 57S.
• resolution - Sentinel 2 products bundle several subdatasets of different resolutions:
• 10m - bands B4, B3, B2, and B8 (base type unsigned short)
• 20m - bands B5, B6, B7, B8A, B11, and B12 (base type unsigned short)
• 60m - bands B1, B8, and B10 (base type unsigned short)
• TCI - True Color Image (red, green, blue char bands); also 10m as it is derived from the B2, B3, and B4 10m bands.
• level - L1C or L2A
If the files collected by "paths" are varying in any of these parameters, the corresponding variables must appear somewhere in the "coverage_id" (as for each combination a separate coverage will be constructed). Otherwise, the ingestion will either fail or result in invalid coverages. E.g. if all data is level L1C with CRS 32757, but still different resolutions, the "coverage_id" could be "MyCoverage_${resolution}"; the other variables can still be specified though, so "MyCoverage_${resolution}_${crsCode}" is valid as well. In addition, the data to be ingested can be optionall filtered with the following options in the "input" section: • resolutions - specify a subset of resolutions to ingest from the data, e.g. only the “10m” subdataset; if not specified, data of all supported resolutions will be ingested. • levels - specify a subset of levels to ingest, so that files of other levels will be fully skipped; if not specified, data of all supported levels will be ingested. • crss - specify a list of CRSs (EPSG codes as strings) to ingest; if not specified or empty, data of any CRS will be ingested. #### 5.5.2.9. Image pyramids¶ This feature (v9.7+) allows to create downscaled versions of a given coverage, eventually achieving something like an image pyramid, in order to enable faster WMS requests when zooming in/out. By using the scale_levels option of wcst_import when importing a coverage with WMS enabled, petascope will create downscaled collections in rasdaman following this pattern: coverageId_<level>. If level is a float, then the dot is replaced with an underscore, as dots are not permitted in a collection name. Some examples: • MyCoverage, level 2 -> MyCoverage_2 • MyCoverage, level 2.45 -> MyCoverage_2_45 Example ingredients specification to create two downscaled levels which are 8x and 32x smaller than the original coverage: Two new WCS-T non-standard requests are utilized by wcst_import for this feature, see here for more information. #### 5.5.2.10. Creating your own recipe¶ The recipes above cover a frequent but limited subset of what is possible to model using a coverage. WCSTImport allows to define your own recipes in order to fill these gaps. In this tutorial we will create a recipe that can construct a 3D coverage from 2D georeferenced files. The 2D files that we want to target have all the same CRS and cover the same geographic area. The time information that we want to retrieve is stored in each file in a GDAL readable tag. The tag name and time format differ from dataset to dataset so we want to take this information as an option to the recipe. We would also want to be flexible with the time crs that we require so we will add this option as well. Based on this usecase, the following ingredient file seems to fulfill our need: { "config": { "service_url": "http://localhost:8080/rasdaman/ows", "mock": false, "automated": false }, "input": { "coverage_id": "MyCoverage", "paths": [ "/var/data/*" ] }, "recipe": { "name": "my_custom_recipe", "options": { "time_format": "auto", "time_crs": "http://localhost:8080/def/crs/OGC/0/AnsiDate", "time_tag": "MY_SPECIAL_TIME_TAG", } } } To create a new recipe start by creating a new folder in the recipes folder. Let’s call our recipe my_custom_recipe: $ cd $RMANHOME/share/rasdaman/wcst_import/recipes_custom/$ mkdir my_custom_recipe
$touch __init__.py The last command is needed to tell python that this folder is containing python sources, if you forget to add it, your recipe will not be automatically detected. Let’s first create an example of our ingredients file so we get a feeling for what we will be dealing with in the recipe. Our recipe will just request from the user two parameters Let’s now create our recipe, by creating a file called recipe.py $ touch recipe.py
$editor recipe.py Use your favorite editor or IDE to work on the recipe (there are type annotations for most WCSTImport classes so an IDE like PyCharm would give out of the box completion support). First, let’s add the skeleton of the recipe (please note that in this tutorial, we will omit the import section of the files (your IDE will help you auto import them)): class Recipe(BaseRecipe): def __init__(self, session): """ The recipe class for my_custom_recipe. :param Session session: the session for the import tun """ super(Recipe, self).__init__(session) self.options = session.get_recipe()['options'] def validate(self): super(Recipe, self).validate() pass def describe(self): """ Implementation of the base recipe describe method """ pass def ingest(self): """ Ingests the input files """ pass def status(self): """ Implementation of the status method :rtype (int, int) """ pass @staticmethod def get_name(): return "my_custom_recipe" The first thing you need to do is to make sure the get_name() method returns the name of your recipe. This name will be used to determine if an ingredient file should be processed by your recipe. Next, you will need to focus on the constructor. Let’s examine it. We get a single parameter called session which contains all the information collected from the user plus a couple more useful things. You can check all the available methods of the class in the session.py file, for now we will just save the options provided by the user that are available in session.get_recipe() in a class attribute. In the validate() method, you will validate the options for the recipe provided by the user. It’s generally a good idea to call the super method to validate some of the general things like the WCST Service availability and so on although it is not mandatory. We also want to validate our custom recipe options here. This is how the recipe looks like now: class Recipe(BaseRecipe): def __init__(self, session): """ The recipe class for my_custom_recipe. :param Session session: the session for the import tun """ super(Recipe, self).__init__(session) self.options = session.get_recipe()['options'] def validate(self): super(Recipe, self).validate() if "time_crs" not in self.options: raise RecipeValidationException( "No valid time crs provided") if 'time_tag' not in self.options: raise RecipeValidationException( "No valid time tag parameter provided") if 'time_format' not in self.options: raise RecipeValidationException( "You have to provide a valid time format") def describe(self): """ Implementation of the base recipe describe method """ pass def ingest(self): """ Ingests the input files """ pass def status(self): """ Implementation of the status method :rtype (int, int) """ pass @staticmethod def get_name(): return "my_custom_recipe" Now that our recipe can validate the recipe options, let’s move to the describe() method. This method allows you to let your users know any relevant information about the ingestion before it actually starts. The irregular_timeseries recipe prints the timestamp for the first couple of slices for the user to check if they are correct. Similar behaviour should be done based on what your recipe has to do. Next, we should define the ingest behaviour. The framework does not make any assumptions about how the correct method of ingesting is, however it offers a lot of utility functionality that help you do it in a more standardized way. We will continue this tutorial by describing how to take advantage of this functionality, however, note that this is not required for the recipe to work. The first thing that you need to do is to define an importer object. This importer object, takes a coverage object and ingests it using WCST requests. The object has two public methods, ingest(), which ingests the coverage into the WCS-T service (note: ingest can be an insert operation when the coverage was not defined, or update if the coverage exists. The importer will handle both cases for you, so you don’t have to worry if the coverage already exists.) and get_progress() which returns a tuple containing the number of imported slices and the total number of slices. After adding the importer, the code should look like this: class Recipe(BaseRecipe): def __init__(self, session): """ The recipe class for my_custom_recipe. :param Session session: the session for the import tun """ super(Recipe, self).__init__(session) self.options = session.get_recipe()['options'] self.importer = None def validate(self): super(Recipe, self).validate() if "time_crs" not in self.options: raise RecipeValidationException( "No valid time crs provided") if 'time_tag' not in self.options: raise RecipeValidationException( "No valid time tag parameter provided") if 'time_format' not in self.options: raise RecipeValidationException( "You have to provide a valid time format") def describe(self): """ Implementation of the base recipe describe method """ pass def ingest(self): """ Ingests the input files """ self._get_importer().ingest() def status(self): """ Implementation of the status method :rtype (int, int) """ pass def _get_importer(): if self.importer is None: self.importer = Importer(self._get_coverage()) return self.importer def _get_coverage(): pass @staticmethod def get_name(): return "my_custom_recipe" In order to build the importer, we need to create a coverage object. Let’s see how we can do that. The coverage constructor requires a • coverage_id: the id of the coverage • slices: a list of slices that compose the coverage. Each slice defines the position in the coverage and the data that should be defined at the specified position • range_fields: the range fields for the coverage • crs: the crs of the coverage • pixel_data_type: the type of the pixel in gdal format, e.g. Byte, Float32 etc You can construct the coverage object in many ways, we will present further a specific method of doing it. Let’s start from the crs of the coverage. For our recipe, we want a 3D crs, composed of the CRS of the 2D images and a time crs as indicated. The two lines of code would give us exactly this: # Get the crs of one of the images using a GDAL helper class. # We are assuming all images have the same CRS. gdal_dataset = GDALGmlUtil(self.session.get_files()[0].get_filepath()) # Get the crs of the coverage by compounding the two crses crs = CRSUtil.get_compound_crs([gdal_dataset.get_crs(), self.options['time_crs']]) Let’s also get the range fields for this coverage. We can extract them again from the 2D image using a helper class that can use GDAL to get the relevant information: fields = GdalRangeFieldsGenerator(gdal_dataset).get_range_fields() Let’s also get the pixel base type, again using the gdal helper: pixel_type = gdal_dataset.get_band_gdal_type() Let’s see what we have so far: class Recipe(BaseRecipe): def __init__(self, session): """ The recipe class for my_custom_recipe. :param Session session: the session for the import tun """ super(Recipe, self).__init__(session) self.options = session.get_recipe()['options'] self.importer = None def validate(self): super(Recipe, self).validate() if "time_crs" not in self.options: raise RecipeValidationException( "No valid time crs provided") if 'time_tag' not in self.options: raise RecipeValidationException( "No valid time tag parameter provided") if 'time_format' not in self.options: raise RecipeValidationException( "You have to provide a valid time format") def describe(self): """ Implementation of the base recipe describe method """ pass def ingest(self): """ Ingests the input files """ self._get_importer().ingest() def status(self): """ Implementation of the status method :rtype (int, int) """ pass def _get_importer(self): if self.importer is None: self.importer = Importer(self._get_coverage()) return self.importer def _get_coverage(self): # Get the crs of one of the images using a GDAL helper class. # We are assuming all images have the same CRS. gdal_dataset = GDALGmlUtil(self.session.get_files()[0].get_filepath()) # Get the crs of the coverage by compounding the two crses crs = CRSUtil.get_compound_crs( [gdal_dataset.get_crs(), self.options['time_crs']]) fields = GdalRangeFieldsGenerator(gdal_dataset).get_range_fields() pixel_type = gdal_dataset.get_band_gdal_type() coverage_id = self.session.get_coverage_id() slices = self._get_slices(crs) return Coverage(coverage_id, slices, fields, crs, pixel_type) def _get_slices(self, crs): pass @staticmethod def get_name(): return "my_custom_recipe" As you can notice, the only thing left to do is to implement the _get_slices() method. To do so we need to iterate over all the input files and create a slice for each. Here’s an example on how we could do that def _get_slices(self, crs): # Let's first extract all the axes from our crs crs_axes = CRSUtil(crs).get_axes() # Prepare a list container for our slices slices = [] # Iterate over the files and create a slice for each one for infile in self.session.get_files(): # We need to create the exact position in time and space in which to # place this slice # For the space coordinates we can use the GDAL # helper to extract it for us, which will return a list of subsets # based on the crs axes that we extracted # and will fill the # coordinates for the ones that it can (the easting and northing axes) subsets = GdalAxisFiller( crs_axes, GDALGmlUtil(infile.get_filepath())).fill() # fill the time axis as well and indicate the position in time for subset in subsets: # Find the time axis if subset.coverage_axis.axis.crs_axis.is_future(): # Set the time position for it. Our recipe extracts it from # a GDAL tag provided by the user subset.interval.low = GDALGmlUtil(infile).get_datetime( self.options["time_tag"]) slices.append(Slice(subsets, FileDataProvider(tpair.file))) return slices And we are done we now have a valid coverage object. The last thing needed is to define the status method. This method need to provide a status update to the framework in order to display it to the user. We need to return the number of finished work items and the number of total work items. In our case we can measure this in terms of slices and the importer can already provide this for us. So all we need to do is the following: def status(self): return self._get_importer().get_progress() We now have a functional recipe. You can try the ingredients file against it and see how it works. class Recipe(BaseRecipe): def __init__(self, session): """ The recipe class for my_custom_recipe. :param Session session: the session for the import tun """ super(Recipe, self).__init__(session) self.options = session.get_recipe()['options'] self.importer = None def validate(self): super(Recipe, self).validate() if "time_crs" not in self.options: raise RecipeValidationException( "No valid time crs provided") if 'time_tag' not in self.options: raise RecipeValidationException( "No valid time tag parameter provided") if 'time_format' not in self.options: raise RecipeValidationException( "You have to provide a valid time format") def describe(self): """ Implementation of the base recipe describe method """ pass def ingest(self): """ Ingests the input files """ self._get_importer().ingest() def status(self): """ Implementation of the status method :rtype (int, int) """ pass def _get_importer(self): if self.importer is None: self.importer = Importer(self._get_coverage()) return self.importer def _get_coverage(self): # Get the crs of one of the images using a GDAL helper class. # We are assuming all images have the same CRS. gdal_dataset = GDALGmlUtil(self.session.get_files()[0].get_filepath()) # Get the crs of the coverage by compounding the two crses crs = CRSUtil.get_compound_crs( [gdal_dataset.get_crs(), self.options['time_crs']]) fields = GdalRangeFieldsGenerator(gdal_dataset).get_range_fields() pixel_type = gdal_dataset.get_band_gdal_type() coverage_id = self.session.get_coverage_id() slices = self._get_slices(crs) return Coverage(coverage_id, slices, fields, crs, pixel_type) def _get_slices(self, crs): # Let's first extract all the axes from our crs crs_axes = CRSUtil(crs).get_axes() # Prepare a list container for our slices slices = [] # Iterate over the files and create a slice for each one for infile in self.session.get_files(): # We need to create the exact position in time and space in which to # place this slice # For the space coordinates we can use the GDAL # helper to extract it for us, which will return a list of subsets # based on the crs axes that we extracted # and will fill the # coordinates for the ones that it can (the easting and northing axes) subsets = GdalAxisFiller( crs_axes, GDALGmlUtil(infile.get_filepath())).fill() # fill the time axis as well and indicate the position in time for subset in subsets: # Find the time axis if subset.coverage_axis.axis.crs_axis.is_future(): # Set the time position for it. Our recipe extracts it from # a GDAL tag provided by the user subset.interval.low = GDALGmlUtil(infile).get_datetime( self.options["time_tag"]) slices.append(Slice(subsets, FileDataProvider(tpair.file))) return slices @staticmethod def get_name(): return "my_custom_recipe" ## 5.6. Data export¶ WCS formats are requested via the format KVP key (<gml:format> elements for XML POST requests), and take a valid MIME type as value. Output encoding is passed on to the the GDAL library, so the limitations on output formats are devised accordingly by the supported raster formats of GDAL. The valid MIME types which Petascope may support can be checked from the WCS 2.0.1 GetCapabilities response: <wcs:formatSupported>application/gml+xml</wcs:formatSupported> <wcs:formatSupported>image/jpeg</wcs:formatSupported> <wcs:formatSupported>image/png</wcs:formatSupported> <wcs:formatSupported>image/tiff</wcs:formatSupported> <wcs:formatSupported>image/bmp</wcs:formatSupported> <wcs:formatSupported>image/jp2</wcs:formatSupported> <wcs:formatSupported>application/netcdf</wcs:formatSupported> <wcs:formatSupported>text/csv</wcs:formatSupported> <wcs:formatSupported>application/json</wcs:formatSupported> <wcs:formatSupported>application/dem</wcs:formatSupported> ... In case of encode processing expressions, besides MIME types WCPS (and rasql) can also accept GDAL format identifiers or other commonly-used format abbreviations like “CSV” for Comma-Separated-Values for instance. ## 5.7. Configuration¶ The petascope configuration can be found in $RMANHOME/etc/petascope.properties; editing this file requires restarting Tomcat.
### 5.7.1. Database connection¶
Below is a list of settings for different databases that have been tested successfully with rasdaman for holding the array geo-metadata (not the array data!); replace db-username and db-password with your individual values (it is a major security risk to use the default values coming during installation). Note that only a single datasource can be specified in petascope.properties at any given time, more than one is not supported for simultaneous use. Note also that changing to another database system requires more than just changing these entries, some migration process is involved instead.
# Postgresql (default)
spring.datasource.url=jdbc:postgresql://localhost:5432/petascopedb
spring.jpa.database-platform=org.hibernate.dialect.PostgreSQLDialect
# HSQLDB
spring.datasource.url=jdbc:hsqldb:file://home/rasdaman/petascopedb.db
# H2
spring.datasource.url=jdbc:h2:file://home/rasdaman/petascopedb.db;DB_CLOSE_ON_EXIT=FALSE
spring.h2.console.enabled=true
For non-postgresql DBMS like H2, HSQLDB, check the petascope.properties to add path to its JDBC jar driver on your system.
# Path to JDBC jar file for Spring datasource
# purpose: If left empty, the default PostgreSQL JDBC driver will be used.
# the corresponding JDBC driver, and set the path to it.
spring.datasource.jdbc_jar_path=
# Path to JDBC jar file for source datasource
# purpose: If left empty, the default PostgreSQL JDBC driver will be used.
# the corresponding JDBC driver, and set the path to it.
When migrating to a different database system (e.g. PostgreSQL to HSQLDB), you need to specify connection details for the existing database like this:
metadata_url=jdbc:postgresql://localhost:5432/petascopedb
### 5.7.2. Standalone deployment¶
petascope
petascope can run as a standalone web application with embedded tomcat by running:
$java -jar rasdaman.war In this case, the port for embedded tomcat will be fetched from server.port configuration in petascope.properties (e.g: 9009). Then petascope can be accessed via URL: http://localhost:9009/rasdaman/ows One can also run embedded petascope with its own dedicated petascope.propeties by adding an option which points to a folder containing this property file, e.g: $ java -jar rasdaman.war --petascope.confDir=/opt/rasdaman/new_etc/
secore
Same as petascope, one can run secore as a standalone web application with embedded tomcat by running:
$java -jar def.war Note Configuration secoredb.path must be set in secore.properties file first to a folder which system user can create XML database files inside it, e.g: secoredb.path=/tmp/ The port for embedded tomcat will be fetched from server.port configuration in secore.properties file (e.g: 9010). Then secore can be accessed via URL: http://localhost:9010/def Start/stop embedded petascope/secore By configuring java_server=embedded in $RMANHOME/etc/petascope.properties and $RMANHOME/etc/secore.properties, one can start rasdaman with these embedded applications by running: $ start_rasdaman.sh
and stop with:
$stop_rasdaman.sh To start/stop only a specific embedded application: $ start_rasdaman.sh --service (secore | petascope)
\$ stop_rasdaman.sh --service (secore | petascope)
### 5.7.3. Logging¶
At the end of petascope.properties you will find the logging configuration. It is recommended to adjust this, and make sure that Tomcat has permissions to write the petascope.log file.
### 5.7.4. Static content via petascope¶
Since v9.8, external static content (HTML/CSS/Javascript) which exists outside of rasdaman.war can be served by petascope at http://petascope-endpoint/rasdaman/ if setting static_html_dir_path in petascope.properties is set to an existing directory (absolute) path containing index.html as entry web page which the user running Tomcat can read.
## 5.8. Database migration¶
Below we outline the steps for migrating petascopedb (from vX.X to vY.Y, or from one DBMS to another, like PostgreSQL to HSQLDB):
1. If using an embedded database like HSQLDB, which does not support multiple connections from different applications, make sure that the (new) petascope 9.5 is stopped.
2. Execute the migration script: ./migrate_petascopedb.sh
3. All coverages in pre 9.5 petascopedb will be read by the old CoverageMetadata model which is imported in the new petascope as a legacy package.
4. If coverage id doesn’t exist in the new petascopedb, a process to translate from old CoverageMetadata model to CIS coverage data model is done and then persisted in petascopedb.
5. While running the migration, all services of the new petascope web application, such as: WCS, WCPS, WMS, and WCS-T, will not be available to make sure the data is migrated safely.
Note
Migrating from v9.4 to v9.5 will create a new database petascopedb, and will not modify the existing petascopedb, just rename it to petascopedb_94_backup.
### 5.8.2. Rollback¶
The following parts of petascope are saved to allow for rollback in the unlikely case of an unsuccessful migration.
• The old petascopedb is preserved (renamed to petascopedb_94_backup) to allow the user to test the new petascope version first. It is their decision, ultimately, whether to drop the previous database or not.
• The old petascope web application will be moved from rasdaman.war to rasdaman.war.old in the Tomcat webapps directory
• The petascope.properties is backed up to petascope.properties.DATE.bak by the update_properties.sh script.
To rollback:
1. rename the new petascope (rasdaman.war and petascope.properties to rasdaman.war.new and petascope.properties.new)
2. rename the old petascope back to the original (rasdaman.war.bak and petascope.properties.DATE.bak to rasdaman.war and petascope.properties).
3. rename the backuped database from petascopedb_94_backup to petascopedb.
4. restart Tomcat
## 5.9. 3rd party libraries¶
Petascope uses various 3rd party libraries, documented on the overall rasdaman code provenance page.
|
2020-02-29 06:35:58
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|
https://mathematica.stackexchange.com/questions/157834/is-building-an-event-based-parser-possible-reasonable-in-mathematica-wl/158251
|
# Is building an event-based parser possible/reasonable in Mathematica (WL)?
Too long? Go to Problems section
## Background
I like to learn by doing small, sometimes artificial, projects. Among other things I had 'parsers', and 'stream methods / streams in MMA' on my to learn list.
So I decided to join it and learn that by building a streaming api for JSON files. We will get to what that means.
I did some research and I think I know what I need to do but I don't see how this can be done in reasonable manner in Mathematica.
## What I want to build
Shortly, such api/parser advances step by step (if told to) through a stream and produces events on which user can do something. Events are specific for a parser/format, so in JSON case they can be 'objectBeginning', 'objectEnd', 'keyName', 'stringValue', 'trueValue' etc.
Simple use case, again shortly, 'parse untill you find a keyName "metadata", read value, close stream'.
The point is, all that is done without reading whole JSON into memory.
https://javaee.github.io/jsonp/
http://www.saxproject.org/event.html
## How I want to build that
I decided to start by more or less imitate javax.json mentioned above.
So there should be a next[stream_] method which should succesively return events:
The parser can generate the following events: START_OBJECT, END_OBJECT, START_ARRAY, END_ARRAY, KEY_NAME, VALUE_STRING, VALUE_NUMBER, VALUE_TRUE, VALUE_FALSE, and VALUE_NULL.
The exact form does not matter because I failed to even Read it properly :)
## Problems
After reading about Read, DefineInputStringMethod (tutorial/StreamMethods) and friends, I came to a conclusion that this framework is not suited for this or I just can't grasp it, thus the question, I want to understand :)
• I don't know how to efficiently implement Read e.g. a STRINGValue
which should return content separated by quotes ("string") but we have to keep in mind that it can contain escaped quotes. ("str \" ing")
E.g.:
Read[StringToStream["\"start \\\"end\""], Word, WordSeparators -> {"\""}]
"start \" (terminated too quickly)
One could go with ReadString
ReadString[StringToStream["\"start \\\"end\""], Except["\\"] ~~ "\""]
"\"start \\"en"
but we lose the last character, represented by Except, as separators are not part of objects. So we need to go back for it. You can already suspect you are doing something wrong when such basic operation gets so messy.
I don't even proceed with this because we need Skip methods and there is no SkipString to support this type.
Escaped tokens/separators seem to be a core of this problem, otherwise e.g. TRUEValue can be implemented by putting "true" inside TokenWords options.
• Speed
While memory is what we care about, we can't spend 2 minutes on parsing/skipping 10MB of JSON. And you can't Compile, even procedural style, code with While Read etc. So it is too high level to be efficient.
I could solve STRINGValue problem by reading Character by Character, handling escaped quotes and all that but this will take forever.
• DefineInputStreamMethod
I don't really see how this could help, it rather seems to provide an api to 'preprocess' streams. Unless I'm mistaken it does not have tools to add new types, easily emmit events or speed up parsing process but taking it 'deeper'.
Let me know if I am wrong.
## Questions
I guess this boils down to what is a reasonable way to do this?
• If my approach is correct:
• How to add low level types support for Read
• How to write fast Read based procedures (ReadList and friends can't be used as we don't see the content in advance
• And if not
• Is there a more idiomatic approach?
• If there is not, why? Isn't that something fundamental for a language?
• Am I right thinking that linking external libraries only make sense if they support all features you need, otherwise building on top will lead to problems outlined in Problems/speed?
Keywords:
event based parser, SAX, SAX2, streaming interface, push parser
Related:
Wrapping a C library with a streaming interface
• My best suggestion would be to build a back-end Association to cache data about, e.g. whether you've got unmatched braces, and use some combination of Read up to various potential tokens, to build a string that can be tested against with a compiled regex and to parse it out like that. Then provide events for when these patterns match. It'd be a bit tedious, but I can see it working with okay performance. – b3m2a1 Oct 17 '17 at 6:54
• @b3m2a1 if I get it right that only makes sense if you plan to parse/work with a specific file more than once, right? For one time data extraction it is not very useful. – Kuba Oct 18 '17 at 8:29
• I wasn't actually necessarily proposing extracting the data. I was picturing parsing some JSON or XML block, where you need to know what part of the block you're in, hence tracking like quantities of open and close brackets. Then I figured read up until you hit any of "{"|"}"|"\""|":" and check to see if you have a complete token or block or whatever, and continue on like that. That's basically the lexing side of things. Then your parser would apply rules to those tokens / blocks. I haven't thought through all of the performance considerations of this strategy though. It might be unworkable. – b3m2a1 Oct 18 '17 at 8:35
• @b3m2a1 So you suggest the logic for the lexer, I think this is not the issue here. Also, notice that all those tokens can be escaped by being in a string so more (not very) sophisticated state tracking is needed and the point of the question is, it seems there are no tools for that. – Kuba Oct 18 '17 at 8:41
• Yeah my backend suggestion was basically to handle all of those escapes and such complications. I agree there are no good tools for it, but I'd argue it's always a bit of a pain to do these kinds of things, based on work I've done in python with DSLs and mini-interpreters. Leonid's streaming work might provide a good backbone for future support of this type of feature, but who knows how far in the future that'd be. – b3m2a1 Oct 18 '17 at 8:46
### Note:
If you want this type of parser added for JSON, I think WRI could do it easily. They already have DeveloperReadRawJSONStream so I think adding some event-based parsing to that wouldn't be too much to ask
This has been kicking around my for the past few days, so here's a quick example of what I discussed in my comment. It is by no means complete, but it's a start.
