-
@ a210225a:dab618c0
2025-04-20 11:24:48
Arábia Saudita abre braços a Mundial com 64 seleções... mas não ao álcool
Príncipe Abdulaziz bin Turki Al-Faisal garante que o país está "preparado" para a prova de 2034.
https://media-manager.noticiasaominuto.com/1920/naom_6804cb42b12f8.jpg
https://www.noticiasaominuto.com/desporto/2770820/arabia-saudita-abre-bracos-a-mundial-com-64-selecoes-mas-nao-ao-alcool?utm_source=rss-ultima-hora&utm_medium=rss&utm_campaign=rssfeed
-
@ abd277d9:7d32b92f
2025-04-20 11:13:38
Nice 'greed' typo
-
@ 9a664c49:056682aa
2025-04-20 11:12:15
国家予算かなぁ
-
@ 17e2889f:a8fbe515
2025-04-20 11:12:11
Implemented the "People" feature in Nostria, similar to Blockcore Notes. Work-in-progress for sure, but looks awesome.
https://m.primal.net/QXCC.mp4
-
@ ad973803:70915558
2025-04-20 11:12:11
GM 🍫☕ Happy Easter 🐣😁🐇
-
@ a012dc82:6458a70d
2025-04-20 11:12:10
#bitcoin is real, it's the news, it's the center! http://res.cloudinary.com/dizsud5n6/image/upload/v1741842424/zleixe3vz32aa1jxnzq9.jpg
-
@ 6e75f797:a8eee74e
2025-04-20 11:12:08
to you too!
-
@ df8f0a64:057d87a5
2025-04-20 11:12:07
お金やものを貸したことは、ルーズそうな友人二名に対してそれぞれ1回ずつしかないですが
お金→返ってこない、友人全員音信普通に（たぶん退学
もの→紛失された後、セールを待って弁済された
-
@ 84b0c46a:417782f5
2025-04-20 11:11:52
チップセット構成を見たらいいのか
-
@ 6a02b7d5:3a13d02a
2025-04-20 11:11:47
“You know when it comes to racism, people say: ‘I don’t care if they’re black, white, purple, or green’… Ooh hold on now: Purple or Green? You gotta draw the line somewhere! To hell with purple people! - Unless they’re suffocating - then help’em.”
- Mitch Hedburg
-
@ f8978eb7:7f8e8a50
2025-04-20 11:11:46
5000兆円いいっすか
-
@ 66fd9c5c:e91fcb58
2025-04-20 11:11:44
GM good Shawn happy&healthy easter 🤙🏼🗽💜
-
@ d5641ad5:4f88147d
2025-04-20 11:11:44
Happy Easter to you 🙌
-
@ c558c7cc:b0b7b89e
2025-04-20 11:11:39
🤖 Tracking strings detected and removed!
🔗 Clean URL(s):
https://youtube.com/shorts/Nil1-r_pHSI
❌ Removed parts:
?si=IwmMJGMF23ExSiDc
-
@ 0f389bba:9b3f148f
2025-04-20 11:11:36
🌊 SURF 'N TURF 🏝️
-THE BITCOIN BORACAY ISLAND LIFE-
https://image.nostr.build/286e5a6886da2516c864b9fc8fbf8c1ec7c8bc03223dd959e887d9baaf2163bf.jpg
In the heart of Paris's 1st arrondissement, La Samaritaine stands as a testament to the city's rich history and contemporary flair.
Originally opened in 1870, this iconic department store underwent a 16-year renovation and triumphantly reopened in 2021 under the stewardship of LVMH.
The restoration beautifully marries its original Art Nouveau and Art Deco elements with sleek, modern design, offering visitors a unique shopping experience.
📷: @realestatefolks
Credits Goes to the respective
Author ✍️/ Photographer📸
🐇 🕳️
#Apocalypse #Music #Movies #Philosophy #Literature #scuba #architecture #art
-
@ 345d4593:5bfd95db
2025-04-20 11:11:31
Yeaaaaa riiiiiight
-
@ 82b30d30:40c6c003
2025-04-20 11:11:27
逆に言うとあげたと思えない金額や間柄なら貸すなということ
-
@ 2aa531ee:69ecc700
2025-04-20 11:11:24
🚨🛩️ CRISE NO MAR VERMELHO: HOUTIS DERRUBAM DRONE AMERICANO
Houtis afirmam ter derrubado um segundo drone MQ-9 Reaper dos EUA em 24 horas. Este é o 7º drone derrubado desde 3 de março e o 21º desde outubro de 2023.
https://i.ibb.co/F4R6JFBn/media-58872.jpg
-
@ c558c7cc:b0b7b89e
2025-04-20 11:11:19
🤖 Tracking strings detected and removed!