We'll simply define a bunch of different tokens to look for and handle each of them differently and then layer a reader on top of that. Here's the core code for that:
jStreamReader[stream : _String | _File | _InputStream] :=
Module[{
jStreamData
},
jStreamData~ClearAttributes~Temporary;
jStreamData =
<|
"InString" -> False,
"BlockDepth" -> <|Association -> 0, List -> 0,
CompoundExpression -> 0|>,
"BlockStack" -> {},
"Cache" -> InternalBag[],
"CacheStack" -> {},
"CachePush" ->
Function[
InternalStuffBag[jStreamData["Cache"], #]
],
"CacheRecurse" ->
Function[
jStreamData["CacheStack"] = {jStreamData["CacheStack"],
jStreamData["Cache"]};
jStreamData["Cache"] = InternalBag[];
],
"CacheReset" ->
Function[
With[{c = jStreamData["CacheStack"]},
jStreamData["CacheStack"] = c[[1]];
jStreamData["Cache"] = c[[2]];
]
],
"CachePart" ->
Function[
InternalBagPart[jStreamData["Cache"], #]
],
"CacheClear" ->
Function[
jStreamData["Cache"] = InternalBag[];
],
"CacheDump" ->
Function[
With[{data = InternalBagPart[jStreamData["Cache"], All]},
jStreamData["Cache"] = InternalBag[];
data
]
],
"Stream" ->
Replace[stream, {
_String :> StringToStream[stream]
}]
|>;
jStreamData[p] = v;
StreamPosition@jStreamData["Stream"];
SetStreamPosition[jStreamData["Stream"], p];
(
Close@jStreamData["Stream"];
jStreamData // Remove
);
]
$jStreamBracketTokenIndicators = {"{", "}", "[", "]", "(", ")"};$jStreamChunkTokenIndicators =
{",", ":"};
$jStreamStringTokenIndicators = {"\""};$jStreamInStringTokenIndicators =
{"\\\"", "\""};
$jStreamPossibleTokenIndicators = Alternatives @@ Join[$jStreamStringTokenIndicators,
$jStreamBracketTokenIndicators,$jStreamChunkTokenIndicators
];
$jStreamInStringTokenIndicators = Alternatives @@$jStreamInStringTokenIndicators;
$jStreamBracketTokenIndicators = Alternatives @@$jStreamBracketTokenIndicators;
$jStreamBracketMap = <| "{" -> {Opening, Association}, "}" -> {Closing, Association}, "[" -> {Opening, List}, "]" -> {Closing, List}, "(" -> {Opening, CompoundExpression}, ")" -> {Closing, CompoundExpression} |>; jStreamReadToSep[reader_] := Module[{ sp = StreamPosition@reader, strm = reader["Stream"], ret, sep }, ret = With[{test = Read[strm, Character]}, If[test === EndOfFile, Throw[EndOfFile]]; SetStreamPosition[strm, sp]; If[reader["InString"], If[StringMatchQ[test,$jStreamInStringTokenIndicators] ||
StringMatchQ[
test <> "\"", $jStreamInStringTokenIndicators], "", ReadString[strm,$jStreamInStringTokenIndicators]
],
If[StringMatchQ[test, $jStreamPossibleTokenIndicators], "", ReadString[strm,$jStreamPossibleTokenIndicators]
]
]
];
sep =
],
];
If[StringMatchQ[sep, $jStreamBracketTokenIndicators] && StringLength@StringTrim[ret] > 0, SetStreamPosition[reader, StreamPosition[reader] - 1]; sep = "" ]; {ret, sep, sp} ]; jStreamHandleSepData[reader_, {ret_, sep_, sp_}] := With[{sepData =$jStreamBracketMap[sep]},
Which[
sep === "",
{ret, sep, Value, Expression},
sep === ":",
{ret, sep, Key, None},
sep === ",",
{ret, sep, Value, Expression},
{ret, sep, None, String},
sep === "\"",
{ret, sep, None, Continue},
sep === "\\\"",
{ret, sep, None, Continue},
sepData[[1]] === Closing,
];
{ret, sep, sepData, Expression},
sepData[[1]] === Opening,
{ret, sep, sepData, None},
True,
{ret, sep, sepData, Expression}
]
];
Block[{segs},
segs = {None,
While[segs[[-1, -1]] === Continue,
segs = {segs,
];
Cases[segs, {_String, _String, __}, \[Infinity]]
]
jStreamBuildToken[segs_] :=
{
Switch[segs[[-1, -1]],
None, Null,
String,
{
ToExpression@StringJoin@segs[[All, ;; 2]],
String
},
_,
{
Replace[StringTrim@StringJoin@segs[[-1, 1]], {
"null" -> Null,
e_ :> ToExpression@e
}],
segs[[-1, -1]]
}
],
Replace[segs[[-1, -2]], {
{o_, "{}"} :> {o, Association},
{o_, "[]"} :> {o, List},
{o_, "()"} :> CompoundExpression
}]
}
This generates a reader symbol that tracks the data in a mutable way, allowing it to act like a prettied-up stream in many ways.
Here's support for reading JSON data types:
(*Different types of read processors *)
jStreamRead[reader_, Key] :=
{Null, Key} :>
{a_, String | Expression} :> a
],
EndOfFile :> EndOfFile,
e_ :>
(
)
}];
{_, {Closing, Association}} :>
{Null, Key} :>
(
(
)
];
),
EndOfFile :> EndOfFile,
e_ :>
(
)
}];
{_, {Closing, List}} :>
{{v_, _}, None | Value} :>
(
),
{Null, {Opening, t_}} :>
(
];
),
EndOfFile :> EndOfFile
}];
{_, {Closing, CompoundExpression}} :>
$wrapper @@ reader["CacheDump"], {Null, {Opening, t_}} :> jStreamRead[reader, t], {{v_, _}, None | Value} :> ( reader["CachePush"][v]; jStreamRead[reader, CompoundExpression] ), {Null, {Opening, t_}} :> ( reader["CachePush"][ jStreamRead[reader, t] ]; jStreamRead[reader, CompoundExpression] ), EndOfFile :> EndOfFile }]; jStreamRead[reader_, Value] := Replace[jStreamReadToken[reader], { {{a_, _}, None | Value} :> a, {Null, {Opening, t_}} :> jStreamRead[reader, t], EndOfFile :> EndOfFile, e_ :> ( reader["CacheAdd"][e]; jStreamRead[reader, Value] ) }]; jStreamRead[reader_, KeyValuePattern] := jStreamRead[reader, Key] -> jStreamRead[reader, Value]; jStreamRead[reader_, Automatic] := Replace[jStreamReadToken[reader], { {Null, {Opening, t_}} :> jStreamRead[reader, t], {{a_, _}, None | Value} :> a }]; jStreamRead[reader_, "Token"] := jStreamReadToken[reader]; We'll then layer a more convenient interface on top of that: JSONStream[strm : _String | _File | _InputStream] := JSONStream[jStreamReader[strm]]; JSONStreamRead[JSONStream[s_Symbol], type_: "Token"] := Replace[jStreamRead[s, type], EndOfFile | (_ -> EndOfFile) :> JSONStreamClose[JSONStream[s]] ]; JSONStreamClose[JSONStream[s_Symbol]] := ( Close@s; Remove[s]; EndOfFile ); JSONStream /: Read[JSONStream[s_Symbol], type___] := JSONStreamRead[JSONStream[s], type]; JSONStream /: Close[JSONStream[s_Symbol]] := JSONStreamClose[JSONStream[s]]; Format[JSONStream[ s_Symbol?(MatchQ[#["Data"]["Stream"], _InputStream] &)]] := With[{is = s["Data"]["Stream"]}, RawBoxes@ BoxFormArrangeSummaryBox[ "JSONStream", JSONStream[s], BoxFormGenericIcon[InputStream], { BoxFormSummaryItem[{"Name: ", Replace[is[[1]], f_String :> FileNameTake@f]}], BoxFormSummaryItem[{"Unique ID: ", is[[2]]}] }, { BoxFormSummaryItem[{"Open: ", Dynamic[Options[is] =!= {}, UpdateInterval -> 1 ] }] }, StandardForm ] ] Finally generate a JSON sample and we can start reading tokens: $jsSample =
"\n" <>
ExportString[
Prepend[ExampleData[{"Dataset", "Planets"}],
"\"EscapedName\"" -> <|"asd" -> "whee", "number" -> 10|>
],
"JSON"
];
json = JSONStream[\$jsSample]
Then here's what Read looks like on it:
Read@json
{Null, {Opening, Association}}
{{{"\"EscapedName\"", String}, None}, {Null,
Key}, {Null, {Opening, Association}}, {{"asd", String},
None}, {Null, Key}, {{"whee", String}, None}, {{Null, Expression},
Value}, {{"number", String}, None}, {Null, Key}, {{10, Expression},
Value}}
Here's using the data type support:
Table[Read[json, KeyValuePattern], 3] // AbsoluteTiming
{0.015792, {"Mercury" -> <|"Mass" -> "330104000000000000000000. kg",
"Radius" -> "2439.7 km", "Moons" -> <||>|>,
"Venus" -> <|"Mass" -> "4867320000000000000000000. kg",
"Radius" -> "6051.9 km", "Moons" -> <||>|>,
"Earth" -> <|"Mass" -> "5972198600000000000000000. kg",
"Moons" -> <|"Moon" -> <|"Mass" -> "73459000000000000000000. kg",
Currently we have Key, Value, KeyValuePattern, Association, List, and "Token" as supported types
• Not handling escapes was just a minor bug (it was written to do so). That I can patch quickly. Getting better event handling (e.g. Key` with associated key value) is a bit tougher, but it could be implemented pretty naturally out this, given the OO way the stream data is handled. The hard part, I think, will be finding the appropriate stream position for a given chunk of data, but I think I can manage that. – b3m2a1 Oct 20 '17 at 17:36
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2019-11-15 08:01:30
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https://zenodo.org/record/3555229/export/dcite4
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Journal article Open Access
# Necessity of Introduction of Electronic Criminal Proceedings
N.S. Topchii
### DataCite XML Export
<?xml version='1.0' encoding='utf-8'?>
<identifier identifierType="DOI">10.5281/zenodo.3555229</identifier>
<creators>
<creator>
<creatorName>N.S. Topchii</creatorName>
</creator>
</creators>
<titles>
<title>Necessity of Introduction of Electronic Criminal Proceedings</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2019</publicationYear>
<subjects>
<subject>electronic criminal proceedings, criminal procedure, electronic document flow, fixation, electronic signature.</subject>
</subjects>
<dates>
<date dateType="Issued">2019-11-25</date>
</dates>
<language>uk</language>
<resourceType resourceTypeGeneral="Text">Journal article</resourceType>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/3555229</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.3555228</relatedIdentifier>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract"><p>The article deals with the necessity of introduction of electronic criminal proceedings in Ukraine. It is noted that today Ukrainian criminal procedural legislation has introduced mixed or partially electronic criminal process, that is, paper proceedings with elements of electronic fixation. In the process of formation of electronic criminal proceedings, which has recently started in Ukraine, it is important to properly use the benefits of electronic document management.</p>
<p>Another advantage of the use of electronic criminal proceedings, to which the EED is integrated, is the instant exchange of documents between law enforcement and judicial authorities.</p>
<p>The time of drafting the electronic document should reflect the time of the decision in criminal proceedings or the completion of the investigative (investigative) action. The legislation stipulates that the electronic document must contain temporal differences in the conduct of investigative (investigative) action or making procedural decision with the moment of their documentary fixation. In view of the criminal proceedings, any procedural document in electronic form can be considered as documented data (information), which is being signed, and the investigator (detective, prosecutor, investigating judge) and other participants in the criminal proceedings - the signatories, ie persons who sign this document using a personal digital signature. The electronic digital signature of the investigator (prosecutor, investigating judge) and the other participant in the criminal proceedings can be verified with a public key, which will allow the author and / or signatory of the procedural and / or other document to be identified.</p>
<p>It is stated that when in accordance with the requirements of the CPC of Ukraine it is necessary to certify with the seal the authenticity of the signature on the documents and the correspondence of copies of the documents to the originals, as well as to ensure the integrity of electronic data and to identify the institution as a signer (author) of the issued documents in electronic form, to carry out information exchange with other law enforcement agencies and legal entities institutions (law enforcement, prosecutor&#39;s office, court, etc.) use a specially designed digital e-mail for such purposes.</p>
<p>It is concluded that the introduction of an electronic document circulation system will facilitate the further formation of domestic electronic criminal proceedings, prompt and efficient drafting of procedural documents at the time of the procedural decision, will accelerate the process of document exchange between law enforcement and judicial authorities, as well as allow increasing the criminal level process.</p></description>
</descriptions>
</resource>
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2020-09-18 18:17:13
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https://astronomy.stackexchange.com/tags/newtonian-gravity/hot
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# Tag Info
48
No you can't and the behaviour of bodies with mass and of light is completely different near a compact, massive object if you use Newtonian physics rather than General Relativity. In no particular order; features that GR predicts (and which in some cases have now been observationally confirmed) but which Newtonian physics cannot: An event horizon. In ...
42
Imagine "gravity" spreading out in a sphere, like light from a bulb. For each doubling of the distance, the sphere has four times the area. The surface area of the sphere is proportional to the square of the radius. If the same gravity is stretched over that sphere, the force of gravity would be inversely proportional to the square of the radius. ...
15
The Hubble expansion has no bearing whatsoever on the length of the year. This is because the whole Milky Way galaxy (and in fact most galaxies, if not all, and even local groups) has decoupled from the Hubble flow long ago. In fact, it could only form after it decoupled. Note that M31, our sister galaxy, is in fact falling onto the Milky Way rather than ...
14
I am not an expert in physics and the explanation of the others is excellent. However, I noticed a flaw in your reasoning which they did not address. You have written: Considering the Newton's Law of Gravity equation $F = GM/r^2$, if the radius of an object becomes super small, then it can technically have immense gravity. Hence I deduce that you read the $... 10 You can use Gauss's law for gravitation to work out the gravity as a function of (interior) radius. $$\oint \vec{g} \cdot d\vec{A} = -4\pi G \int \rho\ dV\ .$$ What this means is that the flux of gravitational field$\vec{g}$out of a closed surface is proportional to the mass enclosed within that surface. Let us assume that the density is a function of (... 9 (Disclaimer: As I already pointed out in a comment to the question above, I never did a calculation with$H_0$before and I might be utterly, horrible wrong with my interpretation.) If you completely ignore the slowly changing orbit of earth and only take expansion of space into account and assume the Hubble-parameter to be pretty constant in the timeframe ... 9 Both expressions are incorrect. The first should be $$\frac{GM_{\text{moon}}}{(R_{\text{moon}}-r_{\text{planet}})^2} - \frac{GM_{\text{moon}}}{{R_{\text{moon}}}^2}\tag{1b}$$ or $$\frac{GM_{\text{moon}}}{{R_{\text{moon}}}^2} - \frac{GM_{\text{moon}}}{(R_{\text{moon}}+r_{\text{planet}})^2}\tag{1a}$$ where$R_{\text{moon}}$is the distance between the center of ... 9 While admiring @ProfRob's answer I'll add some additional perspective/background that may serve as a helpful stepping-stone since not every Astronomy SE reader is prepared to embrace General Relativity in all its glory. Can Newton's gravity equation explain why black holes are so strong? The simple equation1$F = GMm/r^2$doesn't explain anything but it ... 8 Stellar clusters around supermassive black holes are systems in which relativity likely plays a role. Currently, only bright stars can be seen in our own galactic center because there is a ton of neutral gas between us and the galactic center that obscures it. As a result, we only have a few "test particles" out of the many stars that actually orbit the ... 8 The full equation for the time for an object to drop is $$t = \frac{ \arccos \Big( \sqrt{ \frac{x}{r} }\Big) + \sqrt{ \frac{x}{r} \ ( 1 - \frac{x}{r} ) } }{ \sqrt{ 2 \mu } } \, r^{3/2},$$ where$x$is the radius of the sun,$r$is distance of the object, and$\mu=GM=1.327\times10^{20}$. (in SI units, so you will need to convert your distance to metres, ... 7 I like to classify solutions of the problem of the time evolution of the complete initial state of a set of objects at some epoch time, where the objects are subject to Newtonian gravitation into two main groups. One approach is to use orbital elements of some sort. The other is to use a numerical initial value problem solver, aka a numerical integrator. The ... 7 A photon is an entity defined in the context of a relativistic field theory, and so it doesn't really make sense to talk about the Newtonian bending of a photon. Necessarily, we need to substitute an analogous question that's sensible in the Newtonian framework. To do so, we can imagine a classical corpuscle of light--appropriately enough, a theory of light ... 7 If you're asking whether it's sufficient to use a retarded (time-delayed) positions to calculate gravitational forces, then no, that would be much worse than Newtonian gravity. For example, that would predict that the Earth should spiral into the Sun on the order of about 400 years. See also answers to Besides retarded gravitation, anything else to worry ... 7 Planetoids can have moons and the minimum size is "pretty small". For example 2003 SS84is a small Near-Earth asteroid, with a diameter of 120m and a moon of about 60m in diameter, which orbits at a distance of 270m ever 24 hours. It probably didn't form by "attracting the moon" but the moon probably formed as a result of impact splitting ... 6 I can attempt to address the second part of your initial question (*"Is it a particle, a wave,...?") Einstein's theory of general relativity states that mass and energy bend space-time. Space-time, in turn, tells matter how to move (John Wheeler put this more elegantly). This concept is completely different from the theories of the other three fundamental ... 6 Running the math for a 5 meter long pendulum and 1 kg mass, I get an amplitude of 0,017 mm. You are off by quite a bit. There is essentially no horizontal deflection when the Moon is at the horizon. The maximum horizontal deflection occurs when the Moon is about 45 degrees above or below the horizon. The tidal acceleration at some point on the surface of ... 6 Leckner's paper deals with the effect of induced polarization on the spheres. Electrons are redistributed, making the force different from what one would expect. The gravitational counterpart is tidal distortion: since the gravitational field is non-radial when you have two heavy masses close to each other, matter will move to make the surface an ... 5 The short answer because Jupiter is a gas giant, so it's kind of got a very large atmosphere and atmosphere's aren't very dense. Also, if you look at your chart, the gravitation inside the Earth increases until you get to the outer core. This is likely to be much more pronounced on gaseous bodies like gas giants and stars. Longer answer: In layman's ... 5 The ratio$T/\Omega$tells you about the acceleration of the system - or more specifically, the second derivative of its moment of inertia - it does not tell you about the velocity. If the system collapses because it has$T/\Omega<0.5$, then when it reaches$T/\Omega=0.5$it stops accelerating. That doesn't mean it stops collapsing. It overshoots in the ... 5 If Einstein's GR equations are expanded in terms of familiar coordinates (Cartesian, spherical,...), the dominant or leading terms of the expansion (for the acceleration) can be written as the single Newtonian term GM/r^2. The next terms of the expansion can be considered as GR corrections to this leading term. Before the publication of GR, 19th-century ... 4 The magnitude of the force of gravity between two bodies is proportional to the product of their masses: $$F=G\frac{m_1m_2}{r^2}$$ This doesn't change depending on which body you're applying the force to, i.e. if you interchange the masses. The magnitude is the same. What does change is the direction of the force. Force is a vector quantity, denoted as$\...
4
Apart from the field-theoretical standpoint presented by Stan, one can repel objects in a sense, when taking orbital mechanics into account. The slingshot maneuver extracts angular momentum and energy of an orbiting mass by the use of gravity. The trick here is that the probe's velocity just gets redirected in the planet's reference frame. But this results ...
4
The validation is the same as the validation of any astronomical theory: it fits the data. Newton's law of gravitation was formed empirically, by observing the motion of the planets. In particular, he took Kepler's laws, which were observational, and $F=ma$ from his physics and determined that the elliptical orbits we see must be caused by something with an ...
3
Ignoring details such as the oblateness of the Earth, atmospheric drag, third body influences such as the Moon and the Sun, relativity, ..., the period of a satellite of negligible mass (even the International Space Station qualifies as a "satellite of negligible mass") is $T=2\pi\sqrt{\frac {a^3}{\mu_\mathrm{Earth}}}$. Neither Newton's gravitational ...
3
In general relativity, gravity neither pushes nor pulls. To explain why ball travels in an arc you note the start and end points of the throw in 4d space time (3 space co-ordinates and 1 time coordinate) You then find the shortest path between these two 4d points in the curved spacetime surrounding the Earth. This shortest path is the path in spacetime that ...
3
I'm guessing that this misunderstanding is a result of the oft-used rubber sheet analogy. The rubber sheet analogy says that, according to general relativity, mass curves space-time like a heavy bowling ball on a near-taut blanket (or rubber sheet) curves the blanket/sheet. This resulting curve makes other bits of matter/energy move in different ways. I'm ...
3
Newtonian treatments of the bending of light go back to Laplace who, in 1798, wrote about light escaping from massive bodies, ie: black holes! See Appendix A of Hawking and Ellis "Large Scale Structure of Space-Time" where there is a nice translation of Laplace's paper. Newtonian treatments cannot properly deal with all aspects of light bending. Notably, ...
3
Adding to @Guillochon's answer, there are even a number of general relativistic tests in our solar system, the most famous being the precession of the perihelion of Mercury. In short, the location of the point of closest approach to the Sun (perihelion) for the planet Mercury is a changing quantity. Essentially, given one full revolution, it doesn't trace ...
3
If you project the orbits onto a plane, for example the plane of the ecliptic, the projections will cross. But that's only because you're looking at a 3D problem in 2D. If you look at the orbits in 3D, you'll see that Pluto's orbit is highly inclined (17º) from the ecliptic, so it never actually passes through Neptune's orbit. Each time it seems to cross (in ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2021-09-28 07:27:55
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https://www.shaalaa.com/question-bank-solutions/what-condition-necessary-echo-be-heard-distinctly-reflection-of-sound_36740
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# What is the Condition Necessary for an Echo to Be Heard Distinctly? - Physics
Short Note
What is the condition necessary for an echo to be heard distinctly?
#### Solution
Echo is a reflected sound heard after the original sound strikes a rigid obstacle...
The conditions are-
1- The reflecting surface should have a larger reflecting surface than the wavelength of the sound
2- The minimum distance to hear the echo should be 17m in the air or as described by the formula (Vt)/2...
Concept: Reflection of Sound
Is there an error in this question or solution?
#### APPEARS IN
Selina Concise Physics Class 10 ICSE
Chapter 7 Sound
Exercise 7 (A) | Q 7.2 | Page 154
ICSE Class 10 Physics
Chapter 6 Echoes and Vibrations of Sound
Share
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2021-05-15 14:03:52
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https://dmoj.ca/problem/ichb2017p3
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## ICHB Selection Contest '17 Problem 3 - Parallel Universe
View as PDF
Points: 12 (partial)
Time limit: 1.2s
Memory limit: 64M
Author:
Problem type
You are locked in a parallel universe and for you to be able to escape you have to answer queries on an array named with elements. The queries are as follows:
• U x val - Change the value of to ()
• Q x y val - Print . Here, refers to bitwise AND.
#### Input Specification
On the first line you will find and .
On the second line you will find numbers, where the -th number is .
On the next lines you will find the queries.
#### Output Specification
For each Q type query, print each result on a different line.
#### Sample Input
3 3
5 7 15
Q 1 3 7
U 1 0
Q 1 3 15
#### Sample Output
5
0
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2021-08-05 14:26:29
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https://geometrian.com/programming/tutorials/energyblinn/index.php
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~/imallett (Ian Mallett)
Energy-Conserving Blinn-Phong Specular
For BRDFs in graphics, we typically ignore energy conservation, in favor of energy normalization (that is, energy is lost, but at least it isn't gained). Most people are satisfied with that because it models the shadowing and masking effects in microfacet theory. Unfortunately, it completely ignores multiple scattering. The correct answer, then, is somewhere in-between the extremely lossy models typically used and an idealized model that loses none.
This page is my attempt to derive such an idealized model for the Blinn-Phong specular BRDF. I do not succeed. To the first person who can solve the final integral (even just the inner one, as this would make numerically integrating the outer one easier) in closed-form (no sums/integrals/etc.) in terms of elementary functions (sin/cos/etc., no hypergeometric operators/etc., although constants are okay), I will send \$50. The same bounty given if the correct answer to the entire problem is obtained a different way.
The (scalar variant of the) Blinn-Phong specular BRDF (at a point $\vec{x}$ with normal $\vec{N}$, and with energy-conservation factor $\alpha$ and specular exponent $n$) is:
$f_r(\vec{\omega}_i,\vec{\omega}_o) ~:=~ \alpha (\vec{H} \cdot \vec{N})^n = \alpha \left( \frac{ \vec{\omega}_i + \vec{\omega}_o }{ \left \| \vec{\omega}_i + \vec{\omega}_o \right \| }\cdot\vec{N} \right)^n$
We want to solve for $\alpha$.
First, energy-conservation means the following:
$\int_{\Omega_{\vec{N}}} f_r(\vec{\omega}_i,\vec{\omega}_o) \left( \vec{N} \cdot \vec{\omega}_i \right) d \vec{\omega}_i = 1$
We can now substitute in and rearrange:
$\int_{\Omega_{\vec{N}}} \alpha (\vec{H} \cdot \vec{N})^n \left( \vec{N} \cdot \vec{\omega}_i \right) d \vec{\omega}_i = 1\\ \int_{\Omega_{\vec{N}}} \left( \frac{ \vec{\omega}_i + \vec{\omega}_o }{ \left \| \vec{\omega}_i + \vec{\omega}_o \right \| }\cdot\vec{N} \right)^n \left( \vec{N} \cdot \vec{\omega}_i \right) d \vec{\omega}_i = \frac{1}{\alpha}$
To compute $\left \| \vec{\omega}_i + \vec{\omega}_o \right \|$ is actually surprisingly simple. We can consider both vectors to lie in a plane, separated by angle $\gamma$. Without loss of generality, for purposes of computing the length, we can move to 2D: suppose $\vec{\omega}_o:=<0,1>$ and $\vec{\omega}_i:=<\sin(\gamma),\cos(\gamma)>$. Their sum is $<\sin(\gamma),1+\cos(\gamma)>$ and the length of that sum is (Pythagorean theorem):
$\left \| \vec{\omega}_i + \vec{\omega}_o \right \| = \sqrt{ \sin^2(\gamma) + (1+\cos(\gamma))^2 } = \sqrt{ 2 + 2 \cos(\gamma)} = 2 \cos \left(\frac{\gamma}{2}\right)$
Since $\gamma$ is just $\arccos(\vec{\omega}_i \cdot \vec{\omega}_o)$, we have:
$\left \| \vec{\omega}_i + \vec{\omega}_o \right \| = 2 \cos \left(\frac{\gamma}{2}\right) = 2 \cos \left(\frac{1}{2} \arccos(\vec{\omega}_i \cdot \vec{\omega}_o) \right) = 2 \sqrt{\frac{\vec{\omega}_i \cdot \vec{\omega}_o + 1}{2}} = \sqrt{2} \sqrt{\vec{\omega}_i \cdot \vec{\omega}_o + 1}$
Substitute this into the integral:
$\frac{1}{\alpha} = \int_{\Omega_{\vec{N}}} \left( \frac{ \vec{\omega}_i + \vec{\omega}_o }{ \sqrt{2} \sqrt{\vec{\omega}_i \cdot \vec{\omega}_o + 1} }\cdot\vec{N} \right)^n \left( \vec{N} \cdot \vec{\omega}_i \right) d \vec{\omega}_i$
At this point, you have the basic formulas. Now it's time to try to solve them.
The attempt I pushed most on uses spherical coordinates. First, (re-)define $\vec{\omega}_o$ and $\vec{\omega}_i$ in spherical coordinates:
$\vec{\omega}_o = \begin{bmatrix} x_o = \sqrt{1-y_o^2}\\ y_o = \vec{N} \cdot \vec{\omega}_o\\ 0 \end{bmatrix},~~~~ \vec{\omega}_i = \begin{bmatrix} \cos(\Delta\theta)~\cdot &\!\!\!\!\! \cos(\phi)\\ &\!\!\!\!\! \sin(\phi)\\ \sin(\Delta\theta)~\cdot &\!\!\!\!\! \cos(\phi) \end{bmatrix}$
Convert to spherical coordinates, substitute in, and simplify:
\begin{align*} \frac{1}{\alpha} &= \int_0^{\pi/2}\int_0^{2\pi} \left( \frac{ \vec{\omega}_i + \vec{\omega}_o }{ \sqrt{2} \sqrt{\vec{\omega}_i \cdot \vec{\omega}_o + 1} }\cdot\vec{N} \right)^n \left( \vec{N} \cdot \vec{\omega}_i \right) \cdot \cos(\phi) \cdot d \Delta\theta \cdot d \phi \\ &= \int_0^{\pi/2}\int_0^{2\pi} \left( \frac{ \cos(\phi) + y_o }{ \sqrt{2} \sqrt{\smash[b]{ \cos(\Delta\theta)\underbrace{\cos(\phi)\sqrt{1-y_o^2}}_A + \sin(\phi) y_o + 1 }} } \right)^n \cos^2(\phi) \cdot d \Delta\theta \cdot d \phi \\[14pt] &= \int_0^{\pi/2} \cos^2(\phi) \int_0^{2\pi} \left( \frac{ \cos(\phi) + y_o }{ \sqrt{2 A} \sqrt{\smash[b]{ \cos(\Delta\theta) + \underbrace{\frac{\sin(\phi) y_o + 1}{A}}_B }} } \right)^n \cdot d \Delta\theta \cdot d \phi \\[14pt] &= \int_0^{\pi/2} \left(\frac{\cos(\phi)+y_o}{\sqrt{2 A}}\right)^n \cos^2(\phi) \int_0^{2\pi}\left( \cos(\Delta\theta) + B \right)^{-n/2} \cdot d \Delta\theta \cdot d \phi \end{align*}
The inner integral here is surprisingly difficult, even if you assume $n/2$ is an integer. If you can solve this integral, you get the prize mentioned above!
COMMENTS
Ian Mallett - Contact - Donate - 2018 -
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2019-02-21 14:14:13
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https://paperswithcode.com/paper/assessing-the-adversarial-robustness-of-monte
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# Assessing the Adversarial Robustness of Monte Carlo and Distillation Methods for Deep Bayesian Neural Network Classification
7 Feb 2020Meet P. VaderaSatya Narayan ShuklaBrian JalaianBenjamin M. Marlin
In this paper, we consider the problem of assessing the adversarial robustness of deep neural network models under both Markov chain Monte Carlo (MCMC) and Bayesian Dark Knowledge (BDK) inference approximations. We characterize the robustness of each method to two types of adversarial attacks: the fast gradient sign method (FGSM) and projected gradient descent (PGD)... (read more)
PDF Abstract
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2020-07-06 02:35:33
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https://brilliant.org/problems/a-niceunconventional-algebra-question/
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# A nice,unconventional Algebra question.
Level pending
$\begin{cases}\text{Row A}:\ \ 1,2,3...9\\ \text{Row B}:\ \ 2,3,4...10\\ \text{Row C}:\ \ 3,4,5...11\\ .\\.\\.\\.\\ \text{Row I}:\ \ 9,10,11...17\\ \text{Row J}:\ \ 10,11,12...18\end{cases}$.Find the sum of all the numbers in all the rows.
×
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2017-05-25 16:27:09
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https://homework.zookal.com/questions-and-answers/describe-in-vector-form-the-set-of-all-solutions-of-741313460
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1. Math
3. describe in vector form the set of all solutions of...
Question: describe in vector form the set of all solutions of...
Question details
Describe, in vector form, the set of all solutions of the following linear system
2x − y + 3z = 0
x + 2y − 3z = 1
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2021-04-20 14:49:28
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https://de.maplesoft.com/support/help/MapleSim/view.aspx?path=GraphTheory%2FCycleGraph
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CycleGraph - Maple Help
GraphTheory
CycleGraph
construct cycle graph
PathGraph
construct path graph
Calling Sequence CycleGraph(n,opts) CycleGraph(V,opts) PathGraph(n,opts) PathGraph(V,opts)
Parameters
n - positive integer V - list of vertices opts - (optional) one or more options as specified below
Options
The opts argument can contain one or more of the options shown below.
• directed=true or false
This option specifies whether the resulting graph should be directed. The default is false.
• layout=true or false
This option specifies whether a default coordinate assignment for the vertices of the graph should be made. The default is true.
Description
• CycleGraph(n) outputs a graph which is a cycle on n vertices labeled 1, 2, ..., n.
• PathGraph(n) outputs a graph which is a path on n vertices labeled 1, 2, ..., n.
• In both cases you can input the labels for the vertices as a list of integers, strings, or symbols.
Examples
> $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
> $C≔\mathrm{CycleGraph}\left(4\right)$
${C}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 4 vertices and 4 edge\left(s\right)}}$ (1)
> $\mathrm{Edges}\left(C\right)$
$\left\{\left\{{1}{,}{2}\right\}{,}\left\{{1}{,}{4}\right\}{,}\left\{{2}{,}{3}\right\}{,}\left\{{3}{,}{4}\right\}\right\}$ (2)
> $\mathrm{DrawGraph}\left(C\right)$
> $P≔\mathrm{PathGraph}\left(\left[a,b,c,d\right]\right)$
${P}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 4 vertices and 3 edge\left(s\right)}}$ (3)
> $\mathrm{Edges}\left(P\right)$
$\left\{\left\{{a}{,}{b}\right\}{,}\left\{{b}{,}{c}\right\}{,}\left\{{c}{,}{d}\right\}\right\}$ (4)
> $\mathrm{DrawGraph}\left(P\right)$
Compatibility
• The GraphTheory[CycleGraph] and GraphTheory[PathGraph] commands were updated in Maple 2021.
• The directed and layout options were introduced in Maple 2021.
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2023-03-22 17:05:49
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https://www.scielo.br/j/aabc/a/hY7nfhFMxnzWFYqvS7pb8hp/?format=html&lang=en
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# ABSTRACT
Sanitation (which includes national public policies for drinking water, sewage services and waste management) is precarious in Brazil and therefore poses a challenge to a range of actors. Poor sanitation impacts public health, education, the environment, and daily life. Globally, it emits increasing greenhouse gases. Universalization of any major public service appears difficult, if not impossible; however, Brazil’s program to universalize access to electricity proves the opposite, as will be shown in this paper. By describing the successful implementation of electricity for everyone, we show that planned public efforts, coordinated with private initiatives and local communities, have worked, and the same can be achieved for the sanitation sector. An overview of all sectors that touch on sanitation and emissions is also provided, highlighting the challenges and possibilities for infrastructure projects.
Key words:
Solid Waste (SW); water; sewage; sanitation; greenhouse gases; Sustainable Development Goals (SDGs)
# INTRODUCTION
In Brazil, sanitation - water, sewage and waste - and electricity are provided by public bodies directly or indirectly through public concessions. Regarding sanitation, the North and Northeast regions and all rural areas significantly lack access to this basic service in the 21st century; Brazil is still far from experiencing universal access, mainly for sewage (Albuquerque 2011ALBUQUERQUE GR. 2011. Estruturas de financiamento aplicáveis ao setor de saneamento básico. Saneamento Básico. BNDES Setorial, 34, p. 45-94. https://web.bndes.gov.br/bib/jspui/bitstream/1408/1485/1/A%20BS%2034%20Estruturas%20de%20financiamento%20aplic%C3%A1veis%20ao%20setor%20de%20saneamento%20b%C3%A1sico_P.pdf. Accessed on 20 October, 2017.
https://web.bndes.gov.br/bib/jspui/bitst...
, Heller and Castro 2013HELLER L AND CASTRO JE. 2013. Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ). In contrast, electricity has had some successful public programs for access and for universalization and presented positive results measured by the 2010 Demographic Census conducted by the Brazilian Institute of Geography and Statistics (IBGE). In 1999, the government launched the National Rural Electrification Program with access targets, called “Electricity for the Countryside”, which was replaced, in 2003, by “Electricity for Everyone”, with universalization goals, both aimed at poor rural populations.
According to official Brazilian figures, presented by the 2000 Census (IBGE 2000, MME-LpT 2011, 2015), more than 9 million Brazilians in the rural area, or more than 2 million families, and more than 1 million Brazilians in the urban area were living then without electricity; that is, more than 10 million people had no access to electricity (Table I).
TABLE I
According to the 2010 Census (IBGE 2010a), these numbers had significantly improved and dropped to just over 2 million people in the rural area and less than 400,000 in the urban area (Table I). Moreover, by 2015, the rural electrification program had reached more than 15 million families. On the other hand, the 2010 census pointed out that more than 27 million households were not connected to a drainage or sewer system, meaning that more than 100 million Brazilians and more than 7 million households do not have adequate waste collection (IBGE 2010). While the efforts towards electricity universalization were effective, there were no significant results for sanitation (Table I). According to data presented in this paper, there is a true black-out for this latter case.
The 2030 Agenda for Sustainable Development, launched in 2015 by the United Nations Organization (UN), aims to transform the world through measurable, and therefore monitorable, goals, targets and indicators for the pursuit of sustainable development. The 17 Sustainable Development Goals (SDG), subdivided into 169 goals, “seek to build on the Millennium Development Goals (MDG) and complete what they did not achieve. They seek to realize the human rights of all and to achieve gender equality and the empowerment of all women and girls. They are integrated and indivisible and balance the three dimensions of sustainable development: the economic, social and environmental” (United Nations 2015). In fact, differently from the MDGs, the SDGs are a “network of targets”, meaning that each goal is extended through targets that are related to numerous goals and sectors (Blanc 2015BLANC D. 2015. Towards Integration at Last? The Sustainable Development Goals as a Network of Targets Sustainable Development. DESA Working Paper No. 141 ST/ESA/2015/DWP/141. United Nations Press, New York, USA, 19 p.http://www.un.org/esa/desa/papers/2015/wp141_2015.pdf. Accessed on 20 July, 2017.
http://www.un.org/esa/desa/papers/2015/w...
). Planning for development tends to be more integrated and coherent.
Access to drinking water and sanitation, as well as appropriate waste management, addresses primarily SDG 06 (clean water and sanitation), but it is extended to SDG 01 (no poverty), SDG 02 (zero hunger), SDG 03 (good health and well-being), SDG 04 (inclusive and equitable quality education), SDG 10 (reduced inequalities), SDG 11 (sustainable cities and communities), SDG 12 (responsible consumption and production), SDG 13 (climate action), and SDG 15 (life on land). Finally, of course, SDG 17 (partnership for the goals) is addressed, as it includes the means to implement all goals (Blanc 2015BLANC D. 2015. Towards Integration at Last? The Sustainable Development Goals as a Network of Targets Sustainable Development. DESA Working Paper No. 141 ST/ESA/2015/DWP/141. United Nations Press, New York, USA, 19 p.http://www.un.org/esa/desa/papers/2015/wp141_2015.pdf. Accessed on 20 July, 2017.
http://www.un.org/esa/desa/papers/2015/w...
). To achieve these objectives, Brazil will have to make significant efforts for some decades to come. In summary, achieving the targets of the SDG 06 will have immediate spillover effects on other goals. These influences could be a theme of other paper as it will not be dealt in the present article. Indeed, the focus on this work is solely on the possible achievement of the SDG 06.
# AN OVERVIEW OF SANITATION IN BRAZIL
Brazil is divided into five regions: North, Northeast, Southeast, South and Midwest. As shown in Table II, there was a significant increase in the urbanization of the South and Midwest from the 1970s to 2010. The Southeast already presented high levels of urbanization in the late 1950s and early 1970s, which was a period of growth of large metropolises, including São Paulo. The North showed the highest population growth for the period from 1970 to 2010, followed by the Midwest, and both regions showed almost the same population in 2010. The Northeast is the third most populated region in Brazil: its cities are located mainly on the coast, with large population densities and crowded urban centres. While Brazil increased its urban population by 204% overall from 1970 to 2010, the North grew by 517% and the Midwest by 461%. Rapid urban growth in the North and Northeast outstripped public capacity to provide basic services, as will be seen in the indices presented below.
TABLE II
Resident population in Brazil (in thousands).
Analyzing the evolution of the urban and rural population in the country is an important factor in the analysis of the provision of basic services (Table II). In fact, according to Costa and Ribeiro (2013COSTA SS AND RIBEIRO WA. 2013. Dos porões à luz do dia. Um itinerário dos aspectos jurídico-institucionais do saneamento básico no Brasil. In: Heller L and Castro JE (Eds), Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ), even if unsteady, the sanitation service was considered an urban service until the middle of the 20th century. In consonance with the authors, there was an evolution regarding the provision of the service when the federal government began to interfere directly in the provision of these services in 1942, with the Special Public Health Service (SESP); later, in 1960, the SESP Foundation, within the Ministry of Health, also started implementing sanitation actions. In the 1940s, the execution of sanitation works passed to the scope of the Ministry of Works and Transport, with the National Department of Sanitation Works. Subsequently, after the creation of the Superintendence of the Development of the Northeast (SUDENE) in 1959, the creation of state bodies for the provision of these services was strengthened, especially after the formation of the National Fund for Sanitation Works (FNOS) in 1962.
The authors emphasize that in the history of public policies for basic sanitation, there was always “a movement to modify subsidy policies to financing policies” and there were changes in partnerships. Initially, these were via federal government with municipalities until the 1940s; then they became federal government partnerships with state companies during the military government.
It was precisely during the military government, with the National Sanitation Plan (PLANASA), operationalized through the National Housing Bank (BNH), that there was the largest federal effort and the most extensive coverage of water supply and sewage services. This, however, favored the richer regions of the South and Southeast, where there was the greatest possibility of amortization of investments through tariffs (Costa and Ribeiro 2013COSTA SS AND RIBEIRO WA. 2013. Dos porões à luz do dia. Um itinerário dos aspectos jurídico-institucionais do saneamento básico no Brasil. In: Heller L and Castro JE (Eds), Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ). With the abolition of the BNH in 1986, and with the Federal Constitution of 1988, stemming from the re-democratization of the country, there was an institutional vacuum that followed until Law 11,445/2007 (Brasil 2007), the National Basic Sanitation Law of 2007. The LNSB modified the concept of basic sanitation as follows:
“The public services of basic sanitation involve not only the public services of drinking water supply and sanitary sewage, but also the public services of public cleaning, management of solid waste and also those of urban storm water management…being a duty of the Union…instituting a Federal Basic Sanitation Policy” (Costa and Ribeiro 2013COSTA SS AND RIBEIRO WA. 2013. Dos porões à luz do dia. Um itinerário dos aspectos jurídico-institucionais do saneamento básico no Brasil. In: Heller L and Castro JE (Eds), Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ).
In addition, the municipality became the central point of sanitation policy, and it has been the focus of resistance from previously created state-owned enterprises. This fact resulted in major challenges, as listed by Costa and Ribeiro (2013COSTA SS AND RIBEIRO WA. 2013. Dos porões à luz do dia. Um itinerário dos aspectos jurídico-institucionais do saneamento básico no Brasil. In: Heller L and Castro JE (Eds), Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ): the difficulty of making the municipality really do the planning, and of ensuring that the local regulation is independent and that social control is indeed a transparent and integrated policy. The creation of the Ministry of Cities in 2003 was fundamental to integrating existing policies and to providing the centrality of the Federal Basic Sanitation Policy within its National Secretariat of Environmental Sanitation (SNSA) (Costa and Ribeiro 2013).
The results of these decades-old centralized policies in the richest and most urban areas of the country can be glimpsed by analyzing the 2013 Municipal Human Development Index (MHDI) published by the United Nations Development Program (UNDP) for 5,565 cities (Table III), of which 109 cities are counted in the first 100 rankings. The first place with a MHDI of 0.882 is the city of São Caetano do Sul, in São Paulo, and 10 cities are tied in the first 100 places with a MHDI of 0.784 (five in São Paulo, two in Rio Grande do Sul, two in Santa Catarina and one in in Mato Grosso do Sul). The only city in the Northeast in these first 100 places is Fernando de Noronha, in 76th place, a touristic town with a high level of access control.
TABLE III
MDHI 2013 - first 100 rankings.
According to the same data for 2010, 105 cities were classified in the last 104 places, with an MHDI of 0.519 for the six cities tied for 5,461st place, and with the MHDI of 0.418 for last place, rank number 5,565, Melgaço, Pará, according to Table IV. The Northeast has more cities in the lower positions, with 63.81% of the municipalities in the sample; followed by the North, with 35.24% represented in these placements. The worst MHDIs are from Maranhão (22 cities), Pará (20 cities) and Piauí (19 cities). The Northeast has a total of nine states, and six are represented in the last positions of the MHDI. The North has seven states and five are represented. It can be noted that there is a lack of essential services, and abundant poverty and vulnerability, evidenced in this worst index. It should be noted that the lowest MHDI figures do not include states in the Southeast, the South or the Midwest, while among the top places only one state in the Northeast is represented.
TABLE IV
MHDI 2013 - last 104 placements.