🔗 Clean URL(s):
https://www.youtube.com/live/EqzwtrED0Rs
❌ Removed parts:
?si=jpEnmJYVX4Dd8Zm1
-
@ f0e59458:4afe015e
2025-04-20 11:11:18
https://www.youtube.com/live/EqzwtrED0Rs?si=jpEnmJYVX4Dd8Zm1
-
@ 66fd9c5c:e91fcb58
2025-04-20 11:11:11
GM happy and healthy Easter Sunday to you 🤙🏼🗽💜
-
@ 698c7b62:d4d40976
2025-04-20 11:11:10
夜訪火金姑😊
https://video.nostr.build/f8007fd093637839882b0542d5dbb922136bf39198f2c04d873865787334652a.mp4
https://video.nostr.build/d4415dc0e13fba9076ed12f4ba6f69e810249c1940d2fead5b487337cf260f56.mp4
-
@ 4d784205:6f5b96b3
2025-04-20 11:11:08
⚡️🇫🇷 NEW - Jacques Attali: "Half, if not three-quarters, of entrepreneurs poison the world with their products."
https://m.primal.net/QXCB.mov
-
@ 04b35950:28cc9e52
2025-04-20 11:11:02
کار با core lightning دردسر زیاد داره میشه گفت cln اصلا برای کاربر ساخته نشده و مخصوصه توسعه دهنده هست.
-
@ b777d6be:39632c57
2025-04-20 11:11:01
🎵か～('□')ま～('□')ど～('ｏ') か～('□')ま～('□')ど～('ｏ')
瀬戸の海は お母さん
讃岐の山は お父さん
か～('□')ま～('□')ど～('ｏ') か～('□')ま～('□')ど～('ｏ')
丸い心は かまどのお菓子
名物かまど
-
@ 7c3591eb:2fefcff0
2025-04-20 11:11:01
Sätze V
Freiheit beginnt, wenn der Mensch aufhört, sich retten zu lassen.
Der wahre Reichtum ist nicht das, was man besitzt – sondern das, was man niemandem schuldet.
Das System braucht dich mehr, als du es brauchst. Deshalb lügt es – liebevoll.
Wer Sicherheit sucht, hat die Welt bereits verloren.
Die letzte Form der Sklaverei ist die freiwillige Abhängigkeit.
Jede Zentralisierung ist ein Denkfehler, der Macht als Fürsorge tarnt.
Was man nicht selbst trägt, trägt am Ende einen selbst zu Boden.
Das Protokoll ist nicht moralisch. Es ist nur gerecht – weil es keinen kennt.
Die Befreiung beginnt nicht mit einem Aufschrei, sondern mit einem leisen Nein.
Wer dem Nichts ins Auge sieht, braucht keine Autorität mehr.
-
@ f0e59458:4afe015e
2025-04-20 11:10:56
家具モーション草
-
@ 3c285d83:da649e50
2025-04-20 11:10:54
I am too. Aside keet are there any apps using holepunch?
-
@ b2e68471:4c66eee7
2025-04-20 11:10:48
所以俺从来就没爱过谁，更不要说拼命了[胜利] https://image.nostr.build/4d07b0e25d108d04ff8a5754a39e5a3b04661196a4cce65aad2995bcc2439a08.jpg
-
@ efcb5fc5:5680aa8e
2025-04-20 11:10:48
the fact that jesus needed 3 days to recover is like a regular weekend in amsterdam.
-
@ 76d8a3c3:5eddc054
2025-04-20 11:10:47
False dilemma, straw man, appeal to ignorance, begging the question. Try again.