This is the Brazilian situation in the 21st century, a country with severe regional imbalances and socioeconomic inequalities, a national MHDI of 0.755 ( PNUD, Ipea and FJP 2013), a population of approximately 205 million inhabitants, and a GDP of approximately US $1,845 trillion (Banco Central 2017). It is predominantly an urban country (Table II and V). TABLE V Total households (in thousands), % of urban households, total residents (in thousands), and % of urban residents. This paper aims to describe the evolution of the sanitation indices in Brazil over a ten-year period and to provide suggestions for its universal access, that is to say, recommendations to implementing the SDG 06. The main hypothesis is that universal access to sanitation is only possible via the power of the state, by means of investing, catalysing or obliging investments in this sector, as will be shown by using the successful example of rural electrification. First, the overview and the profile of sanitation, as well as its emissions, will be detailed. Next, the program “Electricity for Everyone” will be described, to show how it achieved the universalization of rural electrification. In conclusion, despite being a challenging task, there is, in fact, the possibility of universal access to sanitation. # MATERIALS AND METHODS The paper consists of qualitative and quantitative analyses of indicators of access to energy and sanitation, in order to provide an overview of the provision of these services, and a qualitative investigation of manuals, laws, reports and governmental releases. The main sources of data were the National Institute of Geography and Statistics (IBGE); the Brazilian Association of Public Cleaning and Special Waste Companies (Abrelpe); the Ministry of Cities (MCID); and the Ministry of Science, Technology, Innovation and Communications (MCTIC). Data were collected focusing mainly on a 10-year evolution of statistics, when possible. Some indicators did not present any historical series and were collected in a manner that came as close as possible to a 10-year historical series, as will be detailed. The Brazilian Association of Public Cleaning and Special Waste Companies (Abrelpe) has an annual assessment of solid waste (SW) statistics, so, the authors chose to analyze the ten-year evolution of data (2005 - 2015), but also considered the most up-to-date numbers of Abrelpe (2016). Sanitation and population data were extracted from IBGE, which holds its main indicators in the database Bank of Statistical Tables (SIDRA). The Population Censuses of 2000 and 2010, and the National Sample Survey of Households (PNAD) were collected from SIDRA. A profile of the Brazilian population (urban and rural) and Access to Energy were retrieved from both Censuses and PNAD. From PNAD the subject categories collected were Water Supply, Sewage Treatment, and Solid Waste Destination. The National Secretariat of Environmental Sanitation (SNSA), which is an institution under the auspices of the MCID, gathers the National Sanitation Information System (SNIS).The SNIS is a national database that presents aggregated data, disaggregated data and municipal data. Categories explored under this database were access to Water and Sewage Treatment as well as Level of Investments. GHG emissions were extracted from the SIRENE system, under the MCTIC. Categories explored under this database were the national GHG emission profile for Energy; Industrial Process; Agriculture; Waste; and Land Use, Land-Use Change and Forestry (LULUCF). For the Waste category (IPCCC 1996), the data were extracted for Effluents and Solid Waste. The records were exported from each database into a MS Excel File and subsequently placed into single workbooks according to categories of public services provided. Each workbook contained a macro level of aggregation, and the main analyses were provisions of service to the population in absolute and relative terms, which were divided into the following categories: home location (rural or urban), and national region (North, Northeast, South Southeast, and Midwest). These data were analyzed through two types of comparison: the first one was through the analysis of the factors that impacted each of the indicators developed in this work over time, in a technique known as time series analysis; and the second one occurred through the analysis of various indicators, in a simultaneous comparison of different regions and of housing location (urban/rural), in a technique known as cross-section. The combination of both techniques allows a holistic and at the same time detailed understanding of all the qualitative factors that have a relevant impact on the indicators in quantitative terms. Finally, the National Program for Universal Access and Use of Electric Power, known as the “Electricity for All” program, was analyzed in order to extract the possible drivers of its success by means of an in-depth investigation of its special project and operational manuals (MME - LpT 2009, 2011, 2015), official reports (MME - LpT 2007, 2008), governmental data, laws, and official releases. The purpose of using the “Electricity for All” program as an example is based on a technique choice known as benchmark, where a policy or an activity already implemented serves as a parameter or guide to the development of actions in other segments that have similarities between them. Then the authors suggested possible directions for the universal access to sanitation. # RESULTS The current section shows data analyses for water and sewage, solid waste, and greenhouse gas emissions. Each subsection will present a quantitative and a qualitative analysis. In considering the following data, it is important to introduce the following population overview. ## WATER AND SEWAGE Sanitation in Brazil is regulated by Law 11,445/07 (Brasil 2007), which, by article 52, establishes the need to prepare a National Plan for Sanitation (Plansab), covering “water supply, sewage, solid waste and rainwater management, with cleaning and inspection of the drainage systems, as well as other sanitation actions of interest for the improvement of environmental health, including the provision of toilets and hydro sanitary units for low-income populations”. Plansab was approved in 2013, establishing guidelines, targets and actions for the years 2014 to 2033 (MCID 2013), with its latest update performed in 2015 (SNIS 2015). As detailed below, the plan is far from being fulfilled. According to Plansab, it would be expected to achieve “99% coverage rates in drinking-water supply in 20 years, with 100% coverage rates in the urban area, and 92% in sewerage services, with 93% coverage levels in the urban area. In solid waste, Plansab provides for the universalization of urban collection and the absence of open dumps or dumps in the whole country. For rainwater, another goal is to reduce the number of municipalities where flooding or waterlogging occur, in the urban area of 11%”. The evolution of the national sanitation situation can be verified by the indices of coverage rates for sewerage and water services according to SIDRA and SNIS. According to Table VI, the evolution of access rates to the sewage network shows that its universalization is still very distant for the North region and, to a lesser extent, for the Northeast. Although the North increased the service index for the ten-year period for the total and urban population, the attendance rate in 2015 was still 8.7% for the total population and 11.2% for the urban. Considering that in the North there was the greatest total and urban population increase in recent years, the services did not follow the growth of the number of inhabitants or the expansion of the urban spot (Table II). The volume of sewage treatment generated in the region is low (16.4%), but presents a high percentage of treatment of sewage collected (83.9%). TABLE VI Evolution of service levels - coverage rates for sewage. The North presents the lowest investment values when compared to the values of the other regions for the three-historical series (Table VI). It also presents the lowest numbers of sewage connections nationally (Table VII). The Northeast presented a low increase in coverage rates of the total (6.1%) and urban population (6.3%) in the last ten years, as well as the investment volumes and the number of sewage connections; and, there was a decrease in the treatment volume of the sewage collected (-12.9%) and generated (-4%). Nationally, in 2015, only the Southeast presented more than 50% of the properties with access to the sewage network for the total population (77.2%) and, for the urban population, only the Southeast (81.9%) and the Midwest (54.7%) presented more than 50% of coverage level in 2015 (Table VI). Table VII shows the evolution of extensions connected to the main sewage distribution network. Numbers show more than 2 million inactive connections in 2015. According to SNIS (2015), those inactive connections are the ones that “although registered as users of the services, are not fully operational”. More investments are possibly needed for the maintenance of these facilities. TABLE VII Evolution of service levels - sewage main connections. As shown in Table VIII, the worst coverage rates for water supply are again in the North. In 2015, it was the region with the lowest service attendance rate of the total population (56.9%) and the urban population (69.2%). The amounts invested in this region are the lowest nationally as well as the number of connections to the water supply network (Table IX). The largest losses in distribution are also in this region (46.3%), followed by the Northeast in losses (45.7%). TABLE VIII Evolution of service levels - coverage rates for drinking-water. The South has the best rate of service for the urban population (98.1%) followed by the Midwest (97.4%), both regions of more recent urbanization than the Southeast, which presents a lower urban service, of 96.1%, a lesser index probably because there are areas within the urban area that do not receive basic services, especially in the subnormal clusters scattered around the city (favelas). Except for the Midwest, all other regions showed a decrease in water loss in the distribution in 10 years (Table VIII). Despite this, all regions present significant losses in distribution, exceeding 30%. This index is important for analyzing the quality of water distribution by indicating quality of management and infrastructure (SNIS 2015). The regions with the greatest financial investment in the water supply network are the Northeast and Southeast regions, which are the regions with the highest number of active water connections (Table IX). Apart from the Southeast, all regions experienced a decrease in the urban population’s service attendance rate in the last ten years, even though they increased the attendance of the total population, probably due to a significant increase in the urban population in all regions and a decrease in the rural population. TABLE IX Evolution of service levels - drinking-water connections. Table IX shows the evolution of extensions connected to the main water pipeline. Numbers show more than 5.5 million inactive connections in 2015. As seen in the sewage data, more investments are possibly needed for the maintenance of these facilities. According to Table X, almost 10 million households do not have access to the water supply system or use other types of water supply. The North presents the worst situation. However, in absolute values, the Northeast is the one with the largest contingent of people without access to the water supply, with almost 12 million people without the service (by cross-calculating Table V by the percentages in Table X). In a ten-year period, there was an improvement in national the coverage level of 3%, from 82% to 85%; which is a residual value, evidencing low investment rates in the sector. TABLE X Access to water services. In Table XI, the classification under “other types” includes cesspools, rivers, ditches, other types not specified, and had no access. In fact, these destinations are not suitable for sewage and, according to Atlas de Saneamento 2011, “far from representing alternative solutions are, rather, confirmation of the unsteadiness of sewage collection in the country” (IBGE 2011). TABLE XI Access to sewage services. Another issue to consider is that rainwater drainage is considered as part of the sewage network infrastructure; so even when sewage is directly released into this rainwater system, it is considered under the national index as an appropriate destination. A technical issue regarding this consolidated infrastructure is that the combined sewer system is not usually projected to support the load of the heavy rains (Reda 2006REDA A. 2006. Gestão de qualidade da água em sistema fluvial durante tormenta - Parte I: reconhecendo um problema no sistema de esgoto. In: XIII SIMPEP - Bauru, SP, Brasil, 6 a 8 de novembro de 2006. http://www.simpep.feb.unesp.br/anais/anais_13/artigos/280.pdf. Accessed on 26 October, 2017. http://www.simpep.feb.unesp.br/anais/ana... , MMA 2009), resulting in flooding, cross-contamination, and spread of diseases. On the other hand, there are also systems projected to receive only sewage (separate sewer systems), but these illegally and clandestinely receive effluents from domestic and industrial sources (Dias 2003) Even with these caveats, in 2015, almost 28 million households did not have access to the sewage network - by considering other types and the usage of septic tank (Table XI). The worst index is again in the North, with 14% of the households covered, but the Northeast has the largest number of households without adequate access. Usually, the worse indexes, in any region, are recurrent in irregular settlements in urban areas or in pristine areas in rural areas. The proper provision of public services for these locations would have to consider their realities by means of implementing special projects, as will be discussed in this article. The search for regularization of the informal settlements would not be a solution for this problem because the main issue is usually the location per se (top of hills, hard-to-reach places, alleys, and/or violent communities). Moreover, if the government stand still until the settlements are regularized, it will be a never-ending situation. The rural electrification program is a show-case that demonstrated that the solution must fit in with the realities of the country. If the conditions are appropriate, irregular connections of sewage and water must be regularized as efforts of public policies. In a decade, there was no significant improvement in water supply in rural areas, and the main type of supply is still, in 2015, the artesian well. Considering that the sewerage network and waste management are also incipient in the rural area, artesian wells are in danger of frequent contamination. The main form of water supply in the urban environment is access to the general network; however, it has not yet been universalized even in ten years of providing services to the population, with little variation in the historical series (2.7%). As can be seen in Table XII, the water supply coverage levels for the rural area, for the 2005-2015 historical series, showed an improvement in the coverage of services by 17.7%, but remained below 50% in 2015. TABLE XII Evolution of the coverage levels of the drinking-water network per household (in percentage and by location). Corroborating the information from the series of previous indicators, it is concluded that the greatest challenge of sanitation in Brazil is sanitary sewage (Table XIII). According to Table XIII, in 2015, a little more than half of urban properties have access to sanitary sewage networks (68.0%); and in ten years there was only a small improvement in the service coverage area from 56.3% to 68.0%. The urban population still uses, in 2015, precarious forms for its destination (12.4%) despite improvement in the last ten years. Considering that 85% (Table II) of the population is urban (approximately 173.5 million inhabitants), this volume is significant. TABLE XIII Evolution of the coverage levels of the sewage network per household (in percentage and by location). The worst picture refers to the rural population, in which only 5.4% of the population has access to the sewage network, and most of the sewage is released in inappropriate ways (61.3%). There was an increase in sewage disposal in septic tanks in the rural areas (of 17.5%), remembering also that this sewage is released in natura, that is, without any type of previous treatment (Table XIII). According to the IBGE, of the 5,570 Brazilian municipalities, 2,495 do not have access to the sewer system (IBGE 2011). Both the water supply and the sewage network and treatment are precarious in Brazil, and have a direct impact on the economy, education, the environment, and health. The unsteady system contributes to the increase of GHG emissions in the country because more methane and other greenhouse gases are released into the atmosphere (IPCC 1996). ## SOLID WASTE Waste management is regulated by the National Solid Waste Policy (PNRS), which includes Law 12,305/2010 (Brasil 2010a) and Decree 7,404/2010 (Brasil 2010b). Like the water and sewage sectors, the waste sector is also operationalized by Plansab (MCID 2013), because the plan systematically encompasses sanitation services. According to this Law, article 54 (Brasil 2010a), open dumps should have been closed in 2014, with the possibility of being charged financial penalties due to this environmental crime, as provided by the Law of Environmental Crimes (Law 9,605/1998, art 54). However, this deadline has been subsequently postponed and, still in 2017, “the 3,000 open dumps identified in Brazil affected the lives of 76.5 million people, bringing an economic loss of US$ 1 billion to the public coffers” (ISWA/Abrelpe 2017). Consequently, despite the Laws, the PNRS and the Plansab, the following data describe the evolution of the ten-year indicators as almost unchanged. It should be emphasized that solid waste disposal data are important in quantifying the trajectory of Brazilian GHG emissions for the sector, as poor management of SW means a high level of methane emissions to the atmosphere.
Table XIV shows a slight improvement in the indicators of SW directly collected from households, from 89.7% to 92.8% in ten years. Rural areas have a lower production of waste, but also have the lowest level of waste collected, 27.3%. The North and the Midwest presented the lowest percentage of waste collected in rural properties (18.4% and 16.8%) in 2015 and in a 10-year period (0.7% and 3.0%); whereas the Northeast and the South improved the collection in rural areas (10.1% and 17.1%). Indirect collection and other types of destinations decreased for all the regions and for urban and rural areas, representing an improved situation for the period.
TABLE XIV
Evolution of the coverage levels of SW collected from households per household (in percentage and by location).
According to Abrelpe, there was an increase in the amount of solid waste (SW) produced and in the SW not collected for all the regions as well as for the country from 2005 to 2015 (Table XV). The Midwest is the region which present the highest increased generation of SW (71%), but the largest producer by far is the Southeast (194,790 tons/per day). The South presented the highest percentage of amount of SW not collected (274%), but the Northeast is the one which had the highest quantity of SW not collected (11,701 tons/per day).
TABLE XV
Amounts of solid waste (tons/per day).
From 2005 to 2015, all the regions presented a smaller amount of waste dumped per day except the North, which increased this amount by 4%. In 2015, more than 82,000 tons per day were dumped in inappropriate places in Brazil and multiplying by 26 days of collection per month (Abrelpe 2011), it reaches a total of 25,602,408 per year.
For the 2005 data (Table XV), the category “Controlled Landfill - Open Dump” included solid waste dumping; actions/places include burning or burying in the property; dumping on open land or in public places; throwing in rivers, lakes or sea; or other undeclared/illegal destinations. Whereas for the other historical series the category “Landfill” is the landfills that applied all the international/national rules for an appropriate destination of solid waste, and “Controlled Landfill - Open Dump” included open dumps and controlled landfills, “that do not have the necessary set of systems to protect the environment and public health” (Abrelpe 2006, 2016).
According to Table XVI, the worst situation is in the North and the Northeast as those states present the lowest collection rate of solid waste in properties and the highest inappropriate destination level when measured by households. However, there was a decrease in the coverage level of households that did not have its SW collected.
TABLE XVI
Solid Waste Collection - coverage rates by households.
Table XVII shows that there is an increased number of municipalities presenting selective collection of SW. However, as observed by Abrelpe (2016), “although the number of municipalities with selective collection activities is significant, it is important to consider that these activities are often summarized in the provision of voluntary delivery points to the population or in the simple formalization of cooperative agreements with garbage collectors to perform the services.”
TABLE XVII
Number of municipalities with selective collection of SW.
Brazil produced 79.9 million tons of waste in 2015 and 78.3 million in 2016 (Abrelpe 2017), respectively, with a coverage rate of 90.8% and 91%, accounting for 7.3 million tons not collected in 2015 (Abrelpe 2016) and 7 million not collected in 2016 (Abrelpe 2017). There is still a problem in the final disposal of municipal solid waste (MSW), which got worse from 2015 to 2016. In 2015, 58.7% of the waste collected went to landfills, representing a volume of 42.6 million tons. In 2016, 58.4% of the waste collected went to landfills, representing a volume of 41.7 million tons, with 29.7 million tons of waste inappropriately dumped. In 2016, out of a total of 5,570 municipalities, 3,331 dumped their MSW (Abrelpe 2017).
## ASSESSMENT BY PLANSAB
According to the latest assessment report of Plansab (MCID 2015), a matrix of analysis was created so as to classify service levels from 2014 to 2015 under two categories: Appropriate Service Level; and Deficit, which includes Precarious Service Level; and No Service (Table XVIII).
TABLE XVIII
Plansab assessment - categories.
Data collected also from PNAD and SNIS were used to categorize the results of Plansab from 2013 to 2015 (Table XVIII). It can be seen that when considering the quality of the services provided, the indices are worse (Table XIX) than when only considering the access or not to the public service for the water services (Table VIII) and to the appropriate solid waste management (Table XVI). As was analysed in Table VI, the treatment of the sewage collected is higher than the treatment of sewage generated.
TABLE XIX
Plansab assessment - categories.
## GREENHOUSE GAS EMISSIONS
Brazil has voluntarily committed itself to reducing GHGs under the United Nations Framework Convention on Climate Change (UNFCCC). This commitment was nationally regulated by Law 12,187/2009 (Brasil 2009), known as the National Policy on Climate Change (PNMC). Although it established sectoral plans to implement policies for GHG mitigations, there is no sectoral plan for waste and sewage. There are only reduction targets considered with industrial processes under the PNMC (Brasil 2009).
The evolution of GHG emissions for the “Waste” sector reflects the “grave absence and precariousness” (IBGE 2011) of public policies in the country in this area. According to Table XIX, the indicators of 2014 demonstrate that the Energy Sector presented its greatest variation in the period of 1990 to 2014 (55.2%). The agricultural sector has occupied third place in Brazil’s emissions since 2012, the year in which the energy sector began to occupy second place. The agricultural sector presents smaller variations than the energy sector, despite the growing agricultural production in the country, which is mainly explained by the constant efficiency gain in the Brazilian agricultural industry.
The biggest drop in emissions has been in the Land Use, Land-Use Change and Forestry (LULUCF) sector, which is directly related to a series of command-and-control regulations, mainly avoiding deforestation in the Amazon. Despite the reduction in the LULUCF emissions, it still contributes 18.1% of the total emissions. Given this weight, a study is necessary to deepen the knowledge of the impacts of agriculture and urbanization on deforestation.
There was a low participation of the Waste sector in total emissions, but a significant increase for the historical series 1990-2014 (41%), which is the largest increase among all sectors (Table XX).
TABLE XX
Greenhouse Gas Emissions (in Gg of CO 2 eq GWP-AR2).
Table XXI shows the consolidated GHG emissions for the Waste sector subdivided according to the IPCC Guidelines (IPCC 1996). The Solid Waste Disposal (SWD) sector is the largest source, accounting for 52% in 2014. The precariousness of the population’s housing infrastructure is reflected in these emissions, in which 42.7% of the sewage is treated and only 50.3% of the population is served with an appropriate sewer system in 2015 (Table VI). In addition, more than 40% of the waste is dumped (Table XVI).
TABLE XXI
GHG from Waste (in Gg of CO 2 eq GWP-AR2).
# DISCUSSION
Sanitation is a major Brazilian challenge, and new infrastructure is predominantly dependent on public investments, and on partial or full concessions (Brasil 2007). Sanitation data show that over a period of ten years the situation did not evolve significantly in most regions of Brazil, mainly in the poorest regions of the country: in the North, where most indexes regressed, and in the Northeast, with the largest underserved residents.
According to the World Health Organization (2008), each “$1 investment in sanitation will give a return of$9”. It is so important that the universal access to water and sanitation is an international commitment under the Sustainable Development Goals (SDG), and SDG 06, “Clean water and Sanitation for all”, aims at ensuring availability and sustainable management of water and sanitation for all by means of achieving the following targets (United Nations 2015):
6.1. By 2030, achieve universal and equitable access to safe and affordable drinking water for all;
6.2. By 2030, achieve access to adequate and equitable sanitation and hygiene for all and end open defecation, paying special attention to the needs of women and girls and those in vulnerable situations;
6.3. By 2030, improve water quality by reducing pollution, eliminating dumping and minimizing release of hazardous chemicals and materials, halving the proportion of untreated wastewater and substantially increasing recycling and safe reuse globally;
6.4. By 2030, substantially increase water-use efficiency across all sectors and ensure sustainable withdrawals and supply of freshwater to address water scarcity and substantially reduce the number of people suffering from water scarcity;
6.5. By 2030, implement integrated water resources management at all levels, including through transboundary cooperation as appropriate;
6.6. By 2020, protect and restore water-related ecosystems, including mountains, forests, wetlands, rivers, aquifers and lakes;
6.a. By 2030, expand international cooperation and capacity-building support to developing countries in water- and sanitation-related activities and programmes, including water harvesting, desalination, water efficiency, wastewater treatment, recycling and reuse technologies;
6.b. Support and strengthen the participation of local communities in improving water and sanitation management.
On the other hand, as presented throughout this paper, Brazil is already near to accomplishing SDG 07 (Table I): “affordable and clean energy”, which aims at ensuring access to affordable, reliable, sustainable, and modern energy for all by means of the following targets:
7.1. By 2030, ensure universal access to affordable, reliable and modern energy services;
7.2. By 2030, increase substantially the share of renewable energy in the global energy mix; 7.3. By 2030, double the global rate of improvement in energy efficiency;
7.a. By 2030, enhance international cooperation to facilitate access to clean energy research and technology, including renewable energy, energy efficiency and advanced and cleaner fossil-fuel technology, and promote investment in energy infrastructure and clean energy technology;
7.b. By 2030, expand infrastructure and upgrade technology for supplying modern and sustainable energy services for all in developing countries, in particular least developed countries, small island developing States, and land-locked developing countries, in accordance with their respective programmes of support.
Rural electrification had been the main bottleneck in the universalization of this service for years because rural properties are distant and hard-to-reach, and rural dwellers usually do not have financial resources to pay for the infrastructure needed. Like the sanitation services, electricity is also a public service in Brazil, which is provided by the governments or utility companies. Analysing the history and implementation of the successful program “Electricity for Everyone” (LpT), a federal rural electrification program, will bring new insights to sectoral efforts to universalize sanitation.
The main assumption of this article is that the example demonstrated by the success of universalization of rural electrification shows that there is no universalization of a public service without the strength of the State. For the universalization of sanitation, the same driver applies. In fact, as Heller and Castro argue (2013HELLER L AND CASTRO JE. 2013. Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ), sanitation is a citizen’s right and a State’s duty according to the principles of universality and equity in which, according to the authors:
“Every citizen, regardless of his or her social class, gender, ethnic origin or any other factor of social differentiation, has an unrestricted right to goods and services deemed essential to the maintenance of life in a civilized society... Access to essential services is a fundamental right, which cannot be subject to the individual ability of users to pay and must be guaranteed by the State.”
The purpose of this discussion is to analyze the processes carried out by the State that brought about the universal access to electricity, which can serve as a benchmark for the universal access to sanitation.
One of the major differences between the universal access to electricity and to sanitation is that there is rarely a lack of access to energy services in urban areas. Even in the most deprived areas, electricity wires can reach properties as they are pulled from the nearby infrastructure. The problem of access to energy is primarily in the rural environment. Sanitation demands more complex works or logistics, thus afflicting rural and urban areas. Consequently, as the sanitation infrastructure does not reach deprived urban communities, sewage is thrown in nearby waters, waste is dumped on the slopes of hills and water is taken physically by its residents to their homes.
According to the 2010 Census (IBGE 2010a), there are 3,224,529 permanent households, with more than 11 million inhabitants, located in these poor communities, the so-called “subnormal clusters” (slums, “favelas”, poor communities, villages, among others), characterized by extreme shortages in the provision of public services (IBGE 2010b).
For many years, there was a huge shortage of electricity in the rural areas of the country. The 2000 Census reported almost 11 million people without energy (Table I). In addition to the huge contingent of families without access to electricity in about 4.8 million agricultural establishments, 2.9 million had not yet been electrified according to the 1995/96 agricultural census (Pertusier et al. 2002PERTUSIER F, GUSMÃO MV, PIRES SH, GIANNIN M, CAMACHO C, PESSOA R, LOREIRO E AND OLIVIERI M. 2002. O Programa de Eletrificação Rural Luz no Campo. In: AGRENER, 2002, 4o Encontro de Energia no Meio Rural. Campinas, São Paulo, Brasil. http://www.proceedings.scielo.br/scielo.php?pid=MSC0000000022002000200035&script=sci_arttext. Accessed on 16 June, 2017.
http://www.proceedings.scielo.br/scielo....
). However, unlike sanitation services, more than 15 million people have been included in access to energy services in the last 10 years. According to Table XXII, the average national electricity service is 99.7%, with 46,000 inhabitants living in urban areas and 513,000 in rural areas.
TABLE XXII
Comparative table of public services provided in 2015 for permanent residents.
The number of residents not served by the sewer system is higher in urban areas (more than 57 million) than in rural areas (more than 29 million), mainly in the Northeast, respectively over 21 million and more than 14 million. Nationally, there are more than 100 million people without direct access to a sewage network, considering people using septic tanks.
Besides the underserved sewage services, more than 31 million people do not have access to a water supply network (Tables III and X), and more than 22 million do not have their solid waste collected (Tables VI and X). These numbers are much higher than those that started the electricity universalization program by the 2000 Census (IBGE 2000).
Rural electrification efforts date back a long time, but the most effective ones in Brazil were the “Electricity for the Countryside” (from 1999/2000 to 2003) and “Electricity for Everyone” (from 2003 up to now). “Electricity for the Countryside” had the objective of bringing energy services to 1 million households (or 5 million inhabitants) in four years, beginning in 1999 and being coordinated by the Ministry of Mines and Energy (MME). The financial operation of the program was performed by a public-private partnership, making use of a special fund of the electric sector called Global Reversal Reserve (Reserva Global de Reversão - RGR) of US$540 million. The RGR was formed by charges paid by the electric utilities and passed on to consumers, with a complement of US$280 million from the executors and entities of the Union - states and municipalities (Sugimoto 2002SUGIMOTO L. 2002. Luz para os Esquecidos: Um Balanço do Programa que Visa Levar Energia Elétrica a Um Milhão de Domicílios Rurais. Universidade Estadual de Campinas - 11 a 17 de novembro de 2002. http://www.unicamp.br/unicamp/unicamp_hoje/jornalPDF/198-pag03.pdf. Accessed on 16 June, 2017.
http://www.unicamp.br/unicamp/unicamp_ho...
). The RGR was created by the Decree 41,019/1957 (Brasil 1957), and it was used for promoting “Electricity for Everyone”, as “for works of improvement and expansion of the electric system, in the areas of power generation, transmission and distribution”; it was administered by Eletrobras until May 2017.
This first significant electrification effort was a partnership between the federal government, electric utilities, rural electrification cooperatives and local governments, with implementation in localities with a HDI of less than 0.500. The main bottleneck to the program was the need for payment of the new facilities by final consumers (Fournier and Penteado 2008FOURNIER AC AND PENTEADO CL. 2008. Eletrificação Rural: Desafios para a Universalização da Energia. In: XII Congresso Brasileiro de Energia. Rio de Janeiro, Brasil, Vol. 1, p. 372 -387. http://www2.aneel.gov.br/biblioteca/downloads/livros/eletrificacao_rural_XII.pdf. Accessed on 10 July, 2017.
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), which either indebted an already poor population or made new connections impossible. However, the most important part of this program is the political decision to bring electricity to the needy population with contractual goals for each electric utility. This is an incredible paradigm shift that was to take energy services only to the richest population (Sugimoto 2002SUGIMOTO L. 2002. Luz para os Esquecidos: Um Balanço do Programa que Visa Levar Energia Elétrica a Um Milhão de Domicílios Rurais. Universidade Estadual de Campinas - 11 a 17 de novembro de 2002. http://www.unicamp.br/unicamp/unicamp_hoje/jornalPDF/198-pag03.pdf. Accessed on 16 June, 2017.
http://www.unicamp.br/unicamp/unicamp_ho...
).
The on-going program, “Electricity for Everyone”, was launched at the end of 2003 and aimed to bring energy to 10 million people; this, according to the 2000 Demographic Census, would universalize its access. The priorities of the program were:
“Communities enrolled in federal social programs, rural settlements, indigenous communities, quilombolas (communities of former slaves’ descendants), communities located in extractive reserves or in areas of electricity generation or transmission of electricity, whose responsibility is not the electric utility provider, in addition to schools, health posts and community water wells. The services of the program are totally free, providing for the installation in homes of up to three points of light (one per room), two sockets, conductors, light-bulbs and other necessary materials” (MME 2010).
By 2015, LpT counted more than 15.6 million people served (MME 2015). Then, the program was extended to serve more than 1 million people in the North and Northeast between 2015 and 2018, mainly in pristine areas. Until the beginning of the LpT, the costs of the new facilities were paid by the rural dwellers. This program guaranteed the free installation of the electrical installation to the interior of the residence determined by the government in the contract.
To ensure the transparency of the program, the MME has launched the Program Operations Manual. This manual has defined the operational structure, objectives, procedures, technical and financial criteria, priorities and functioning, that is, has transparently outlined simple and objective rules. In addition, as a participatory forum, it created a Management Committee in each State, placing priority and monitoring the implementation (MME - LpT 2011).
LpT was managed as a public policy, and encompassed a federal, state and municipal structure with an impressive local capillarity. It was coordinated by the Ministry of Mines and Energy (MME), operated by the Brazilian Electric Power Plants (Eletrobras), and regulated by the National Electric Energy Agency (Aneel), the energy regulatory agency.
The implementation of the phases was performed by the electric utilities and rural cooperatives. It was inspected by five institutions: MME, Eletrobras, National Management Committee of Universalization - CGN, Regional Coordinators and State Management Committees - CGE, each with its clearly delineated competence.
A unique financial balance was created to enable free access to new connections. Part of the program was made possible because of sectoral energy funds: from the Energy Development Account (CDE), a federal government subsidy, and the Global Reversal Reserve (RGR); and because of special lines of financing from the federal bank “Caixa Econômica Federal” (CEF). The rest of the investment was shared between state governments and electric power distribution companies. Total investments were US$6.9 billion, including US$ 5.1 billion from the federal government (MME 2010).
As the final consumer did not bear the costs of the new installation, the consumers of the entire concession area were the ones who paid for it. The investment equation is the division among states and the federal government (10%), consumers (90%), limiting the tariff to 8%, and the rest paid by the electric utility responsible for the area of concession, without cost coverage obligation (Fournier and Penteado 2008FOURNIER AC AND PENTEADO CL. 2008. Eletrificação Rural: Desafios para a Universalização da Energia. In: XII Congresso Brasileiro de Energia. Rio de Janeiro, Brasil, Vol. 1, p. 372 -387. http://www2.aneel.gov.br/biblioteca/downloads/livros/eletrificacao_rural_XII.pdf. Accessed on 10 July, 2017.
http://www2.aneel.gov.br/biblioteca/down...
).
In addition to the management and public-private partnership, there was direct collaboration of several ministries through actions integrated into the MME, such as the Ministry of Education (schools, night classes), Ministry of Health (hospitals and health posts), Ministry of Transport (roads), Ministry of Communications (digital inclusion) and other coordinated actions (MME - LpT 2008).
The project also included an “Integrated Actions Plan” (PAI) and a line of “Special Projects”. PAI created strategies to integrate projects and social programs into LpT projects, enabling partnerships and articulations with local actors, seeking to improve the quality of life of rural populations.
Special projects arose from the need to make the program viable. In the beginning, the connections were made by extensions of conventional electricity wires or by fossil fuel thermal power plant units. The great challenge was to serve extremely isolated populations or those in locations of low population density (MME - LpT 2007). Thus, Special Projects were launched in 2009, financed partly by economic subsidy (85%) and partly by executing agents (15%). They are transparently regulated by the Manual of Special Projects to serve this population:
“By means of decentralized electricity generation, using renewable sources compatible with the local reality, as well as by means of the construction of small stretches of distribution networks in primary and / or secondary voltages - mini-grids, including, when necessary, the use of unconventional distribution grids (for underwater crossings, crossings in forests and others), using technologies under current legislation” (MME - LpT 2009).
The power of the state to foster the rural electrification program as “an instrument of development and social inclusion” (MME - LpT 2015) was likely to be the main driver of its success. The differentials of the program and what has possibly led to the almost universal access to energy services - which can be used for the universal access to sanitation - were: specific public and private financial sources and funds; the free installations for new customers (Camargo and Ribeiro 2015CAMARGO E AND RIBEIRO F. 2015. Programa Luz Para Todos: Avanços e Retrocessos - Um Novo Estoque de Excluídos. In: Agrener GD (Ed), 10º Congresso sobre Geração Distribuída e Energia no Meio Rural 11 a 13 de novembro de 2015. USP, São Paulo, Brasil. http://www.iee.usp.br/agrener2015/sites/default/files/tematica3/908.pdf. Accessed on 10 July, 2017.
http://www.iee.usp.br/agrener2015/sites/...
), (paid for by the companies, by the federal fund, by the governments, and by the consumers with better incomes); its implementation as a public policy for socioeconomic development; regulation, implementation and operation agencies; a system of tariffs shared with consumers and companies; and the coordination among various ministries. Also, for pristine areas, the project used the special project category, which fostered local solutions with the power of the State, by means of partnerships with local communities and municipalities. And, among all, the focus on the underprivileged, which is a complete differential when compared to pure market forces.
Like the Rural Electrification Program, the National Plan for Sanitation (Plansab) is incredibly detailed (MCID 2013), and it is regularly assessed by the National Secretariat of Environmental Sanitation (SNSA), an institution under the auspices of the Ministry of the Cities (MCID), as explained in the article. It establishes goals, deadlines, and amount of investments; regulates the participation of private sector; describes competencies and actions of each federative entity, and the possibility of cooperation of public-private agents to promote strategic and long-term management; and establishes Management Committees and Investment Funds, but its results were meagre. Brazil has legal structure, and national and international budgets to provide universal access to sanitation. “However, these remain only as potential if proper governance and accountability mechanisms are not put in place” (Nhamo 2016NHAMO G. 2016. New Global Sustainable Development Agenda: A Focus on Africa. Sust Dev 25: 227-241.).
The Plansab evaluation report points to some causes for this failure (Inecon/FGV 2008) and the main ones are “the existence of an unstable regulatory environment, with entities that perform the supervisory or regulation works with weak technical and institutional capacity, and contractual goals that are not always clearly defined and difficult to audit”. In addition, there is a lack of coordination between expected resources and annual budget planning required; federal assistance in investment and resource allocation; and no regulatory agency for the sector. On top of that, States and municipalities, which are mainly responsible for the operationalization of the Plan (differently from the provision of energy services), are mostly in debt and have a low investment potential.
Considering the low tariffs, lack of supervision in the investments and operation, the inadequacy of the technical staff and the high level of losses in distribution (the national average of losses in the distribution of water was 36.7% in 2015), the result is the low level of investment in the necessary works and of the participation of the private sector in certain localities (Senado Federal, 2016FEDERAL S. 2016. Saneamento: A Linha Divisória da Saúde Pública, no. 27. Senado Federal Brasileiro, Brasília, Distrito Federal, Brasil. http://www12.senado.leg.br/emdiscussao/edicoes/saneamento-basico/@@images/arquivo_pdf/. Accessed on 17 June, 2017.
). The tension between short-term and long-term goals will always be present in this sector because of the capital intensity and the huge levels of investment needed (Cepal 2017).
The national scenario for a proper implementation of universal access for sanitation does not seem very optimistic, but neither did the one for rural electrification. Plansab is an incredible plan, but it is premature to analyze its results. This article aimed to analyze a ten-year evolution of the sector so as to conclude that universal access is possible.
In considering the example of rural electrification, the following points should also be considered. As simple as it might seem, a universal access program to sanitation would have to design an operational manual, with institutions and roles. A regulatory agency should be created, together with clear roles assigned to the existing organizations. A specific secretary for the program also has to be articulated with committees for national, regional and local articulation.
It would establish its own special project manual based on social technologies applied in each region. Social technologies are defined here as “technologies that are mainly oriented towards simplicity, low cost, easy applicability and social impact, but are not necessarily associated with collective organizations. They are good and affordable ideas, but people do not need to organize collectively to better use them” (Lassance and Pedreira 2004LASSANCE A AND PEDREIRA J. 2004. Tecnologias sociais e políticas públicas. In: Banco do Brasil. Tecnologia social: uma estratégia para o desenvolvimento. Fundação Banco do Brasil, Rio de Janeiro. http://www.oei.es/historico/salactsi/Teconologiasocial.pdf. Accessed on 24 October, 2017.
http://www.oei.es/historico/salactsi/Tec...
). There is a myriad of ministries, local governments, and institutions that already implement social technologies in their projects. There should be a concentrated effort to provide a manual to describe their use under a universal access to sanitation program.
As an example, social technologies have already been implemented as a public policy since 2003, when the financing started to build cisterns for harvesting water in rural area (MDS 2016), which delivered 1.2 million cisterns from 2003 to 2016. In March 2017, under the Decree 268/2017 of the Ministry of Cities, which regulates the National Rural Housing Program (Brasil 2017), rural households started to have access to finance to pay (1) for cisterns for the collection and storage of rainwater “according to project technical specifications of the National Program to Support Rainwater Harvesting and Other Social Technologies (Cisterns Program) and (2) for effluent treatment solutions by means of systems for wastewater disposal according to the manual of the National Health Foundation of the Ministry of Health (FUNASA) and of biodigester septic tanks, according to the approved or developed projects of the Brazilian Agricultural Research Company (Embrapa 2010).
A financial structure to implement and to operate the program should be developed, with subventions from the governments and shared responsibilities for the provider of the services; with an appropriate system of transparency and social control. A new and specific tariff for those services must be included in this planning, considering that the underprivileged ones should not bear those costs. According to Peixoto (2013PEIXOTO JB. 2013. Aspectos da Gestão Econômico-financeira dos serviços de Saneamento Básico no Brasil. In: Heller L and Castro JE (Eds), Política Pública e Gestão de Serviços de Saneamento. Rio de Janeiro: Editora Fiocruz; Belo Horizonte: Editora UFMG, 567 p. ), “the access to services of sanitation only for the ones who pay tariffs or fees has been contributing to the exclusion of the poorest part of the population from this social right”. A possible initiative, which was indeed applied in the rural energy program, would be to implement two Articles of Law 14,445/97 (Brasil 2007, Peixoto 2013). These are Article 29, which provides for “a subsidy policy for the users or localities which do not have capacity for payment or the economic scale to cover the costs of installations”, and Article 13, which provides for a fund to pay for the universalization of public sanitation services”. Finally, a transparency portal should be established with targets, investments, subsidies, funds, financing, loans, services provided and timelines; organization and public positions should be established for this universalization program in order to keep appropriate social control.
In summary, as discussed thorough this section, key success factors that brought about the universal access to electricity should be adapted and used for the universal access to sanitation, and these policies would include: specific public and private financial sources and funds as well as transparency on the administration of these resources; the free installation and restoration of connections or the implementation of special sustainable projects for new customers (paid for by the companies, by the federal fund, by the governments, and by the consumers with better incomes); its implementation as a public policy for socioeconomic development considering the impacts that the SDG 06 have on other SDGs; regulation, implementation and/or operation of public agencies; a system of highly subsidized rates with tariffs shared with economically well-off consumers and companies; and the coordination among various ministries. And, among all, as advocated in the rural electrification case, the focus on the underprivileged, which is a complete differential when compared to pure market forces.
The universal access to sanitation should be a concerted action among the Union, States and municipalities, as the universalization of electricity was. The success of rural electrification shows that it is possible to achieve universal access to sanitation, with planning, implementation and operation; investment; transparency; and, above all, political will.
# CONCLUSIONS
It is firmly lodged in the Brazilian popular imagination that underground works do not attract votes and that sanitation infrastructure is always at the bottom of their politicians’ agenda because it involves subterranean and thus invisible benefits. Legend or fact, Brazil presents impressively precarious indexes for sanitation, with severe consequences. The latest epidemics in Brazil, for instance, were directly related to lack of sanitation. The “Instituto Trata Brasil” study shows that the 10 worst cities in Brazil regarding sanitation recorded 3 to 5 times more cases of hospitalization and deaths related to diarrhoea, dengue and Leptospirosis than the top 10 (ITB 2017). According to discussions in the Federal Senate, epidemics caused by Aedes aegypti (such as dengue, chicungunha, zika), and new cases of yellow fever, demonstrate the inadequacy of Plansab and the sanitation infrastructure (Senado Federal, 2016). Zika virus was even more acute and was considered a global health emergency on the 1st February 2016 by the World Health Organization (WHO 2016).
There are regulatory milestones for the universalization of the sanitation service with implementation far from expected. However, based on the successful experience of the rural electrification program, it is concluded that there is a possibility of a new universalization program that may result in the inclusion of millions of people within the most basic services of society: access to the sewer system, water supply and the collection and proper disposal of waste. Access means the right to life, health and a healthy environment, and it would finally accomplish a Brazilian international commitment: the SDGs.
# Publication Dates
• Publication in this collection
16 Apr 2018
• Date of issue
Apr-June 2018
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2022-05-20 17:35:00
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https://documen.tv/question/dan-was-the-team-s-star-batter-he-had-a-batting-average-of-60-if-dan-had-30-hits-last-summer-how-20753604-65/
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Dan was the team’s star batter. He had a batting average of 60%. If Dan had 30 hits last summer, how many at bats did he have?
Question
Dan was the team’s star batter. He had a batting average of 60%. If Dan had 30 hits last summer, how many at bats did he have?
in progress 0
3 months 2021-08-06T09:59:21+00:00 1 Answers 4 views 0
50 bats total
Step-by-step explanation:
To solve this problem, all one has to do is, set up a proportion, remember, a proportion is;
In this case;
It is given that;
percent – 60%
hits – 30
Now substitute in the values and solve;
Solve, first simplify;
Now use cross products;
150 = 3(total_bats)
Inverse operations;
150 = 3(total_bats)
/3 /3
50 = total_bats
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2021-12-08 01:00:55
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https://math.stackexchange.com/questions/1676206/how-to-prove-a-splitting-field-sigma-for-f-over-k-can-be-one-for-l-in-t
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# How to prove a splitting field $\Sigma$ for $f$ over $K$ can be one for $L$ in the following case?
Q.If $\Sigma$ is the splitting field for $f$ over $K$ and $K\subseteq L \subseteq \Sigma$, show that $\Sigma$ is the splitting field for $f$ over $L$.
I give up, I have tried for 2 hours and no I don't get even how to solve this. I have seen he exact same question(not mine) in a past post but it did not provide any insight, what is more, it had flawed arguments as you can see.
(Splitting fields for $f$ over field $K$) A subfield $\Sigma$ of $\mathbb{C}$ is a splitting field for the nonzero polynomial $f$ over the subfield $K$ of $\mathbb{C}$ if
1.$K \subseteq \Sigma$
2.$f$ splits over $\Sigma$
3.If $K \subseteq \Sigma' \subseteq \Sigma$ and if $f$ splits over $\Sigma'$ then $\Sigma = \Sigma'$
Now, I know that $\Sigma$ is a splitting field of some $f$ over $K$. That is one information.
Also, $k \subseteq L \subseteq \Sigma$. Information two.
But with this scarce information, how can I draw the conclusion that $\Sigma$ is a splitting field for $f$ over $L$?
I first thought conditions $3$ in the definition is the trick. It seems like $L= \Sigma'$. But I quickly discarded this because it's "IF $f$ splits over $\Sigma"$ then $\Sigma = \Sigma'$" which does not help me in actually proving it splits over $\Sigma'$ or, in our case $L$.
So I tried to go by definition. Namely, show that
1.$L \subseteq \Sigma$
2.$f$ splits over $\Sigma$
3.If $L \subseteq \Sigma' \subseteq \Sigma$ and if $f$ splits over $\Sigma'$ then $\Sigma = \Sigma'$
Well, conditions $1$ and $2$ are satisfied. So all good up to there. But again, conditions $3$ is a pain.
I have tried to argue as follows but am very NOT confident with it.
Suppose that $\Sigma'$ such that $L \subseteq \Sigma' \subseteq \Sigma$ exists. And, if $f$ does not split over $\Sigma'$, we are done.(...Right?)
If $f$ does split over $\Sigma'$, then $\Sigma'= \Sigma$ because $\Sigma$ is the smallest field extension of $K$ such that $f$ splits and $K \subseteq L \subseteq \Sigma' \subseteq \Sigma$. If $\Sigma ' \neq \Sigma$ then $\Sigma'$ would be the smallest field extension of $K$ that $f$ splits and thus a contradiction.
Thus all $3$ conditions have been satisfied and hence shown.
I need more practice with this area of abstract math, but can someone look at this problem and point me in the right direction at least if I am wrong up there? Please help
So $\;\Sigma/K\;$ is the splitting field of $\;f(x)\in K[x]\;$ , and this means in simple words that
(1) $\;\Sigma\;$ contains all the roots of $\;f\;$ , or what is the same : $\;f\;$ splits as a product of linear factors in
$\;\Sigma[x]\;$, and
(2) $\;\Sigma\;$ is the minimal (w.r.t set inclusion) field extension of $\;K\;$ that fulfills (1).
Now, if $\;K\subset L\subset \Sigma\;$ , then clearly also $\;f(x)\in L[x]\;$ and all the roots of this polynomial are in
$\;\Sigma\;$ . If there was a field $\;L\le M\lneqq\Sigma\;$ containing all the roots of $\;f\;$ , then this field would also be
an extension of $\;K\;$ since $\;K\subset L\subset M\;$ and we'd get a contradiction to the minimality of $\;\Sigma\;$ as
the minimal field extension of $\;K\;$ where $\;f\;$ splits in linear factors.
• Thanks for helping out. One question, what does $\;L\le M\rlap{\;\,/}<\Sigma\;$ mean in field theory? I know it means subgroup in groups but is that supposed to mean "a subfield of"? And, so assuming such an $M$ exists for $f(x) \in L[x]$ leads to a contradiction, and thus $\Sigma$ must be the splitting field over $L$ for $f(x)$... yes? – John Trail Feb 29 '16 at 20:25
• @JohnTrail Sorry, that was a typo. I already fixed. It should have been $\;L\le M\lneqq\Sigma\;$, meaning: proper subfield. – DonAntonio Feb 29 '16 at 20:53
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2019-09-22 16:10:58
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https://www.illustrativemathematics.org/content-standards/5/NF/B/7/tasks/1120
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Update all PDFs
How many marbles?
Alignments to Content Standards: 5.NF.B.7.b 5.NF.B.7.c
Julius has 4 blue marbles. If one third of Julius' marbles are blue, how many marbles does Julius have? Draw a diagram and explain.
IM Commentary
This task is intended to complement "5.NF How many servings of oatmeal?" and "7.RP Molly's run.'' All three tasks address the division problem $4 \div \frac{1}{3}$ but from different points of view. "How many servings of oatmeal'' presents a how many groups version of $4 \div \frac{1}{3}$ while "Molly's run" approaches this division problem from the point of view of rates. This task provides a how many in each group version of $4 \div \frac{1}{3}$.
To recall in this setting the difference between a how many groups version and a how many in each group version of the equation $$4 \div \frac{1}{3} = 12$$ notice that there are two different multiplication equations which can give rise to this division equation:
\begin{align} 12 \times \frac{1}{3} &= 4 \\ \frac{1}{3} \times 12 &= 4. \end{align}
In the first of these equations $12$ groups of $\frac{1}{3}$ make $4$ and so $12$ is the answer to how many thirds there are in $4$. In the second equation $\frac{1}{3}$ of a group of $12$ make $4$ and so $12$ is the answer to how much is in a group if one third of that group is $4$.
This task should be done together with the "How many servings of oatmeal" task with specific attention paid to the very different pictures representing the two situations. A good picture will determine which version of division, how many groups or how many in each group, is being modeled in a given situation.
This task is appropriate for assessment or for instruction.
Solutions
Solution: 1
If one third of Julius' marbles are blue, this means that $\frac{2}{3}$ of his marbles are colors other than blue. This means that Julius has two times as many marbles of colors other than blue than he has blue marbles. Since Julius has $4$ blue marbles, this means that he has $8$ marbles of other colors and so he has $12$ marbles total.
Below is a picture representing Julius' marbles:
Since $\frac{1}{3}$ of Julius' marbles are blue, we can also record this as a missing factor problem: $\frac13 \times$ ____ $= 4.$ This missing factor problem is equivalent to the division problem: $4 \div \frac13 =$ ____. In either case, the answer is 12 marbles, as we saw in the picture.
Solution: Using a tape diagram
The number of blue marbles is represented by 1 unit. We can find the total using the missing factor sentence:
$4 = \frac13 \times$ ____.
This missing factor sentence is equivalent to the division problem:
$4 \div \frac13 =$ ____.
As the diagram shows, this is equivalent to solving:
$4 \div \frac13 = 4 \times 3 = 12.$
Julius has 12 marbles.
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2019-01-17 17:24:34
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https://www.ams.org.cn/CN/10.11900/0412.1961.2019.00158
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金属学报 2020, Vol. 56 Issue (2): 240-248 DOI: 10.11900/0412.1961.2019.00158
研究论文 本期目录 | 过刊浏览 |
1. 大连理工大学工业装备结构分析国家重点实验室 大连 116024
2. 大连理工大学工程力学系 大连 116024
Mechanical Properties and Strengthening Mechanism of Graphene Nanoplatelets Reinforced Magnesium Matrix Composites
ZHOU Xia1,2(),LIU Xiaoxia2
1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China
2. Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China
全文: PDF(31802 KB) HTML
Abstract
To improve the mechanical properties of Mg alloys and broaden their application fields, high performance Mg matrix nanocomposites have received more and more attention nowadays. Therefore, the research on the basic mechanical properties and strengthening mechanism of new Mg matrix composites at nanoscale has important theoretical and practical significance. The mechanical properties of pristine single-layer graphene nanoplatelets (GNPs) and single-side and double-side nickel-coated GNP (Ni-GNP, Ni-GNP-Ni) reinforced Mg composites (GNP/Mg, Ni-GNP/Mg, Ni-GNP-Ni/Mg) are studied under uniaxial tension by molecular dynamics (MD) simulations. Meanwhile, their tensile properties are also compared with those of double-side nickel-coated GNP with vacancy defects (Ni-defected GNP-Ni) and double-side nickel-coated multilayer GNPs (Ni-nGNPs-Ni) reinforced Mg-based composites. The simulated results show that the mechanical properties of Mg matrix composites are improved significantly by the addition of GNPs. Compared with single crystal Mg, the tensile strength and elastic modulus of GNP/Mg nanocomposites at 300 K and 1×109 s-1 are increased by 32.60% and 37.91%, respectively; while the tensile strength and elastic modulus of Ni-GNP-Ni/Mg composites are increased by 46.79% and 54.53%, separately. In addition, there is a larger increase in the elastic modulus and tensile strength but a smaller increase in the fracture strain for Ni-defected GNP-Ni/Mg composites, while there is a larger increase in the tensile strength and fracture strain but a smaller increase in the elastic modulus for Ni-GNP/Mg composites as compared with those of GNP/Mg composites. The elastic modulus, tensile strength and fracture strain of Ni-GNP-Ni/Mg composites decreases with increase in temperature, showing a temperature softening effect, but the variation in the elastic modulus of the composites is insensitive to temperature. With increasing of the layers or volume fractions of GNPs in Ni-nGNPs-Ni, the elastic modulus, tensile strength and fracture strain of the composites are all increased significantly, and the composites show excellent comprehensive mechanical properties. It is concluded that the main strengthening mechanisms for Ni-GNP-Ni/Mg nanocomposites are strong interface bonding, effective load transfer from the Mg matrix to the Ni-GNP-Ni and dislocation strengthening by analysis of the evolution of atomic structure.
Key wordsgraphene nanoplatelet magnesium matrix composite molecular dynamics simulation mechanical property strengthening mechanism
ZTFLH: TB331
Corresponding author: Xia ZHOU E-mail: zhouxia@dlut.edu.cn
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2020-08-15 19:50:21
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https://hal.archives-ouvertes.fr/L2C/hal-03197323
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# Canonical structure of minimal varying $\Lambda$ theories
3 CPT - E4 Gravité quantique
CPT - Centre de Physique Théorique - UMR 7332
Abstract : Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and Pontryagin densities multiplied by $1/\Lambda$. We identify the canonical structure of these theories which turn out to represent an example of irregular systems. We find five degrees of freedom on generic backgrounds and for generic values of parameters, whereas if the parameters satisfy a certain condition (which includes the most commonly considered Euler case) only three degrees of freedom remain. On de Sitter-like backgrounds the canonical structure changes, and due to an emergent conformal symmetry one degree of freedom drops from the spectrum. We also analyze the self-dual case with an holomorphic action depending only on the self-dual part of the connection. In this case we find two (complex) degrees of freedom, and further discuss the Kodama state, the restriction to de Sitter background and the effect of reality conditions.
Document type :
Journal articles
Domain :
https://hal.archives-ouvertes.fr/hal-03197323
Contributor : L2c Aigle Connect in order to contact the contributor
Submitted on : Tuesday, April 13, 2021 - 4:53:07 PM
Last modification on : Friday, October 22, 2021 - 3:02:18 PM
### Citation
Sergey Alexandrov, Simone Speziale, Tom Zlosnik. Canonical structure of minimal varying $\Lambda$ theories. Classical and Quantum Gravity, IOP Publishing, 2021, 38 (17), pp.175011. ⟨10.1088/1361-6382/ac1852⟩. ⟨hal-03197323⟩
Record views
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2021-11-29 19:04:53
|
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https://repository.uantwerpen.be/link/irua/95646
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Publication
Title
$LiZnNb_{4}O_{11.5}$ : a novel oxygen deficient compound in the Nb-rich part of the $Li_{2}O-ZnO-Nb_{2}O_{5}$ system
Author
Abstract
A novel lithium zinc niobium oxide LiZnNb(4)O(11.5) (LZNO) has been found in the Nb-rich part of Li(2)O-ZnO-Nb(2)O(5) system. LZNO, with an original alpha-PbO(2) related structure, has been synthesized by the routine ceramic technique and characterized by X-ray diffraction and transmission electron microscopy (TEM). Reflections belonging to the LZNO phase, observed in X-ray powder diffraction (XRPD) and electron diffraction, have been indexed as monoclinic with unit cell parameters a=17.8358(9)angstrom, b=15.2924(7)angstrom, c=5.0363(3)angstrom and gamma=96.607(5)degrees or as alpha-PbO(2)-like with lattice constants a=4.72420(3)angstrom, b=5.72780(3)angstrom, c=5.03320(3)angstrom, gamma=90.048(16)degrees and modulation vector q=0.3a*+1.1b* indicating a commensurately modulated alpha-PbO(2) related structure. The monoclinic cell is a supercell related to the latter. Using synchrotron powder diffraction data, the structure has been solved and refined as a commensurate modulation (superspace group P112(1)/n(alpha beta 0)00) as well as a supercell (space group P2(1)/b). The superspace description allows us to consider the LZNO structure as a member of the proposed alpha-PbO(2)-Z (3 + 1)D structure type, which unifies both incommensurately and commensurately modulated structures. HRTEM reveals several types of defects in LZNO and structural models for these defects are proposed. Two new phases in Li(2)O-ZnO-Nb(2)O(5) system are predicted on the basis of this detailed HRTEM analysis. (C) 2009 Elsevier Inc. All rights reserved.
Language
English
Source (journal)
Journal of solid state chemistry. - London
Publication
London : 2010
ISSN
0022-4596
Volume/pages
183:2(2010), p. 408-418
ISI
000274497600020
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address
External links
Web of Science
Record
Identification Creation 01.03.2012 Last edited 04.12.2017 To cite this reference
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2017-12-14 21:06:54
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http://elliottbiondo.com/
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• C/C++11
• Python
• CUDA
• MATLAB
• git
• LaTeX
I am an R&D Associate Staff Member at Oak Ridge National Laboratory (ORNL) in Oak Ridge, Tennessee. I work in the Radiation Transport Group, as a developer of the Shift Monte Carlo radiation transport code. I develop, implement, and analyze new methods for improving the performance and accuracy of nuclear reactor simulations on leadership-class supercomputers.