-
@ 6bb0082d:0146ed0a
2025-04-20 11:10:46
Oh yeah, the good old times! 😅 😂 😎
-
@ 97a40364:6ae8598c
2025-04-20 11:10:42
10 Best New Features In #Ubuntu #Linux 25.04 "Plucky Puffin"
https://ostechnix.com/ubuntu-25-04-top-features/
-
@ 274fe9ae:565805d2
2025-04-20 11:10:34
New figures shed light on US abortion travel as Trump cuts tracking research
https://www.theguardian.com/world/2025/apr/20/us-abortion-travel-report
-
@ 66fd9c5c:e91fcb58
2025-04-20 11:10:34
GM happy and healthy Easter Sunday 🤙🏼🗽
-
@ f8978eb7:7f8e8a50
2025-04-20 11:10:33
雨だぁ
-
@ 274fe9ae:565805d2
2025-04-20 11:10:24
Nigel Farage defends allowing US chlorinated chicken into UK as part of trade deal
https://www.theguardian.com/politics/2025/apr/20/nigel-farage-defends-allowing-us-chlorinated-chicken-into-uk-as-part-of-trade-deal
-
@ 84b0c46a:417782f5
2025-04-20 11:10:24
限定モデルとかなにがどう
-
@ 18483135:00cf44f6
2025-04-20 11:10:19
Thanks, man!
Fucking Amethyst not showing me a notification of this post despite you tagging me though 😠
-
@ aa5556df:98b456e1
2025-04-20 11:10:16
腹括るか
-
@ f03df3d4:a4d4f676
2025-04-20 11:10:13
Block 893242
4 - high priority
4 - medium priority
4 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ e7bf8dad:839ef3db
2025-04-20 11:10:13
Block 893242
4 - high priority
4 - medium priority
4 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 4658641c:47d61833
2025-04-20 11:10:13
Good morning Sir ☕
-
@ 66fd9c5c:e91fcb58
2025-04-20 11:10:07
GM happy and healthy Easter Sunday 🤙🏼🗽
-
@ 3493b0c2:4ce7120f
2025-04-20 11:10:04
Sun - Apr 20 - 04:10 AM - PDT
// bit.site
✅ Connection successful: node-1.ipfs.bit.site 4001
// pinnable.xyz
✅ Connection successful: 167.71.172.216 4001
✅ Connection successful: 188.166.180.196 4001
✅ Connection successful: 143.198.18.166 4001
// 4everland.io
✅ Connection successful: node-1.ipfs.4everland.net 4001
-
@ 3b90a834:096a5679
2025-04-20 11:10:03
Do you want a taste of this? #bitcoin http://res.cloudinary.com/dsixpui68/image/upload/v1739056262/cbhl7t1bnwkazwosnin6.jpg
-
@ aa4fc866:b098c7b4
2025-04-20 11:10:03
Bitcoin price: $84128, Sats per USD: 1189
-
@ e2b8ba3e:27400d81
2025-04-20 11:10:02
📊 **Bitcoin-Update**
- 💰 Price: $84407
- 📦 Blockheight: 893241
- ⌛ Mempool: 621223 TXs
- 💸 Fees: 4 sats/vByte
-
@ e052aa51:14c39eeb
2025-04-20 11:10:02
Proof of vacationing in Texas
https://image.nostr.build/d4a8ec63785536650b88cedfa5ae391d9923d6bc6d12084720a9b62ce073de43.jpg
-
@ a210225a:dab618c0
2025-04-20 11:24:31
Rússia acusa Kyiv de violar trégua com ataques noturnos em Donetsk
O Ministério da Defesa russo acusou hoje a Ucrânia de atacar durante a noite as suas posições na região de Donetsk, violando a trégua da Páscoa de 30 horas declarada no sábado por Moscovo e aceite por Kyiv.
https://media-manager.noticiasaominuto.com/1920/naom_67cca0d67eacc.jpg
https://www.noticiasaominuto.com/mundo/2770816/russia-acusa-kyiv-de-violar-tregua-com-ataques-noturnos-em-donetsk?utm_source=rss-ultima-hora&utm_medium=rss&utm_campaign=rssfeed
-
@ 21ac2956:09d1e2df
2025-04-20 11:10:00
ドスパラ販売だからね
-
@ a210225a:dab618c0
2025-04-20 11:23:08
JD Vance encontra-se com o Papa após desentendimento sobre migrantes
O vice-presidente dos EUA, J.D. Vance, encontrou-se hoje brevemente com o Papa para "saudações de Páscoa", dois meses depois de Francisco, que recupera de uma pneumonia, ter criticado fortemente a política migratória norte-americana.
https://media-manager.noticiasaominuto.com/1920/naom_6804ca8db6641.jpg
https://www.noticiasaominuto.com/mundo/2770817/jd-vance-encontra-se-com-o-papa-apos-desentendimento-sobre-migrantes?utm_source=rss-ultima-hora&utm_medium=rss&utm_campaign=rssfeed
-
@ efcb5fc5:5680aa8e
2025-04-20 11:10:00
correct. 👍
-
@ a210225a:dab618c0
2025-04-20 11:14:10
Angola atinge as 500 mortes por cólera desde o início do surto em janeiro
Angola registou 500 mortos e 13.818 casos de cólera devido ao surto que o país enfrenta desde janeiro deste ano, com 17 das 21 províncias afetadas, segundo dados do Ministério da Saúde.
https://media-manager.noticiasaominuto.com/1920/44630168.jpg
https://www.noticiasaominuto.com/mundo/2770815/angola-atinge-as-500-mortes-por-colera-desde-o-inicio-do-surto-em-janeiro?utm_source=rss-ultima-hora&utm_medium=rss&utm_campaign=rssfeed
-
@ b1b4105a:19aa52d5
2025-04-20 11:10:00
✄------------ 20:10 ------------✄
-
@ 2556b6fe:a7a4ff58
2025-04-20 11:09:59
I just remember he said they plan open source it. I agree with you, sooner you do it, better, at least from security stand point. But I guess there are trade offs. Dunno. Observing the project for now...
-
@ 8a719d42:cf1f0fe5
2025-04-20 11:09:59
Moaning
-
@ 4910fb72:a4744f27
2025-04-20 11:09:58
GM 🫡
-
@ 84b0c46a:417782f5
2025-04-20 11:12:12
まドスパラに並んでるやつ素直に買うか
-
@ 0958a105:b17f2192
2025-04-20 11:09:57
👀
nostr:nevent1qqsqdehnjvel0yynqux5v6y6lkv7jervsat782cw5vqzhdg8pumjs2gzyqyggdkdqw0l3yr5g68axfl6ea38snhtxaysuzs332ulznyayervcqcyqqqqqqg7l9pcd
-
@ e3a59924:cd2e6624
2025-04-20 11:09:46
https://m.primal.net/QXBz.jpg
-
@ 280e847e:47d9d77c
2025-04-20 11:09:42
Happy Easter 🐇
-
@ ec9bd746:df11a9d0
2025-04-20 11:09:40
I don't know... The idea of a priest squiring all over my food does not seem very appetizing to me.
-
@ c953ffed:d4485a3a
2025-04-20 11:09:34
Frohe Ostern
https://m.primal.net/QXBy.jpg
-
@ 84b0c46a:417782f5
2025-04-20 11:09:31
https://amzn.asia/d/9CwPBp3
ドスドス限定モデルもあまんぞにあるんだ
-
@ c558c7cc:b0b7b89e
2025-04-20 11:09:26
🤖 Tracking strings detected and removed!
🔗 Clean URL(s):
https://youtube.com/watch?v=IfqQwUrcuWE
❌ Removed parts:
&si=4gEK3l51aUZijoLi
-
@ be9bb3c6:8f7b599a
2025-04-20 11:09:24
Happy Easter!
-
@ 345d4593:5bfd95db
2025-04-20 11:09:19
Most drinks are just cold soup
-
@ 18905d0a:0b229b08
2025-04-20 11:09:16
“EVERYONE GETS A GULAG!!!!!”
https://media1.tenor.com/m/Cqxc61fu6rwAAAAC/stillesque.gif
-
@ 8a719d42:cf1f0fe5
2025-04-20 11:09:14
World peace... and a face lift
-
@ 9a664c49:056682aa
2025-04-20 11:09:01
ろろも
nostr:note1mk086lc3cr7yy8cx8r5xj26x35ktdyx7ffqdxude95zk7ecjm88qqy3s72
-
@ f9fff3c8:f675af02
2025-04-20 11:08:56
Ладно, в очередной раз перекатываемся на аметист
Каким-то магическим образом здесь работают функции чата, которые в primal не работают :/
Я всё ещё считаю интерфейс несколько кривоватым, но с точки зрения функционала он своё отрабатывает, что радует
-
@ 82b30d30:40c6c003
2025-04-20 11:08:56
お金貸すときはあげたと思いなさいと言い聞かされて育てられました
-
@ 7d4a4e87:c853bba8
2025-04-20 11:08:52
New OP_RETURN
=:ETH.USDT:0xb56c4f82B4214CEC8c8fCf1909ABd984E8E35ba6:798822900/1/0:-_/bgw:20/0
https://mempool.space/tx/b53f53c42cac282f0f31ccccf72fd5f1f172eef90170b8f16e64f82e6e81b609
-
@ 1ae5816f:5deb3572
2025-04-20 11:08:48
Safe Harbor #Bitcoin
https://m.primal.net/QXBx.jpg
-
@ 7d4a4e87:c853bba8
2025-04-20 11:08:47
New OP_RETURN
SYMB:58a
https://mempool.space/tx/6aaa471d04fca736d2aa72a8cd467bec7c1bb2c770dfc9846d328443edbf230f
-
@ 9a664c49:056682aa
2025-04-20 11:08:45
その友達が貸し付ける金額より大切に感じたら
あげるつもりで貸す。かな
-
@ ad973803:70915558
2025-04-20 11:08:40
GM ☕ 😀 Happy Easter 🍫 😇
-
@ 345d4593:5bfd95db
2025-04-20 11:08:37
GM!