I grew up in the D.C. metro area, before attending the University of Minnesota where I double majored in chemical engineering and chemistry. As an undergraduate I worked as a process engineering intern at Polar Semiconductor Inc. and conducted research in synthetic organic chemistry in the Noland Research Group. It was during my junior year that I was first exposed to scientific computing in a numerical methods course and also became interested in nuclear energy as a way to mitigate climate change.
These interests lead me to join the Computational Nuclear Engineering Research Group at the University of Wisconsin, where I earned my Ph.D. in nuclear engineering. As a graduate student, I had coursework in advanced mathematics, numerical methods, algorithms, and high-performance computing. I gained nuclear engineering analysis experience performing calculations in support of the SHINE Medical Technologies medical isotope facility. My software development skills matured as a leading contributor to the Python for Nuclear Engineering Toolkit and as an intern at ORNL working on the ADVANTG code. My dissertation research focused on optimizing Monte Carlo simulations for biological dose rate calculations for nuclear fusion reactors by approximating the nuclear transmutation process.
## Contact Details
elliott.biondo@gmail.com
# Selected Publications
1. E. Biondo, G. Davidson, T. Pandya, S. Hamilton, T. Evans, “Deterministically Estimated Fission Source Distributions for Monte Carlo k-Eigenvalue Problems,” Annals of Nuclear Energy, Vol. 119, pp. 7-22, 2018. [link]
2. E. Biondo, P. Wilson, “Transmutation Approximations for the Application of Hybrid Monte Carlo/Deterministic Neutron Transport to Shutdown Dose Rate Analysis,” Nuclear Science and Engineering, Vol. 187, Issue 1, pp. 27-48, 2017. [link]
3. E. Biondo, A. Davis, P. Wilson, “Shutdown Dose Rate Analysis with CAD Geometry, Cartesian/Tetrahedral Mesh, and Advanced Variance Reduction,” Fusion Engineering and Design, Vol. 106, pp. 77–84, 2016. [link]
4. E. Biondo, P. Wilson, “Application of the Multi-Step CADIS Method to Fusion Energy Systems Analysis,” International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, South Korea, 2017.
5. E. Biondo, A. Ibrahim, S. Mosher, R. Grove. “Accelerating Fusion Reactor Neutronics Modeling by Automatic Coupling of Hybrid Monte Carlo/Deterministic Transport on CAD Geometry.” Joint International Conference on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method (ANS MC2015), Nashville, TN, 2015.
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2019-11-18 20:55:36
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https://www.ias.ac.in/listing/bibliography/pram/G._Sridhar
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• G Sridhar
Articles written in Pramana – Journal of Physics
• Physics and technology of tunable pulsed single longitudinal mode dye laser
Design and technology demonstration of compact, narrow bandwidth, high repetition rate, tunable SLM dye lasers in two different configurations, namely Littrow and grazing incidence grating (GIG), were carried out in our lab at BARC, India. The single longitudinal mode (SLM) dye laser generates single-mode laser beams of $\sim 400$ MHz (GIG configuration) and $\sim 600$ MHz (Littrow configuration) bandwidth. Detailed performance studies of the Littrow and GIG dye laser resonators showed that GIG dye laser results in narrower linewidth and broad mode hop free wavelength scanning over 70 GHz. In this paper we present experimental studies carried out on the high repetition rate SLM dye laser system.
• Cavity ring-down technique for measurement of reflectivity of high reflectivity mirrors with high accuracy
A simple, accurate and reliable method for measuring the reflectivity of laser-grade mirrors ($R$ > 99.5%) based on cavity ring-down (CRD) technique has been success-fully demonstrated in our laboratory using a pulsed Nd:YAG laser. A fast photomultiplier tube with an oscilloscope was used to detect and analyse the CRD signal. The cavity decay times were measured for three cavities formed by a combination of three mirror pairs. The absolute reflectivities $R_{1}$, $R_{2}$, $R_{3}$ were determined to be 99.94%, 99.63%, 99.52% at normal incidence. The reflectivity of mirrors is measured to an accuracy of 0.01%.
• Temporal dynamics of high repetition rate pulsed single longitudinal mode dye laser
Theoretical and experimental studies of temporal dynamics of grazing incidence grating (GIG) cavity, single-mode dye laser pumped by high repetition rate copper vapour laser (CVL) are presented. Spectral chirp of the dye laser as they evolve in the cavity due to transient phase dynamics of the amplifier gain medium is studied. Effect of grating efficiency, focal spot size, pump power and other cavity parameters on the temporal behaviour of narrow band dye laser such as build-up time, pulse shape and pulse width is studied using the four level dye laser rate equation and photon evolution equation. These results are compared with experimental observations of GIG single-mode dye laser cavity. The effect of pulse stretching of CVL pump pulse on the temporal dynamics of the dye laser is studied.
• Measurement of flow fluctuations in single longitudinal mode pulsed dye laser
A simple technique had been demonstrated for measuring flow-induced fluctuations in the single longitudinal mode (SLM) pulsed dye laser. Two prominent frequency components of 10.74 Hz and 48.83 Hz were present in the output of the Nd:YAG-pumped SLM dye laser. The flow-induced frequency component of 48.83 Hz was present due to the revolution per minute of the motor attached to the magnetically coupled gear pump. The time average bandwidth of 180 MHz has been obtained for this SLM dye laser. The effect of pump pulse energy on the bandwidth of the SLM dye laser was studied. The bandwidth of the SLM dye laser was increased to 285 MHz from 180 MHz, when the pump pulse energy was increased to 0.75 mJ from 0.15 mJ for a constant dye flow velocity of 0.5 m/s.
• # Pramana – Journal of Physics
Volume 94, 2020
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019
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2021-01-23 08:23:42
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http://www.solutioninn.com/libra-company-is-purchasing-100-of-the-outstanding-stock-of
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# Question
Libra Company is purchasing 100% of the outstanding stock of Genall Company for \$700,000. Genall has the following balance sheet on the date of acquisition:
Appraisals indicate that the following fair values for the assets and liabilities should be acknowledged:
Accounts receivable . . . . . . . . . . . . . . . \$300,000
Inventory . . . . . . . . . . . . . . . . . . . . . . . . 215,000
Property, plant, and equipment. . . . . . . 700,000
Computer software . . . . . . . . . . . . . . . . 130,000
Current liabilities . . . . . . . . . . . . . . . . . . 250,000
Bonds payable . . . . . . . . . . . . . . . . . . . 210,000
1. Prepare the value analysis schedule and the determination and distribution of excess schedule.
2. Prepare the elimination entries that would be made on a consolidated worksheet prepared on the date of purchase.
Sales4
Views149
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2016-10-21 17:01:40
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http://rebo.ruhoh.com/why-dci-contexts/
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In a recent reddit post and more generally on his website, Gregory Brown raised some valid issues with DCI and in particular queried the value of DCI contexts to represent use-cases.
In this article I will do my best to present some reasons as to why Contexts can be useful.
### What is a Context in DCI?
When programming in DCI style a context declares an interaction between a set of objects. It does this by assigning objects roles, these objects then interact as their roles.
Usually a Context is a class which is initialised with role-playing objects, then called with the parameters of the interaction.
### Not a new idea
The idea of using Contexts to govern interactions between objects is not a new one. The concept that we can organise system behaviour into encapsulated procedures is a very common one in programming.
For instance Transaction Scripts are one way of organising an interaction between different components of a system.
### Coding without Contexts
When not using a context to organise object interactions we are relying on our classes and objects to work together to implement our use-cases. This isn't necessarily bad if our classes are simple and easily understandable.
For instance in the following code we may be writing code for an online store. We need an invoice to be generated when a product is bought.
Product = Struct.new(:name, :price, :description)
Invoice = Struct.new(:address, :details, :total) do
def print
p "#{details}, sent to: #{address}, totalling #{total}"
end
end
class User
@name = name
@purchases = []
end
purchases << product
end
end
class Accounts
def initialize
@invoices = []
end
description = "#{product.name} - #{product.description} @ #{product.price} ea."
total = product.price
invoice = Invoice.new(address, description, total )
@invoices << invoice
invoice
end
end
pants = Product.new("red pants", 10.0, "A Pair of nice red pants")
user = User.new("Prince Charles", "Buckingham Palace")
accounts = Accounts.new
p invoice.to_s
A user, is sent the #buy_product method to store that product in his list of purchased items. The purchased item is then passed to the #generate_invoice method of the accounts department, this then triggers an invoice to be created which gets stored in the accounts departments @invoices array. Finally the invoices is printed to screen with Invoice#print
The program flow is spread throughout the methods on the classes.
No, not really.
Programmers have been coding like this forever and it mostly works well. However, I suspect it's fairly common for good practice to emerge:
• Commonly called chains of methods are grouped together.
• Methods will only be passed parameters that they can handle.
• Shared methods may be extracted to a mix-in.
• Internally called methods are hidden as private.
Look at my calling of the above classes, I call User#buy_product, then Accounts#generate_invoice and finally Invoice#print. I dare say, in a full blown application, a similar order of method calls will be repeated in some form and quite possibly listed in its own method or class. Sounds kinda like a context to me.
In-fact when you think about it we are almost always writing code in a context. When writing a method I'm thinking under what circumstances might this method will be called, what parameters might it receive, who might send them. We are always referring to some context, even if its an implicit one. Even if we don't actually identify contexts as such we use them all the time, for instance ActionController methods can be considered a form of a context.
In my opinion, contexts are synonymous with Commands, or Queries, or Tests, or even View Presenters. They are any explicit codified instruction to carry out object interactions in a clear and understandable way.
### So why DCI Contexts?
I think DCI contexts can enable many of the best practices that we try to do when writing code:
• In a DCI Context, by definition, order of execution is defined explicitly.
• Methods are limited to roles within a context.
• Shared methods are put into roles.
• We know what parameters will be passed between objects because we control the entire interaction.
In addition to encouraging good practice, DCI Contexts have some other advantages:
• As use-case behaviour is encapsulated in a context object, we can easily swap out behaviour in our system.
• Use-cases become a testable unit. The number of pathways that need to be tested in code is reduced because a use-case can be tested in an isolated way.
• We can make changes to one use-case without affecting or breaking any of the others in our system.
### Some Code Examples
To be honest, I'm not sure how best to write this section. Example code can often be far too simplistic and not show the benefits of using a particular technique, or it becomes too domain specific and the approach is lost in the details. I'll present a few examples of simple use-cases, and then an extract from some existing code.
Lets consider the scenario above, and rewrite it in DCI style. I want to be able to show how we can naturally move from domain objects, to easily implementable use-cases. As with all my DCI stuff I am using my AliasDCI library, it is a proof of concept only, in order to get the principles of DCI working in ruby as much as possible.
We start with the domain objects, these are User, Product, Accounts, & Invoice classes without any behaviour.
class User
@name = name
@purchases = []
end
end
Product = Struct.new(:name, :price, :description)
class Accounts
def initialize
@invoices = []
end
end
[User, Product, Invoice, Accounts].each{|k| k.send :include, AliasDCI::DataObject}
These objects are about as simple as you can get. Very easy to understand as they have no behaviour or interacting methods. This is what the "System Is" the contexts will provide what the "System Does".
Now we can begin to write contexts in a straightforward way to implement the following requirements
#### Story: Purchase process
• In order to keep track of purchases
• As an accounts department
• I want to manage invoices when a product is bought
#### Scenario 1: Invoices should be stored in the accounts department
General requirement:
• When a product is purchased by a customer
• An invoice is created and stored in accounts
As a test:
1. Given a customer has selected red pants costing £10
2. When he buys red pants
3. Then I should have an invoice totalling £10
Writing the context directly as per the use-case:
class PurchasingProcess
include AliasDCI::Context
def initialize(user, product, accounts)
assign_named_roles(:customer => user,
:selected_product => product,
:accounts_department => accounts)
end
def call
in_context do
accounts_department.generate_invoice
end
end
role :customer do
purchases << selected_product
end
end
role :selected_product do
def invoice_desc
"#{name} - #{description} @ #{price} ea."
end
end
role :accounts_department do
def generate_invoice
invoice = Invoice.new(customer.address, selected_product.invoice_desc, total )
invoices << invoice
end
end
end
The above context is independent of my domain objects, it is self contained and it cannot affect any other use-case or code in my application. The PurchasingProcess instance simply becomes a 'blackbox' that mutates our domain objects. This can be tested independently from the rest of the system. There are no side-effects as our domain objects do not have behaviour.
Because we are strictly implementing a specific interaction it doesn't hugely matter that these methods are coupled. This is because this logic is executing only within this context. All the code is in front of us, and we don't need to worry too much about making methods generic so they can be used in different circumstances.
There isn't any risk of other object's calling the accounts department's #generate_invoice method or the customer's #buy_product method because they don't exist anywhere else. The methods can be written purely to deliver this use-case.
In theory I could delete the above code, and nothing else would break in my application.
The other advantage of DCI contexts is that they can be versioned and/or forked. Maybe during the holiday sales season there needs to be a different purchasing process. With a DCI context it is as simple as instantiating HolidaySalesPurchasProcess#new instead of the regular PurchaseProcess. This lets us modularise our business processes.
#### Scenario 2: Product is on Sale
• When an on-sale product is bought
• The invoice amount is reduced by 10%.
As a test:
1. Given a customer has selected a samsung phone costing £300
2. And samsung products are on sale
3. When he buys the phone
4. Then I should have an invoice for £270
To deliver this we add a #on_sale? method to the selected_product role, to return true if that item is on sale. We also modify the invoice generation method in the accounts_department role.
# in selected_product role:
def on_sale?
['samsung', 'nokia'].any? {|s| name.include?(s)}
end
# in accounts_department role:
def generate_invoice
total = selected_product.price
total *= 0.9 if selected_product.on_sale?
...
end
Every new use-case or requirements generally adds or modifies methods in our system. If we were not using DCI Contexts then these methods would usually be added to class files. The class files grow, and methods get shared between use-cases. If not careful unintended coupling can then occur because modifying the code that implements one use case can affect another.
Uncessary methods can also get added to classes, for instance why does the User class really need an #buy_product method? That method only really makes sense in a purchasing context.
#### Story: Customers are charged for engineer visits. (Yes, a very mean business!)
General requirement:
• When an engineer is sent to a customer to fix a broken product
• An invoice is created and saved in the accounts department
As a test:
1. Given a customer has already purchased a DVD Player
2. And I currently have an accounts department
3. When a £100 a day engineer is sent to fix his DVD Player
4. Then I should email the user to confirm attendance
5. And I should have an invoice totalling £100
Here we write a context in a straightforward way, we do not need to worry with clashing with previous code we've written, as its in a separate context.
class EngineerCallOut
include AliasDCI::Context
def initialize(customer, product, accounts)
assign_named_roles(:customer => customer,
:purchased_item => product,
:accounts_department => accounts)
end
def call( callout_rate )
in_context do
customer.confirm_attendance
accounts_department.generate_invoice(callout_rate)
end
end
role :customer do
def confirm_attendance
p "Emailing user:#{name} - An engineer has been booked to fix your #{purchased_item.name}"
end
end
role :purchased_item
role :accounts_department do
def generate_invoice(callout_rate)
description = "Call out charge for engineer to fix #{purchased_item.name}"
invoices << invoice
end
end
end
As you see in this instance, our accounts department has a different generate_invoice method. This is perfectly fine, we do not need to worry about existing behaviour on the Accounts class because there is none.
### Summary
In the above examples we added two processes to our system, a purchasing process and an engineer callout process. The processes are completely independent from each other, and behaviour in one does not affect the other, even when similar entities like invoices are being generated.
Furthermore these processes are largely decoupled from our domain objects, only relying on exposure of a few key properties. Instead of sending an engineer to a user, we can actually send an engineer to any object that has a name and an address:
starbucks = Company.new(:name => "Starbucks", :address=>"1 Times Square", :company_id => "666", :business_category=> "Coffee and Food")
EngineerCallOut.new(starbucks, dvd_player, accounts).call(200)
### A Context In Use
Below is an example of a context I am currently working on for a maintenance firm. It gets Jobs and Faults and needs to register and monitor them, eventually attending jobs and closing out faults.
With this command handler, I have segregated all of this logic from the rest of my system. I can isolate and test it, and I know as long as I call it with job_attributes and fault_attributes My entities will be created as expected. It is also independent from the web-stack, so this plus the domain objects can be used in rails, or Sinatra, or just plain ruby files.
I will leave this article at that, I hope I've presented some ideas as to why DCI contexts may be useful when developing applications with multiple use-cases.
class CreateJobWithFaultCommandHandler
include AliasDCI::Context
#
# The interface to the command, accepts job_attribute and fault_attributes hash
#
def self.execute(job_attributes, fault_attributes)
command_handler = self.new(job_attributes, fault_attributes)
command_handler.call
end
#
# Initializes a blank new job, new fault as roles.
#
def initialize(job_attributes, fault_attributes)
@job_attributes = job_attributes
@fault_attributes = fault_attributes
assign_named_roles(:new_job => Job.new , :new_fault => Job::Fault.new ,:command => self)
end
#
# The logic of the command, checks for pre existing fault, assign job attributes
# and assign's the fault to the new job, then saves the job and the fault.
def call
in_context do
unless pre_existing_fault?
new_job.assign_attributes
new_fault.assign_attributes
new_job.assign_fault
new_job.persist
else
fail OpManError.new("Cannot Create Job as Fault Number already exists.")
end
end
end
# The new_job role, responsible for assigning a fault, and persisting
# the job & fault
role :new_job do
def assign_attributes
self.status = :open
self.location = command.job_attributes[:location]
self.description = command.fault_attributes[:description]
self.site = command.job_attributes[:site]
self.contract = command.job_attributes[:contract]
self.client = command.job_attributes[:client]
end
def assign_fault
self.fault = new_fault
new_fault.job = self
end
def persist
Job.transaction do
self.save
new_fault.save
end
end
end
#
# The new fault role stores a description and a fault number
#
role :new_fault do
def assign_attributes
self.status = :open
self.description = command.fault_attributes[:description]
self.fault_no = command.fault_attributes[:fault_no]
end
end
#
# The command context, checks for pre_existing fault
#
role :command do
def pre_existing_fault?
fault_no = fault_attributes[:fault_no]
Job::Fault.first(:fault_no => fault_no) ? true : false
end
end
end
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2016-05-02 08:14:45
|
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|
https://eeebooks4u.wordpress.com/category/engineering-mathematics/fourier-series/
|
# Basics of Fourier Series
$latex \Rightarrow &s=2 &bg=ffffff$ Fourier series is used for representing the Periodic power signals. $latex \Rightarrow &s=2 &bg=ffffff$ In Fourier series, a periodic signal is expanded in terms of its harmonics which are sinusoidal or complex exponential and orthogonal to each other. Types of Fourier Series Trigonometric Fourier Series \$latex \displaystyle x(t) = a_0 + \sum_{n=1}^{\infty} [a_n cos(n … Continue reading Basics of Fourier Series
# Fourier Series
Fourier series is used for representing the Periodic Power signal, the Periodic power signal is expanded in terms of its harmonics which are sinusoidal or complex exponential and orthogonal to each other. Fourier series for any sinusoidal signal is signal itself. Types of Fourier Series 1). Trigonometric Fourier Series:- 2). Complex Exponential Fourier Series:- Cn → Complex Exponential … Continue reading Fourier Series
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2019-02-21 18:03:05
|
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|
https://www.physicsforums.com/threads/electric-field-of-a-charged-disc.594825/#post-3858410
|
# Electric field of a charged disc
... with constant charge density σ = Q/((pi)a^2)
The Electric field is, after some calculation, is given by E_p below:
z is the z-axis, and a is the radius of the disc.
Now for the questions at the bottom of the page, here are my thoughts:
σ is independent of a because as a->2a, Q->4Q, and a^2 -> 4a^2. Same for all changes of scale.
As a -> infinity, E_p -> σ/(2ε_0)
But the second one I'm not sure about.
As a -> 0, surely the charge density stays constant i.e. at σ. Thus the field appears to be the 0 vector. However, we know that the field due to a point charge is proportional to r^/r^2, where r^ is the outward/inward unit vector and r is it's magnitude.
I know our area tends to 0 as a -> 0, so our charge Q must tend to 0 also. But this means our field from the "point charge" must be 0, disagreeing with the usual electric field for a point charge...
## Answers and Replies
Philip Wood
Gold Member
Regarding the second question, you've thrown away the baby with the bath-water, when taking your limit. You need to work to first order in (a/z)2...
$$\frac{1}{\left(z^2+a^2\right)^\frac{1}{2}} = \frac{1}{z}\left(1+\frac {a^2}{z^2}\right)^{-\frac{1}{2}}\approx\frac{1}{z}\left(1-\frac {a^2}{2z^2}\right).$$
Make this substitution, and you'll finish up with the usual equation for the field due to a point source.
Last edited:
Right. At first I tried taylor series at x=0 but didn't try it at x = infinity. I guess I hadn't come across using expansion about infinity in physics yet... only complex analysis.
Maybe there is something simple I am missing but why do you automatically look for expansion about infinity?
Attempt to answer own question: because we are taking limit of a tending to 0. Expansion about z = 0 is a polynomial in z with a^i on the bottom, so the expansion will be something like infinity - infinity + infinity - ... which won't help us. Using expansion about infinity, we get a^i's on top and so the limit as a -> 0 is valid and useful. Amirite?
Also, your ways works because the 1/z's cancel, giving the simple answer, as opposed to a polynomial in z, where we can't make progress without taking steps backwards...
Last edited:
Philip Wood
Gold Member
I'm not regarding it as an expansion about infinity. I'm regarding (a/z), and therefore (a/z)2 as << 1, and expanding about (a/z) = 0. This amounts to using the binomial series (a special Taylor series), which is what I'm quoting, to first order in (a/z)2.
Last edited:
I'm not sure I get that at all. Are you sure you're not considering (a/z)^2 and therefore (a/z)^4 << 1 and similar for higher order terms? Because then the Binomial expansion formula would seem to work. I'm not used to using it with the exponent non-integer.
What I said in my last post is basically just writing out the Taylor series which is the same as the Binomial expansion because the Binomial expansion is the special case of Taylor we are dealing with...
Philip Wood
Gold Member
I am, as I said, taking the case of (a/z)<<1. This implies that (a/z)2<<<1 and (a/z)4<<<< 1, and so on. Therefore I'm neglecting all terms higher than the one in (a/z)2. It was one of Newton's discoveries that the binomial expansion also worked with non-integral indices, but went on for ever. It is extremely useful in Physics.
$$(1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 ...$$
Last edited:
I see. Considering (a/z)<<1 or instead considering (a/z)^2<<1 leads to the same result (no information is lost w.r.t. the Binomial expansion approximation). But in both cases x = (a/z)^2
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2021-11-30 18:21:53
|
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|
https://antontarasenko.com/2015/08/15/growth-diagnostics-in-russia-getting-started/
|
# Growth Diagnostics in Russia: Getting Started
I’m going to do a couple of case studies in growth diagnostics. The first country is Russia for reasons I’ll explain in the next post. The second country is likely to be China, but you’re still free to send your suggestions.
I’m using a constraint analysis framework by Hausmann–Rodrik–Velasco (HRV). HRV developed a comprehensive, yet structured, framework with a 10-year record of practical applications. It includes a formal model and handy heuristics. It’s also compatible with the literature on growth factors, such as physical and human capital.
# The Formal Model
The formal model comes from HRV (2004) — an early draft that still contains all the math of an augmented neoclassical model of economic growth. The equation of interest:
where $r$ is the return on capital defined as
The first equation describes accumulation of capital and consumption under distortions. The distortions are denoted with the Greeks and fall into five categories:
A very formal approach would require picking values for these parameters and simulating the model to compare it with actual values of consumption and capital. A well-calibrated model would predict responses to the changes in the parameters, which would immediately reveal the constraint. I won’t follow this approach because some parameters have no direct or estimable counterparts in the data.
Instead, I’m using this formal model for discipline and test candidate constraints with heuristics. The summary so far:
# Heuristics
The shortcut to growth constraints is a useful table from HRV (2008):
Compared to the formal model, this table includes human capital and specific tests for each constraint mentioned in the header.
Estimating the responses to constraints may be challenging. For example, if you have an indicator for expropriation, you can’t readily say by how much an increase in “expropriation” would reduce economic growth. There’s no universal solution to this problem. For this, I’ll focus on constraints we can estimate with reasonable confidence.
# The Helpers
A candidate for the binding variable is often a compromise among different priorities. The interest rate has to balance inflation and unemployment. Taxes raise some costs via taxation and reduce other costs via public goods. Macro stability after government spending cuts may be followed by political instability.
In this case, growth diagnostics would send contradictory signals. You must increase and decrease the same variable simultaneously! This seems possible in politics, but not in mathematics. To clarify such ambiguities, constraint testing requires a few more models.
Though the list of models is open, most of the job is done by a few conventional macro tools.
# The Next Post
In the text post, I’ll briefly review the Russian economy and challenges it poses to growth diagnostics.
The entire case study will be accompanied with the replication files, which I try to make suitable for an immediate replication for any other major economy.
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2018-10-19 00:26:05
|
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|
https://gmatclub.com/forum/for-integers-a-b-c-x-y-and-z-x-a-b-c-z-b-y-x-and-a-248302.html
|
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# For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a >
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For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > [#permalink]
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30 Aug 2017, 23:21
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For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > z. Which of the following is the median of the six integers?
A. z−a
B. (x+y)/2
C. (a+z)/2
D. z
E. (c−y)/2
_________________
Director
Joined: 18 Aug 2016
Posts: 631
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > [#permalink]
### Show Tags
30 Aug 2017, 23:31
Bunuel wrote:
For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > z. Which of the following is the median of the six integers?