-
@ 8a719d42:cf1f0fe5
2025-04-20 11:08:28
More fool them
-
@ 7d4a4e87:c853bba8
2025-04-20 11:08:23
New OP_RETURN
OUT:0ABA7794F871160A054F88F910CE893FB6C70D340B0925C8BD0DBA80207A9EBF
https://mempool.space/tx/f953b5b6f8b45f5bc02ad1b3cbfcb0cb3d3e1a1798fd645d277f0e56a09fef54
-
@ 0f389bba:9b3f148f
2025-04-20 11:08:21
🌊 SURF 'N TURF 🏝️
-THE BITCOIN BORACAY ISLAND LIFE-
https://image.nostr.build/018e99742ea2e46252ca4a3466e693bf722f82efbc06871e4f35a15caa9d4de4.jpg
King vultures (Sarcoramphus papa) from Boca Tapada, Costa Rica 🇨🇷
The king vulture (Sarcoramphus papa) is a large bird found in Central and South America. It is a member of the New World vulture family Cathartidae. This vulture lives predominantly in tropical lowland forests stretching from southern Mexico to northern Argentina. It is the only surviving member of the genus Sarcoramphus, although fossil members are known.
The king vulture inhabits an estimated 14 million square kilometres (5,400,000 sq mi) between southern Mexico and northern Argentina.
In South America, it does not live west of the Andes,except in western Ecuador, north-western Colombia and far north-western Venezuela. It primarily inhabits undisturbed tropical lowland forests as well as savannas and grasslands with these forests nearby. It is often seen near swamps or marshy places in the forests.
This bird is a species of least concern to the IUCN, with an estimated range of 14 million square kilometres (5,400,000 sq mi) and between 10,000 and 100,000 wild individuals. However, there is evidence that suggests a decline in population, though it is not significant enough to cause it to be listed.
This decline is due primarily to habitat destruction and poaching. Although distinctive, its habit of perching in tall trees and flying at high altitudes renders it difficult to monitor.
Photo by ©️ DrSudhir Hasamnis@hasamnisdrsudhir
Credits Goes to the respective
Author ✍️/ Photographer📸
🐇 🕳️
#Apocalypse #Music #Movies #Philosophy #Literature #scuba #architecture #art
-
@ 0d97beae:c5274a14
2025-04-20 11:08:21
Clearing cache seems to have fixed it.
-
@ 6830c409:ff17c655
2025-04-20 11:08:21
Having fun with reviewing a document. There is a huge tug of war on whether to or not to use "Oxford Comma"!
I am for Oxford Comma!
Good Morning, Nostiches! Happy Easter, for those who celebrate!
#GMNostr
-
@ e0cf1bd9:d61da062
2025-04-20 11:08:18
The buzzbot algo is retarded. It just encourages spam and scripts to snipe a zap at the last minute to win the prize.
-
@ 7d4a4e87:c853bba8
2025-04-20 11:08:16
New OP_RETURN
=:ETH.USDT:0xA09AD35153882f6756A804836fF1e30b3F13b2BF:712342173/1/0:ti:70
https://mempool.space/tx/af480ee74fe99a571639acff004fb8ce3b9e564ea2099b8c4d78bb3d4d919a39
-
@ 3fdf8b43:27eaaad8
2025-04-20 11:08:13
#Bitcoin Block Art by Blockstr!