A. z−a
B. (x+y)/2
C. (a+z)/2
D. z
E. (c−y)/2
y>x>a>z>b>c
(a+z)/2
C
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Luckisnoexcuse
Senior Manager
Joined: 07 Jul 2012
Posts: 343
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > [#permalink]
### Show Tags
31 Aug 2017, 00:09
x>a and a>z
Thus, x>a>z
x>a>z and y>x
Thus, y>x>a>z
y>x>a>z and z>b
Thus, y>x>a>z>b
y>x>a>z>b and b>c
Thus, y>x>a>z>b>c
Since there are 6 items in the series
Median= $$\frac{(3rd item+4th item)}{2}$$= $$\frac{(a+z)}{2}$$
Kudos please if you like my explanation!
_________________
Kindly hit kudos if my post helps!
Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > [#permalink]
### Show Tags
31 Aug 2017, 03:58
Given that :
x>a
b>c
z>b
y>x
a>z
If we combine all 5 given equations we can write : y>x>a>z>b>c
Now we have 6 terms.. so median will be average of center 2 terms, ie average of 3rd and 4th term
( if no. of terms odd, median is center term, if no. of terms even median is average of center 2 terms)
our series is : y>x>a>z>b>c So center 2 terms are : a and z
Median = (a+z)/2
SC Moderator
Joined: 22 May 2016
Posts: 1837
For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > [#permalink]
### Show Tags
31 Aug 2017, 16:34
Bunuel wrote:
For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > z. Which of the following is the median of the six integers?
A. z−a
B. (x+y)/2
C. (a+z)/2
D. z
E. (c−y)/2
x > a
b > c
z > b
y > x
a > z
To find the greatest and least variables in a sequence, look for the variables that show up only one time on list above, e.g..
Here, those variables are y (the greatest) and c (the smallest). Start on one end, high or low: y > x. Now find x on left side. x > a. Find "a" on left side, etc.
Reverse the process on the low end. c is the smallest number. c < b. Look on right side for b. b < z, etc.
c < b < z < a < x < y
For an even number of terms, the median is the average of the middle two:
$$\frac{a + z}{2}$$
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Affiliations: Target Test Prep
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Re: For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > [#permalink]
### Show Tags
02 Sep 2017, 07:20
Bunuel wrote:
For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > z. Which of the following is the median of the six integers?
A. z−a
B. (x+y)/2
C. (a+z)/2
D. z
E. (c−y)/2
Using the given information, we can determine the following:
c < b < z < a < x < y
Thus, the median is (z + a)/2.
_________________
Jeffery Miller
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
Re: For integers a, b, c, x, y, and z, x > a, b > c, z > b, y > x, and a > &nbs [#permalink] 02 Sep 2017, 07:20
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# Events & Promotions
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
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2018-07-23 10:09:37
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5390040278434753, "perplexity": 2998.6481449450516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676596204.93/warc/CC-MAIN-20180723090751-20180723110751-00127.warc.gz"}
|
http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1186.30037
|
Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
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Display: entries per page entries
Zbl 1186.30037
Xu, Junfeng; Han, Qi; Zhang, Jilong
Uniqueness theorems of meromorphic functions of a certain form.
(English)
[J] Bull. Korean Math. Soc. 46, No. 6, 1079-1089 (2009). ISSN 1015-8634
Author's abstract: We show that, for any entire function $f$ and all positive integers $m, n\in \Bbb{N}$, possibly except for the special case $m=n=1$, the function $f^m(f^n-1)f^{\prime}$ has no non-zero finite Picard value. Furthermore, we show that, for any two non-constant meromorphic functions $f$ and $g$, if $f^m(f^n-1)f^{\prime}$ and $g^m(g^n-1)g^{\prime}$ share the value 1 weakly, then $f\equiv g$ provided that $m$ and $n$ satisfy some conditions. In particular, if $f$ and $g$ are entire, then the restrictions on $m$ and $n$ can be greatly reduced.
[Kazuya Tohge (Kanazawa)]
MSC 2000:
*30D35 Distribution of values (one complex variable)
30D20 General theory of entire functions
30D30 General theory of meromorphic functions
Keywords: entire function; meromorphic function; Picard value
Highlights
Master Server
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2013-05-21 12:53:45
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8477325439453125, "perplexity": 1215.628334825965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368700014987/warc/CC-MAIN-20130516102654-00084-ip-10-60-113-184.ec2.internal.warc.gz"}
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https://codereview.stackexchange.com/questions/10125/making-a-flat-file
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Making a flat file
Source XML (since I haven't bothered with a schema):
<?xml version="1.0"?>
<ContactDetails>
<Names>
<FullName>
Nicholas Example
</FullName>
<AltName context="Nickname">
Nick
</AltName>
<AltName context="Online">
oxinabox
</AltName>
</Names>
<Phones>
<Phone context="Mobile">04 1234 1234</Phone>
</Phones>
Contrived Apartments
<number> 5 </number> <street>Some Rd</street>
<town>Newtown</town> <state>ST</state>
<Emails>
<Email context="Work">examplen@work.com</Email>
<Email context="Personal">nick99@ManMail.com</Email>
</Emails>
<Websites>
<Website>http://www.a2b3c4.com</Website>
</Websites>
<Banking>
<BankAccount context="Everyday"
Name="Nicholas Example"
BSB="123 123"
AccountNumber="111 222 333" />
</Banking>
</ContactDetails>
and here is the actual XSLT I would like a review of. It is supposed to turn the XML in to a human readable flat file (and does except for addresses which I am still working on):
<?xml version="1.0" ?>
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:fn="http://www.w3.org/2005/xpath-functions"
>
<xsl:output
method="text"
omit-xml-declaration="yes"
indent="no"
media-type="text/plain"/>
<xsl:strip-space elements="*"/>
<xsl:template match="ContactDetails">
<xsl:apply-templates/>
</xsl:template>
<xsl:template match="Names">
<xsl:value-of select="FullName"/>
<xsl:for-each select="AltName">
<xsl:text> AKA </xsl:text><xsl:value-of select="normalize-space(.)"/>
</xsl:for-each>
<xsl:text>
</xsl:text>
</xsl:template>
<xsl:template match="//Phone">
<xsl:text>
Ph (</xsl:text><xsl:value-of select="@context"/> <xsl:text>): </xsl:text>
<xsl:value-of select = "."/>
</xsl:template>
<xsl:template match="//Email">
<xsl:text>
Email (</xsl:text><xsl:value-of select="@context"/> <xsl:text>): </xsl:text>
<xsl:value-of select = "."/>
</xsl:template>
<xsl:template match="//Website">
<xsl:text>
Website: </xsl:text>
<xsl:value-of select = "."/>
</xsl:template>
<!-- <xsl:value-of select ="."/>
<xsl:for-each select="*">
<xsl:value-of select = "."/>
<xsl:if test="fn:name(.)=town">
<xsl:text>, </xsl:text>
</xsl:if>
</xsl:for-each>
-->
</xsl:template>
<xsl:template match="Banking">
<xsl:text>
Bank Details:
------------
</xsl:text>
<xsl:for-each select="BankAccount">
<xsl:value-of select="@context"/> <xsl:text> Account: </xsl:text>
<xsl:value-of select="@BSB"/>-<xsl:value-of select="@AccountNumber"/>
</xsl:for-each>
</xsl:template>
</xsl:stylesheet>
• I tend to like email addresses in First Last <name@place.domain> format. It lets me easily select just the name. And if I select the whole thing their name shows up in the outgoing email and my mail software will remember them by their name. – Omnifarious Mar 18 '12 at 15:45
<xsl:output
method="text"
omit-xml-declaration="yes"
indent="no"
media-type="text/plain"/>
Consider using XSLT 2.0, which can't hurt but could help if you need a XSLT 2.0 function in the future. Also note that you don't need omit-output-declaration since you're outputing text. Ditto for indent.
<xsl:template match="ContactDetails">
<xsl:apply-templates/>
</xsl:template>
This is the default template for every element, which means it's not needed.
<xsl:template match="//Email">
Why the //? It makes more sense without it, eg. match="Email". This applies to all your templates.
<xsl:text>
Ph (</xsl:text><xsl:value-of select="@context"/> <xsl:text>): </xsl:text>
<xsl:value-of select = "."/>
You're using xsl:text too much. This could become:
Ph (<xsl:value-of select="@context"/>): <xsl:value-of select = "."/>
Besides, I'm not sure context is a good choice for an attribute name. "Context node" already has a specific meaning in XSLT.
• When shound/shouldn't I use xsl:text? – Lyndon White Mar 18 '12 at 23:40
• I personally only use it to introduce \n to my output. – Quentin Pradet Mar 19 '12 at 7:19
• It seems ifiremoveany of the xsl:text tags I start seeing strange new lines next to every piece of text I put in – Lyndon White Mar 19 '12 at 11:51
• XSLT 2.0 engines are is so incredibly rare. To my knowledge the only freeone is Saxon. – Lyndon White Feb 10 '15 at 14:47
you should really work on the indentation of your code, there is nothing worse than trying to read code that isn't properly indented.
<xsl:template match="Names">
<xsl:value-of select="FullName"/>
<xsl:for-each select="AltName">
<xsl:text> AKA </xsl:text><xsl:value-of select="normalize-space(.)"/>
</xsl:for-each>
<xsl:text>
</xsl:text>
</xsl:template>
What it should look like
<xsl:template match="Names">
<xsl:value-of select="FullName"/>
<xsl:for-each select="AltName">
<xsl:text> AKA </xsl:text>
<xsl:value-of select="normalize-space(.)"/>
</xsl:for-each>
<xsl:text>
</xsl:text>
</xsl:template>
Again, Yours
<xsl:template match="//Phone">
<xsl:text>
Ph (</xsl:text><xsl:value-of select="@context"/> <xsl:text>): </xsl:text>
<xsl:value-of select = "."/>
</xsl:template>
Proper
<xsl:template match="//Phone">
<xsl:text>Ph (</xsl:text>
<xsl:value-of select="@context"/>
<xsl:text>): </xsl:text>
<xsl:value-of select = "."/>
</xsl:template>
there is nothing worse than having to stop and think to see what is nested inside of what. some people have a different style of indenting but what you have posted looks very confusing.
another proper way to write the Phone Template
<xsl:template match="//Phone">
<xsl:text>
Ph (
</xsl:text>
<xsl:value-of select="@context"/>
<xsl:text>
):
</xsl:text>
<xsl:value-of select = "."/>
</xsl:template>
I know this was nitpicky but it helps to keep your code organized in a similar manner to other people that will be reviewing your code, debugging your code, or adding to your code, so that they can understand what is going on quickly.
(most of this you probably already know and just had a fun time trying to get your code to paste right into the Code Review Question box)
• Actually, my indenting is that way, because I have constant worries and issues with ensuring that my output in not indented/ line broken in the wrong place. Especially since the output format is a flat file, and so I can not rely on xhtml to only acknowledged <br> and to remove an needed whitespace. It may be my paranoia was for nothing. – Lyndon White Nov 17 '13 at 2:21
• @Oxinabox, have you tried it this way? don't use the last example. I could see how that last example would add newlines in your flat file. but the other "proper" examples shouldn't do that. because the static text is inside of text tags – Malachi Nov 17 '13 at 5:22
• I don't know this was over 18 months ago – Lyndon White Nov 17 '13 at 7:04
|
2021-05-07 23:16:32
|
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|
https://www.electro-tech-online.com/threads/led-voltage-meter-lm339-design-question.103616/
|
# LED voltage meter LM339 design question
#### namezero111111
##### New Member
Hello folks,
I just registered for this forum.
I am trying to design a circuit to determine lead-acid battery charge level.
I determined that at 77*F, a 100% charge would be 12.63V, and a 50% charge would be 12.00v.
I also have data for every 10%.
I designed the circuit as indicated in the attached file, and have tested it in LTspice, which indicates that the circuit would work (see the second picture).
However, I believe that this circuit is very difficult to built (it seems cumbersome). I have read about the LM3914 (?) that can be used to drive a bar display, but I don't think it could measure such small voltage changes that are also non-linear.
So I was wondering, if I were to build this, is there any better way than using odd resistors like 6579 or 7353 ohms? I'd have to be very close to those values so that the bar display is reasonably accurate.
I've also seen designs where the voltage divider on the measured side is "cascaded" instead of every comparator having its own little voltage divider. If I were to make such a design, how would I calculate the values of the resistors required?
Do you see any problem with the design as is? I might be worried about the low current in the diodes as indicated on the diagram, would that be a problem?
-namezero
#### Attachments
• 180.4 KB Views: 444
• 186.8 KB Views: 832
• 9.1 KB Views: 239
Last edited:
#### ericgibbs
##### Well-Known Member
hi,
The LM3914 can be 'offset' such that it works over a limited range of input voltage.
eg: can be set for 11V thru 13V, so that the 10 LED's represent a 2Volt input span.
Is this what you have in mind.?
EDIT:
Check the polarity of the LED's in your schematic, they are the wrong way around.
Last edited:
#### namezero111111
##### New Member
Indeed they were. I didn't know the LM339 couldn't source current. I found that in another thread. That way around it seems to work. But now the the lights come on when the voltage is BELOW the threshold, not above it.
When I swap the +/- inputs on the 339, LTspice shows some dramatic noise where is oscillates back and forth on the transition, even if I put a resistor for hysteris in there.
The reason I was using the 339 and not the 3914 is that this way I can learn a lot more about what is going on instead of using a microcontroller and having no idea. I'm also trying to advance myself a little in the field of simple electronics : )
And by the way, the way you drew the circuit looks so much cleaner!!
So I guess my only question remains, how would one better approximate the values of the resistors?
My idea was to use a math program called Derive6 and ruthe voltage divider formula through it.
(i.e. 5.0 = 12.36 * R1/(R1+R2) and then create a table with R1 in 100 ohm steps or so and looks for a value where I can match R2.
But I am sure there is a better solution out there.
Thank you again!
-namezero
#### ericgibbs
##### Well-Known Member
So I guess my only question remains, how would one better approximate the values of the resistors?
My idea was to use a math program called Derive6 and ruthe voltage divider formula through it.
(i.e. 5.0 = 12.36 * R1/(R1+R2) and then create a table with R1 in 100 ohm steps or so and looks for a value where I can match R2.
But I am sure there is a better solution out there.
Thank you again!
-namezero
hi,
The actual LM3914 uses a resistive chain to create the individual comparator reference voltages.
By driving the chain with different voltages it effects the individual switching points.
Why dont you explore that method.?
#### namezero111111
##### New Member
I want to. I am still a little confused about the resistor chain, but am looking into it right now actually.
My confusion arises from the fact that R1 for each successive 339 increases, so R2 must increase, too.
I found a document that says that V_i=i/N * V_ref for equal resistors.
I am currently looking into that, and the diagram here: here.
I need the voltages to be 12.6 12.5 12.4 12.24 12.12 12.00 11.9 11.8 volts, so there is a slight divergence from a linear relationship in the middle, and I am trying to figure out the math for the resistors in such a chain.
Thank you!
-namezero
#### ericgibbs
##### Well-Known Member
I want to. I am still a little confused about the resistor chain, but am looking into it right now actually.
My confusion arises from the fact that R1 for each successive 339 increases, so R2 must increase, too.
I found a document that says that V_i=i/N * V_ref for equal resistors.
I am currently looking into that, and the diagram here: here.
I need the voltages to be 12.6 12.5 12.4 12.24 12.12 12.00 11.9 11.8 volts, so there is a slight divergence from a linear relationship in the middle, and I am trying to figure out the math for the resistors in such a chain.
Thank you!
-namezero
hi,
Looking at your voltage list it appears to have three groupings of steps.
Why not use three Vrefs to drive three separate resistor chains, one for each group.?
Code:
[B]12.6 12.5 12.4 0.1v 12.24 12.12 12.00 [/B] .12v 11.9 11.8 0.1v [/B]
Last edited:
#### MikeMl
##### Well-Known Member
Attached is a similar circuit which required non-equally spaced trip points. However, look at the schematic. You might pick up a couple of pointers about how to add a little hysteresis at each trip point. Note how I used a behavioral voltage source to create a non-linear function.
#### Attachments
• 86.1 KB Views: 506
#### namezero111111
##### New Member
Thank you so much!
I solved the problem by placing one 100 ohm resistor in the chain and 62 ohms otherwise.
The plot for all voltages is almost identical to the one I had before with separate dividers.
I only have one problem now, that is when the diodes switch on and off I get hysteris problems over a few milliseconds. I tried adding a 220k resistor from the output to the + terminal of the comparator, but that had no effect.
Is that something that only occurs in simulation but would make no difference in real life?
It just bothers me because it causes the simulation to run very slowly.
What do you think of this circuit now?
-namezero
#### Attachments
• 223.5 KB Views: 183
• 428.7 KB Views: 252
• 6.5 KB Views: 154
#### ericgibbs
##### Well-Known Member
Thank you so much!
I solved the problem by placing one 100 ohm resistor in the chain and 62 ohms otherwise.
The plot for all voltages is almost identical to the one I had before with separate dividers.
I only have one problem now, that is when the diodes switch on and off I get hysteris problems over a few milliseconds. I tried adding a 220k resistor from the output to the + terminal of the comparator, but that had no effect.
Is that something that only occurs in simulation but would make no difference in real life?
It just bothers me because it causes the simulation to run very slowly.
What do you think of this circuit now?
-namezero
hi,
You have the INV and NI inputs crossed over, you cannot apply hysteresis from the outputs to the NI inputs because you have them decoupled to 0V via that power rail.
EDIT:
This is a simple example of an equally spaced Vgap, note the comp input sense
Use the method as shown by MikeL
Last edited:
#### namezero111111
##### New Member
I see. So where I have it connected to + I should have connected it to - and vice versa, right?
The reason I did it this way is because otherwise the diodes light up when they shouldn't and vice versa.
I had it the other way around before.
Hm maybe I am still confused as to the operation of comparators. Non-inverting is the + input right?
I am a little new to this : ) Sorry if I ask irrelevant questions.
#### namezero111111
##### New Member
Thank you! Everything works, I just built the circuit.
I had never used a computer program before, to check circuits, I didn't know they existed for free.
First time I built a circuit and it worked right away!! This is much more fun!
Thank you!
Now I will add a timer so you can push a button and the voltmeter stays on for let's say 20 seconds!
Last edited:
|
2019-04-23 06:12:20
|
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|
https://metacpan.org/pod/LaTeX::PGF::Diagram2D
|
Dirk Krause
# NAME
LaTeX::PGF::Diagram2D - Perl extension for drawing 2D diagrams.
# SYNOPSIS
use LaTeX::PGF::Diagram2D;
my $Uq = 1.0; my$Ri = 4.0;
sub I($) { my$RL = shift;
my $back =$Uq / ($Ri +$RL);
return $back; } # 10 centimeters wide, 6 centimeters high my$d = LaTeX::PGF::Diagram2D->new(10.0, 6.0);
$d->set_font_size(12.0); # R (on the x axis) is in the range 0 ... 10$d->axis('b')->set_linear(0.0, 10.0)->set_grid_step(1.0)
->set_tic_step(1.0);
# I (on the y axis) is in the range 0 ... 0,3
$d->axis('l')->set_linear(0.0, 0.3)->set_grid_step(0.05) ->set_tic_step(0.1); my$p = $d->plot('b', 'l');$p->set_xy_fct(\&I);
\$d->write("test001a.pgf");
# DESCRIPTION
The module can be used to draw 2D diagrams following DIN 461 (a german standard) for use with LaTeX. The output of the module is a *.pgf file. In your LaTeX source make sure to have
\usepackage{pgf}
in the preamble. The *.pgf files can be used with both latex/dvips and pdflatex.
Use code like
\begin{figure}%
{\centering%
\input{file.pgf}\caption{My caption}\label{blablablubb}%
}%
\end{figure}
to include the produced graphics.
None by default.
# CLASSES
The following classes are involved:
LaTeX::PGF::Diagram2D
represents a diagram.
LaTeX::PGF::Diagram2D::Axis
represents one axis of the diagram.
LaTeX::PGF::Diagram2D::Plot
represents one item to plot (a function or a point set).
# Methods
## Constructor
LaTeX::PGF::Diagram2D->new(width, height)
creates a new diagram object. Width and height of the canvas are specified in centimeters.
## Setup
set_font_size(size)
specifies the font size of the LaTeX document in point.
axis(name)
returns a reference to the LaTeX::PGF::Diagram2D::Axis object for the name. The name can be one of bottom'', left'', right'' or top'' or one of the abbreviations b'', l'', r'' or t''. The object reference can be used to invoke the setup methods for the axis, see LaTeX::PGF::Diagram2D::Axis.
## Create plot objects
plot(xaxisname, yaxisname)
creates a new plot object and saves it to the diagram. A referernce to the LaTeX::PGF::Diagram2D::Plot object is returned, this reference can be used to configure the plot object, see LaTeX::PGF::Diagram2D::Plot.
copy_plot(plotobjectreference)
duplicates a plot object and returns the reference to the new object. This is useful if you want to print i.e. a point set with an interpolation curve, so your need one object for the curve and another one for the dots.
label(xaxisname, yaxisname, x, y, text [, anchor ])
adds a text label. The axis names decide which axis the coordinates belong to. The optional anchor argument is left'', right'', top'', bottom'' or a comma-separated combination of a horizontal and a vertical position.
polyline(xaxisname, yaxisname, arrayreference)
creates a polyline object. The third parameter is a reference to an array containing the x- and y-coordinates for each point.
## Output
write(filename)
writes the graphics to the named file. If the filename suffix is .tex'' an entire LaTeX file is written, a file containing a PGF image otherwise.
|
2017-02-19 22:04:50
|
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|
https://socratic.org/questions/what-is-the-oxidation-number-of-nitrogen-in-nitrogen-gas-n-2#289900
|
# What is the oxidation number of nitrogen in nitrogen gas N_2?
$\text{Dinitrogen is zerovalent}$
At any rate, the formal oxidation number of $N$ is ZERO.
|
2022-05-18 03:39:45
|
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|
https://www.controlbooth.com/threads/hello-cb.564/
|
# Hello, cb!
#### Projectionist
##### Member
I am an actor/techie (don't kill me!), and I am new to these boards. I was refered here by a good friend of mine, Nephilim, and I just wanted to give a shout and say hello to the boards.
I am SMing an upcoming musical, and any help would be greatly appreciated.
I hope my experience on these boards can be resourceful and entertaining as well.
Projectionist
#### zac850
##### Well-Known Member
Welcome,
I use-to be an actor/techie, i even was the lead in the Christmas Carol. I was onstage for the entire show, decided that that was enough, and went to teching. Then i realized i liked it so much better...
acutely, most of my friends and the actors in the school are bi-techual (as someone posted somewhere earlier)
As always, our web-master, dvsDave will be by shortly to welcome you.
Anyway, welcome to the boards!!!
#### Projectionist
##### Member
it's good to know that people are all pretty cool around here.
#### dvsDave
##### Benevolent Dictator
Senior Team
CB Mods
Fight Leukemia
here I am to welcome you to the board!!
Don't worry about standing on both the light and dark side of the theater we have a lot of people on CB who do that!! Not an issue!
Welcome to the site, enjoy yourself, and don't be afraid to ask any question, big or small... we will answer all (should probably reword that so it doesn't sound like a dorky rhyme, but I am being lazy at the moment :roll: )
hope to see you on the board often!!
-dvsDave
#### Projectionist
##### Member
nice to meet the one and only dvsDave!
#### Nephilim
##### Active Member
Hm, whether or not to reveal Matt's greatest secret.... nah, I'll let his username speak for itself.
Glad to see you took me up on the offer Welcome aboard!
#### Projectionist
##### Member
being a projectionist is nothing to keep secret. i get paid 7.25/h to thread 4 movies (6 min total of threading) per every 2 hours! i'm living the high life!
#### wolf825
##### Senior Team Emeritus
Projectionist said:
I am an actor/techie (don't kill me!), and I am new to these boards. I was refered here by a good friend of mine, Nephilim, and I just wanted to give a shout and say hello to the boards.
I am SMing an upcoming musical, and any help would be greatly appreciated.
I hope my experience on these boards can be resourceful and entertaining as well.
Projectionist
Hiya and welcome aboard. Hope you visit and contribute often!! This is a fun site where everyone has input to the questions asked--and we welcome questions on all tech areas and backgrounds. Hope you have fun here!
-wolf
#### DMXtools
##### Active Member
I can remember when a feature film was six or more reels of 35mm film, and each theater had 2 projectors - we had to watch for cue marks (little dot that appears in the upper right corner of the frame 10 seconds before the reel ends and again just as it ends) about every 15 minutes. While the first reel was running, you'd thread the second reel on the second projector. First cue mark, start second projector. Second cue mark, open shutter on second projector, close shutter on first. Do it smoothly and accurately and nobody knows you did it. Miss a cue mark and get reamed by the manager. Then rewind reel 1 and thread reel 3 onto projector 1 and watch for reel 2's cue marks. Don't dare get interested in the film itself - that's a way to guarantee you'll miss them.
Now they splice all six regular-size reels onto this big honkin' platter and run it all through one projector. More complex to thread, but you only have to do it once per movie. Usually the cue marks are still there if you watch for them - there's still a few old-school theaters running two projectors. Those projectionists probably get more than $7.25 an hour, but there's not a lot of them left... or not a lot of places for them to work. This is by no means a put-down of your craft. The new way is easier, but you've still got to know what you're doing and what to do in case of a problem. It's honest work deserving of respect. By the way, welcome! I'm one of the older (in terms of age, not length of membership) people you'll meet here on ControlBooth. Not much help on stage management, but I try to be of assistance with sound and lighting technical questions... and I'm learning quite a bit about other aspects of technical theater, too. I look forward to seeing you around the boards. John #### Projectionist ##### Member DMXtools said: I can remember when a feature film was six or more reels of 35mm film, and each theater had 2 projectors - we had to watch for cue marks (little dot that appears in the upper right corner of the frame 10 seconds before the reel ends and again just as it ends) about every 15 minutes. While the first reel was running, you'd thread the second reel on the second projector. First cue mark, start second projector. Second cue mark, open shutter on second projector, close shutter on first. Do it smoothly and accurately and nobody knows you did it. Miss a cue mark and get reamed by the manager. Then rewind reel 1 and thread reel 3 onto projector 1 and watch for reel 2's cue marks. Don't dare get interested in the film itself - that's a way to guarantee you'll miss them. you know, I've always wondered what those marks were for, and now I know! you're the guy i give credit to. thanks! #### Nephilim ##### Active Member Projectionist said: you know, I've always wondered what those marks were for, and now I know! you're the guy i give credit to. thanks! First shutters, now cue marks... dude, seriously read the howstuffworks article you sent me; it's all in there... #### Projectionist ##### Member you picked the only two things on god's green goodness that I didn't know. fine, i'll read your little website. but I won't like it! :wink: #### HMOcidalmaniac ##### Member howdy there only$7.25?
jeez i get paid \$10 and hour to clean this ladies house-
#### DMXtools
##### Active Member
Shall I talk about how much fun it was to strike the carbon arc some of the bigger projectors (and indeed, some old-school followspots) used as a light source?
sure! go for it!
#### wemeck
##### Active Member
Welcome!! Being an actor will not be held against you, too much. Been forced to act myself while an ASM on an opera. Hope to see you around the forums.
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2021-01-28 04:46:48
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https://docs.rtems.org/branches/master/eng/coding-formatting.html
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6.3.2. Formatting¶
6.3.2.1. Rules¶
• Adhere to the Eighty Character Line Limit.
• Use spaces instead of tabs.
• Use two spaces for one indentation level.
• Put function return types and names on one line if they fit.
• Put function calls on one line if they fit.
• No space between a function name or function-like macro and the opening parenthesis.
• Put braces on the same line as and one space after the conditional expression ends.
• Put the opening brace of a function definition one line after the closing parenthesis of its prototype.
• Put a single space inside and outside of each parenthesis of a conditional expression. Exception: never put a space before a closing semi-colon.
• Put a single space before and after ternary operators.
• Put a single space before and after binary operators.
• Put no space between unary operators (e.g. *, &, !, ~, ++, --) and their operands.
• No spaces around dereferencing operators (-> and .).
• Do not use more than one blank line in a row.
• Do not use trailing white space at the end of a line.
6.3.2.2. Eighty Character Line Limit¶
Code should look good for everyone under some standard width assumptions. Where a line wraps should be the same for anyone reading the code. For historical reasons, RTEMS uses 80 characters as the maximum width for each line of code. The newline (\n) character terminating the line does not count for the 80 character limit.
If you find yourself with code longer than 80 characters, first ask yourself whether the nesting level is too deep, names too long, compound expressions too complicated, or if some other guideline for improving readability can help to shrink the line length. Refactoring nested blocks into functions can help to alleviate code width problems while improving code readability. Making names descriptive yet terse can also improve readability. If absolutely necessary to have a long line, follow the rules on this page to break the line up to adhere to the 80 characters per line rule.
6.3.2.3. Breaking Long Lines¶
The if, while, and for control statements have their condition expressions aligned and broken on separate lines. When the conditions have to be broken, none go on the first line with the if, while, or for statement, and none go on the last line with the closing parenthesis and the curly brace. Long statements are broken up and indented at operators, with an operator always being the last token on a line. No blank spaces should be left at the end of any line. The continuation of a broken line is indented by one level. Here is an example with a for loop.
for ( initialization = statement; a + really + longish + statement + that + evaluates + to < a + boolean; another + statement ) {
some_variable = a + really + longish + statement + that + needs + two + lines + gets + indented + four + more + spaces + on + the + second + and + subsequent + lines + and + broken + up + at + operators;
}
Should be replaced with
for (
initialization = statement;
a + really + longish + statement + that + evaluates + to <
a + boolean;
another + statement
) {
some_variable = a + really + longish + statement + that + needs +
two + lines + gets + indented + four + more +
spaces + on + the + second + and + subsequent +
lines + and + broken + up + at + operators;
}
Similarly,
if ( this + that < those && this + these < that && this + those < these && this < those && those < that ) {
should be broken up like
if (
this + that < those &&
this + these < that &&
this + those < these &&
this < those &&
those < that
) {
Note that each expression that resolves to a boolean goes on its own line. Where you place the boolean operator is a matter of choice.
When a line is long because of a comment at the end, move the comment to just before the line, for example
#define A_LONG_MACRO_NAME (AND + EXPANSION) /* Plus + a + really + long + comment */
can be replaced with
/* Plus + a + really + long + comment */
#define A_LONG_MACRO_NAME (AND + EXPANSION)
C Preprocessor macros need to be broken up with some care, because the preprocessor does not understand that it should eat newline characters. So
#define A_LONG_MACRO_NAME (AND + EXCESSIVELY + LONG + EXPANSION + WITH + LOTS + OF + EXTRA + STUFF + DEFINED)
would become
#define A_LONG_MACRO_NAME ( \
AND + EXCESSIVELY + LONG + EXPANSION + WITH + LOTS + OF + EXTRA + STUFF + \
DEFINED \
)
Notice that each line is terminated by a backslash. The backslash tells the preprocessor to eat the newline. Of course, if you have such a long macro, you should consider not using a macro.
Function declarations can be broken up at each argument, for example
int this_is_a_function( int arg1, int arg2, int arg3, int arg4, int arg5, int arg6, int arg7, int arg8, int arg9 );
would be broken up as
int this_is_a_function(
int arg1,
int arg2,
int arg3,
int arg4,
int arg5,
int arg6,
int arg7,
int arg8,
int arg9
);
Excessively long comments should be broken up at a word boundary or somewhere that makes sense, for example
/* Excessively long comments should be broken up at a word boundary or somewhere that makes sense, for example */
would be
/*
* Excessively long comments should be broken up at a word boundary or
* somewhere that makes sense, for example.
*/
Note that multiline comments have a single asterisk aligned with the asterisk in the opening /*. The closing */ should appear on a line by itself at the end.
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2021-03-07 05:36:07
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https://hal.inria.fr/hal-01265983v2
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# Fast computation of minimal interpolation bases in Popov form for arbitrary shifts
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We compute minimal bases of solutions for a general interpolation problem, which encompasses Hermite-Pad\'e approximation and constrained multivariate interpolation, and has applications in coding theory and security. This problem asks to find univariate polynomial relations between $m$ vectors of size $\sigma$; these relations should have small degree with respect to an input degree shift. For an arbitrary shift, we propose an algorithm for the computation of an interpolation basis in shifted Popov normal form with a cost of $\mathcal{O}\tilde{~}(m^{\omega-1} \sigma)$ field operations, where $\omega$ is the exponent of matrix multiplication and the notation $\mathcal{O}\tilde{~}(\cdot)$ indicates that logarithmic terms are omitted. Earlier works, in the case of Hermite-Pad\'e approximation and in the general interpolation case, compute non-normalized bases. Since for arbitrary shifts such bases may have size $\Theta(m^2 \sigma)$, the cost bound $\mathcal{O}\tilde{~}(m^{\omega-1} \sigma)$ was feasible only with restrictive assumptions on the shift that ensure small output sizes. The question of handling arbitrary shifts with the same complexity bound was left open. To obtain the target cost for any shift, we strengthen the properties of the output bases, and of those obtained during the course of the algorithm: all the bases are computed in shifted Popov form, whose size is always $\mathcal{O}(m \sigma)$. Then, we design a divide-and-conquer scheme. We recursively reduce the initial interpolation problem to sub-problems with more convenient shifts by first computing information on the degrees of the intermediate bases.
Keywords :
Type de document :
Communication dans un congrès
41st International Symposium on Symbolic and Algebraic Computation, Jul 2016, Waterloo, ON, Canada. Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation. 〈10.1145/2930889.2930928〉
Domaine :
Littérature citée [34 références]
https://hal.inria.fr/hal-01265983
Contributeur : Vincent Neiger <>
Soumis le : vendredi 13 mai 2016 - 09:43:22
Dernière modification le : mardi 16 janvier 2018 - 15:35:42
Document(s) archivé(s) le : mercredi 16 novembre 2016 - 03:36:11
### Fichier
fast_pib.pdf
Fichiers produits par l'(les) auteur(s)
### Citation
Claude-Pierre Jeannerod, Vincent Neiger, Eric Schost, Gilles Villard. Fast computation of minimal interpolation bases in Popov form for arbitrary shifts. 41st International Symposium on Symbolic and Algebraic Computation, Jul 2016, Waterloo, ON, Canada. Proceedings of the 41st International Symposium on Symbolic and Algebraic Computation. 〈10.1145/2930889.2930928〉. 〈hal-01265983v2〉
### Métriques
Consultations de la notice
## 184
Téléchargements de fichiers
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2018-01-20 14:04:18
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https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/year/2006/docId/1693
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## Langzeiterfolg der Zweit- und Dritttherapie mit Radioiod bei der Autoimmunthyreopathie vom Typ Morbus Basedow
### Long term success of patients with Graves´disease treated with a second or third radioiodine therapy
Please always quote using this URN: urn:nbn:de:bvb:20-opus-18998
• The influencing factors long on term success of initial radioiodine therapy are controversialy discussed. Aim of this project was to analyse the long term results in patients with Graves´disease treated with a second or third radioiodine therapy. The collected data was then compared to the results of the first radioiodine therapy. In this retrospective study the data of 106 patiens was collected. All individuall suffered from Graves disease and were treated with a second or third radiodine therapy. Thyroid volume, iodine turnover andThe influencing factors long on term success of initial radioiodine therapy are controversialy discussed. Aim of this project was to analyse the long term results in patients with Graves´disease treated with a second or third radioiodine therapy. The collected data was then compared to the results of the first radioiodine therapy. In this retrospective study the data of 106 patiens was collected. All individuall suffered from Graves disease and were treated with a second or third radiodine therapy. Thyroid volume, iodine turnover and thyrostatic medication were identified to be predictive influencing variables on long term success of the second radiodine therapy. Due to a lack of a statistical relevant number of patient we were unable to investigate if a certain gender or age predisposed to a relapse with need of a second or third radiodine intervention. In this study the thyroid function had no influence on the clinical outcome. However, before entering the therapeutic regime, a balanced hormone level has to be reached due to the higher iodine turnover on hyperthyroid patients. We concluded that further variables which are still partially unknown influence the outcome of the radiodine therapy essentially. As a consequence of this investigation an increase of the target dose at initial radioiodine therapy to 250 – 300 Gy seems reasonable because this dosage was successful during the second radiodine therapy. This could result in a significant reduction of the relapserate.
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2023-03-25 17:05:00
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https://www.physicsforums.com/threads/general-solution-of-the-first-order-differential-equation.504908/
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# General Solution of the first order differential equation
dy/dt + y =$$\infty$$$$\sum$$n=1Sin(nt)/n^2
Last edited:
$$\frac{\mathrm{d}y}{\mathrm{d}t} = P(t)y(t) + Q(t)$$
$$P(t)\equiv -1$$ and $$Q(t):=\sum_{n\ge 1}{\frac{\sin(nt)}{n^2}}$$. So, try with the formula
$$y(t) = \exp\left(\int{P(t)\mathrm{d}t}\right)\left(\int{Q(s)\exp\left(-\int{P(s)}\mathrm{d}s\right)\mathrm{d}s})\right) \biggr|_{s=t}$$
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2021-06-18 09:05:12
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https://chemistry.stackexchange.com/tags/pnictogen/hot
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# Tag Info
35
Each of these molecules has a pair of electrons in an orbital - this is termed a "lone pair" of electrons. It is the lone pair of electrons that makes these molecules nucleophilic or basic. As you move down the column from nitrogen to bismuth, you are placing your outermost shell of electrons, including the lone pair, in a larger and more diffuse orbital (...
18
Reproducibility is more important than stability. To obtain black phosphorus, you have to heat your sample under high pressure for quite a while, and even then it may still contain a significant number of random crystal defects, so its properties are not quite the same each time you make it. White phosphorus, on the other hand, is prepared by sublimation and ...
13
$\ce{N5P3}$ is more commonly written as $\ce{P3N5}$, and known as triphosphorus pentanitride. It's a crystalline solid at ambient conditions and not a molecular compound. From the first publication that reported the pure compound and its structure [1]: In the solid a three-dimensional cross-linked network structure of corner sharing $\ce{PN4}$ tetrahedra ...
11
This answer uses electronegativities for the calculation of oxidation states as proposed in the Expanded Definition of the Oxidation State by Hans-Peter Loock in 2011. Comparing Electronegativities The following table shows an excerpt from Pauling electronegativities ($\chi_{\mathrm{Pauling}}$): $$\begin{array}{cc} \hline \text{Element} & \chi_{\... 11 Let me create background first. Oxidizing agents are the chemical that helps something else oxidize and itself gets reduced.(reduction in charge) \ce{N} in \ce{HNO3} is in the +5 oxidation state - how do we know that? \ce{H} is +1, \ce{O} is -2 and the overall \ce{HNO3} has a zero net charge. The same goes for \ce{H3PO4} resulting in +5 ... 10 Oxyphosphorus compounds, all of which contain phosphorus-oxygen linkages, are the most dominated subset in Phosphorus Chemistry. You may find good review of oxyphosphorus compounds in Ref.1. In particular, most of these commonly known as phosphates are described in Chapter 3 of Ref. 1 (Pages 169-305) which states that: Oxyphosphorus compounds may be ... 8 As M. Farooq pointed in the comments, the concept of n-factor is applied to the reactions a given compound participates in, namely of the following types: acid-base, neutralization (in a context of Arrhenius approach, i.e. the amount of transported hydronium ions); redox (total change in oxidation state per mole of the substance); precipitation and double ... 8 What really happens in nature has higher priority than our believe what happens or should happen. See Dinitrogen_trioxide with the structure, bond lengths and angles. Be aware both \ce{NO} and \ce{NO2} are radicals with an unpaired electron. \ce{N2O3} being( \ce{ON-NO2} ) as 2 paired radicals is the direct analogy to the dimer \ce{N2O4} being \ce{... 8 The simplest types of chemical formulas are called empirical formulas, which use only letters and numbers indicating atomic proportional ratios (the numerical proportions of atoms of one type to those of other types). Molecular formulas indicate the simple numbers of each type of atom in a molecule of a molecular substance, and are thus sometimes the same as ... 7 Bismuth certainly has other known crystal structures at elevated pressures and temperatures, at least 4 others in addition to the rhombohedral structure stable at room temperature and pressure. One place to start would be an article from NIF on shock physics of bismuth. For a scholarly article, you might start with 'Phase Diagrams of Arsenic, Antimony, and ... 7 In chemistry, some chemical species can still react with nitrogen so argon is usually favored, but, in the case of wines, none of the two should react whatsoever. In both cases, however, the high density of argon is an advantage because it will always fall down to be in contact with the liquid in order to avoid contact with oxygen. By contrast, nitrogen ... 6 Most of the online data banks such as PubChem don't bother with showing proper bond multiplicity since they are focused on searching for the compounds based on connectivity graphs. It doesn't mean that those are bad or unreliable, it's just not their primary focus. The source of confusion here, I think, is terminology. Pyrophosphorous acid is an obsolete ... 6 Although nitric oxide is thermodynamically unstable, it is kinetically stable as its decomposition rate is very slow[ref] and so it is considered stable and won't normally react to anything. So, nitric oxide wouldn't normally hydrolyze easily. But in the presence of air, it forms nitrous acid (\ce{HONO}):$$\ce{4NO + O2 + 2 H2O -> 4 HNO2}$$However, ... 6 Frost Diagrams explain it very nicely as well. Look at the G/F = zE/V, very positive for HNO3, which makes it a potent oxidizing agent (much less stable). H3PO4 is basically the complete opposite. 6 Realise that there is a notable drop in basicity from nitrogen to phosphorus and then a slow and continuous further diminishing. The notable drop is due to the difference of the molecular structures of ammonia and phosphane. As I answered elsewhere on this network, the ‘ideal’ bonding situation from an orbital point of view would be to just use p-orbitals ... 6 The hydrides of nitrogen family have one lone pair of electrons on their central atom. Therefore,they act as Lewis bases.As we go done the group, the basic character of these hydrides decreases. Nitrogen atom has the smallest size among the hydrides.Therefore the lone pair is concentrated on a small region and electron density on it is the maximum.... 5 According to the work of Ninet et al. published in 2014 [1], ammonia has a β-phase at 150 GPa, where it transitions into ionic crystalline form, forming \ce{[NH4+][NH2-]}. References Ninet, S.; Datchi, F.; Dumas, P.; Mezouar, M.; Garbarino, G.; Mafety, A.; Pickard, C. J.; Needs, R. J.; Saitta, A. M. Experimental and Theoretical Evidence for an Ionic ... 5 If we try to calculate the oxidation state of nitrogen in \ce{N2O} using the familiar algebraic method, we get oxidation state +1 for both nitrogen atoms and that's what I found when I looked it up on the internet. Well … you get an average oxidation state. This calculation arguably implicitly assumes that all nitrogen atoms be equivalent. In some cases ... 4 Pyrophosphorous acid is the acid anhydride of phophorous acid:$$\ce{H3PO3 + H3PO3 -> H4P2O5 + H2O}$$Phosphorous acid in water occurs in two forms, \ce{H3PO3} and \ce{H2PHO3}, with no direct bonds between phosphorous and hydrogen in the first case, and one direct bond between phosphorous and hydrogen in the second case, see Why is phosphorous acid ... 4 This NIST publication lists the dipole moment as zero, while drugfuture.com (I've never heard of this site) reports a value of 0.50 as measured in benzene at \pu{25^oC}. 4 Nitrogen triiodide \ce{NI3} is an extremely sensitive explosive that explodes with the slightest touch when dry. Nitrogen trifluoride \ce{NF3} is so stable that it is a greenhouse gas global warming concern, with lifetime in the atmosphere of hundreds of years. \ce{NI3} is unstable due to steric strain as you are saying. 4 In the case of boron, a reaction with nitrogen does occur under some eye-popping conditions: Combustion of boron powder in nitrogen plasma at 5500 °C yields ultrafine boron nitride used for lubricants and toners.[1] The characteristic molecular thermal energy kT at this temperature is roughly half an electron volt, which is enough to at least partially ... 4 All group 13 elements (can technically) form nitrides from the direct combination of the elements (elemental reaction). Boron: See @Oscar's answer. Also, see references(1,2) Aluminum: There is a paper(3) which discussed about combustion of aluminum in a high-temperature and high pressure (up to 300 MPa) nitrogen atmosphere to form aluminum nitride. Gallium: ... 4 The oxidation state of \ce{Zn} as calculated by you is incorrect. The correct oxidation state of \ce{Zn} is +2 as it is associated with two mono negatively charged \ce{NO3-} ions. Thus the unbalanced reaction with correct oxidation states would be:$$\ce{\overset{0}{Zn} + \overset{+1}{H}\overset{+5}{N}\overset{-2}{O_3}\longrightarrow \overset{+2}{Zn}(...
4
Aqua regia doesn't actually dissolve lead metal. It converts to insoluble lead salt. From here: When we are working with an acidic chloride solution, like HCl (with an oxidizer) or aqua regia, most of the lead will become an insoluble lead chloride which if it is left to settle can be removed by careful decanting of the solution and filtering, what lead ...
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I think you assume that Nitrogen Sesquioxide is formed by a dehydration reaction of an acid of Nitrogen, hence necessitating the presence of a bridged oxygen. This isn't the case. It is created due to the addition of the radical on the Nitrogen of $\ce{NO}$ to the radical on the Nitrogen on $\ce{NO2}$. Hence why the structure is the way it is.
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Phosphorus is most common as white phosphorus (but more stable as red phosphorus) and in this form, it exists as a tetrahedron, or $\ce{P4}$. Chlorine is most stable as a diatomic molecule, as you may have learnt it with the other common gases that exists as diatomic molecules
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I'm not sure why previous answer cited only the first paper on phosphorus(V) nitride $\ce{P3N5}$. A couple of years later the same team reported three polymorphs $\ce{α,β,γ-P3N5}$ with three-dimensional network. For $\ce{α-P3N5}$ and $\ce{γ-P3N5}$ crystal structures have been refined. Both modifications demonstrate vastly different structural types and ...
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There is actually an erroneous explanation in your textbook. There is how the nitrogen monoxide molecular structure is explained in school: as there are no extended methods known by pupils or moreover the teacher, it's ok children to think that third unpaired electron on nitrogen atom is resonating between two atomic kernels as it's presented on picture ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2021-10-24 03:26:20
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https://engineering.stackexchange.com/questions/8285/deriving-the-turbulent-kinetic-energy-equation
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# Deriving the turbulent kinetic energy equation
I'm trying to understand the derivation of the turbulent kinetic energy equation, as described in this link: Evaluation of RANS turbulence models for flow problems with significant impact of boundary layers.
I'm able to follow up to equation 2.26 on slide 11 (i.e. page 9), which states
$$\rho \overline{\frac{\partial u_i'}{\partial t}u_i'} + \rho\left( \overline{u_j\frac{\partial u_i}{\partial x_j}u_i} -\bar{u}_j\frac{\partial u_i'}{\partial x_j}\bar{u}_i\right) = -\overline{\frac{\partial p'}{\partial x_j}u_i'} + \nu\overline{u_i'\nabla^2u_i'} + \rho \frac{\partial (\overline{u_i'u_j'})}{\partial x_j}\bar{u}_i,$$
where the overbars denote the ensemble averages of the quantities under the bars. Note that here, the average of a product is not necessarily equal to the product of the average of each term.
According to the link, using only averaging rules, the term
$$\left( \overline{u_j\frac{\partial u_i}{\partial x_j}u_i} -\bar{u}_j\frac{\partial u_i'}{\partial x_j}\bar{u}_i\right)$$
can be simplified to become
$$\overline{u_i'\frac{u_i'}{\partial x_j}}\bar{u}_j + \overline{\frac{\partial u_i'}{\partial x_j}u_i'u_j'} + \overline{\frac{\partial u_i'}{\partial x_j}u_j'}\bar{u}_i + \overline{u_j'u_i'}\frac{\partial u_i}{\partial x_j}.$$
If I substitute this directly into the previous equation, I get
$$\rho \left( \overline{\frac{\partial u_i'}{\partial t}u_i'} + \overline{u_i'\frac{u_i'}{\partial x_j}}\bar{u}_j + \overline{\frac{\partial u_i'}{\partial x_j}u_i'u_j'} + \underbrace{\overline{\frac{\partial u_i'}{\partial x_j}u_j'}\bar{u}_i}_{\text{my 4th term}} + \overline{u_j'u_i'}\frac{\partial u_i}{\partial x_j}\right) = -\overline{\frac{\partial p'}{\partial x_j}u_i'} + \nu\overline{u_i'\nabla^2u_i'} + \rho \frac{\partial (\overline{u_i'u_j'})}{\partial x_j}\bar{u}_i.$$
However, their derivation yields
$$\rho \left( \overline{\frac{\partial u_i'}{\partial t}u_i'} + \overline{u_i'\frac{u_i'}{\partial x_j}}\bar{u}_j + \overline{\frac{\partial u_i'}{\partial x_j}u_i'u_j'} + \underbrace{\overline{\frac{\partial u_i'u_j'}{\partial x_j}}\bar{u}_i}_{\text{their 4th term}} + \overline{u_j'u_i'}\frac{\partial u_i}{\partial x_j}\right) = -\overline{\frac{\partial p'}{\partial x_j}u_i'} + \nu\overline{u_i'\nabla^2u_i'} + \rho \frac{\partial (\overline{u_i'u_j'})}{\partial x_j}\bar{u}_i.$$
The only difference between my derivation and theirs is the 4th term on the left hand side of the equation. I'm sure that their 4th term is correct, since it is supposed to cancel out with a term on the right hand side of the equation. However, I can't seem to figure out how they obtained their 4th term on the LHS of the equation. The link suggests that the chain rule and the incompressiblity assumption are involved, but I'm not sure how.
In particular, the overbar term $\overline{u_i'u_j'}$ is treated as a single term. Thus, how can I apply the chain rule to $\frac{\partial (\overline{u_i'u_j'})}{\partial x_j}$?
Any hints to complete the missing steps would be greatly appreciated.
The two terms are equal due to the product rule and continuity equation. The use of the continuity equation might not be obvious, however.
In their notation, the Reynolds decomposition is $u_i = \overline{u}_i + u^\prime_i$. Taking the continuity equation and averaging leads to:
$$\frac{\partial \overline{u}_j}{\partial x_j} = 0$$
Subtract the equation above from the non-averaged continuity equation to see that the fluctuations also are divergence free:
$$\frac{\partial u^\prime_j}{\partial x_j} = 0$$
Now, apply the product rule to the term of interest (before averaging):
$$\frac{\partial u^\prime_i u^\prime_j}{\partial x_j} = u^\prime_j \frac{\partial u^\prime_i}{\partial x_j} + u^\prime_i \frac{\partial u^\prime_j}{\partial x_j}$$
The second term is zero by continuity as seen above, and this completes the derivation. The averages commute, so the average of a derivative is the same as the derivative of the average.
• The term "chain rule" here is misleading... The product rule is what is really being applied, not the chain rule. – Paul Apr 5 '16 at 1:36
• Yes, you are correct. I was thinking what you suggested but ended up doing something different. I've corrected the answer. Thanks. – Ben Trettel Apr 5 '16 at 1:38
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2020-07-11 21:51:50
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https://web2.0calc.com/questions/pls-help_36
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+0
# Pls help
0
93
1
Find the largest prime number that divides the quantity $$0! + (1!) \times 1 + (2!) \times 2 + (3!) \times 3 + \cdots + (50!) \times 50$$
Oct 6, 2018
#1
+4000
+1
$$\text{apparently }\sum \limits_{k=1}^n ~k! \cdot k = (n+1)! - 1 \\ 0!=1 \\ \text{so the expression shown }=(n+1)!-1+1 = (n+1)! \\ \text{so the largest prime }<(n+1) \text{ is what we're after}\\ \text{and this is }47.$$
.
Oct 6, 2018
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2019-02-22 07:33:00
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