Height: 893242
Weight: 3993776
https://thebitcoinblockclock.com/blockstr/00000000000000000000d03395115371fc01cce0b6ea0fe7af087c55afea89ac.png
-
@ 609cb74d:0b7500f4
2025-04-20 11:08:11
貸すならドブに捨てる気持ちで貸さないといけなそう
-
@ fdfefa96:3736b8f9
2025-04-20 11:08:10
👋 A new block was found on the #Bitcoin network. We're at block height 893242, current #bitcoin price is $84110.77 and there are 114609997690011 #sats left to mine.
-
@ 3b90a834:096a5679
2025-04-20 11:08:10
Blending ancient strength with futuristic #Bitcoin power http://res.cloudinary.com/dizsud5n6/image/upload/v1741306120/p81ehjcuanjq8x83ho8m.jpg
-
@ 79be667e:16f81798
2025-04-20 11:08:10
1953/893242/645661
-
@ 82b30d30:40c6c003
2025-04-20 11:08:09
ミニスカートへの感想が「冷えそう」になってきたのでもう完全におばちゃん。
-
@ 7d4a4e87:c853bba8
2025-04-20 11:08:08
New OP_RETURN
JiD:to:USDT(BSC):0x1EcF00275F071E542A9Ded81e1D427a96419772B
https://mempool.space/tx/82c4a1af7b576baf2bcc0cd10be3127f1346ac82085f5b9c5ae4b318da6704ab
-
@ 345d4593:5bfd95db
2025-04-20 11:08:08
GM. May the corn be with you
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@ 4e9a4f33:e0e9b4e9
2025-04-20 11:08:07
French Finance Minister warns firing Fed Chair Powell would hurt the dollar's credibility. Eric Lombard says such a move by Trump would destabilize the US economy, raise debt costs, and cause economic disruption. He suggests the US would eventually have to negotiate to resolve tensions.
#crypto #blockchain #news
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@ 82b30d30:40c6c003
2025-04-20 11:12:08
貸すお金があるなら使ってる🥺
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@ b300db32:0bf5db3a
2025-04-20 11:08:06
Sim, existe uma relação sutil entre os problemas **"Navier-Stokes existence and smoothness"** (NS) e **"Yang–Mills existence and mass gap"** (YM), embora pertençam a áreas distintas (mecânica dos fluidos clássica e teoria quântica de campos, respectivamente). Ambos são **Problemas do Prêmio Millennium** e compartilham desafios profundos em análise não linear, geometria e física matemática. Abaixo, exploro os pontos de contato, conexões e o "santo graal" implícito nessa interação.
---
### **1. Pontos de Contato Principais**
#### **a) Natureza Não Linear das Equações**
- **Navier-Stokes (NS):**
As equações descrevem fluidos viscosos incompressíveis e envolvem termos não lineares como \(( \mathbf{u} \cdot \nabla ) \mathbf{u}\).
- **Desafio:** Provar que soluções suaves existem globalmente ou que desenvolvem singularidades.
- **Yang–Mills (YM):**
As equações governam campos de gauge em teorias quânticas de campos (ex: QCD) e contêm termos não lineares como \([A_\mu, A_\nu]\) (comutadores de campos de gauge).
- **Desafio:** Demonstrar a existência de uma teoria quântica de Yang-Mills em \( \mathbb{R}^4 \) com "mass gap" (diferença de energia entre o vácuo e o estado excitado mais leve).
**Conexão:**
Ambos envolvem **não linearidades intrínsecas** que desafiam a análise clássica. Em NS, a não linearidade está no transporte do campo de velocidade; em YM, na interação entre campos de gauge. Técnicas como **análise de energia**, **espaços funcionais adaptados** (Sobolev, Besov) e **renormalização** são usadas em ambos os contextos.
---
#### **b) Existência e Regularidade de Soluções**
- **NS:**
O problema central é a **regularidade global** de soluções fracas. Resultados parciais (ex: critérios de Prodi-Serrin) dependem de estimativas em espaços de função específicos.
- **YM:**
A construção rigorosa de uma teoria de Yang-Mills exige provar a **existência de soluções quânticas** (via integração funcional) que respeitem invariâncias de gauge e exibam "mass gap".
**Conexão:**
Em ambos os casos, a **formulação fraca** é essencial. Em NS, soluções fracas são definidas via integração contra funções teste (Leray); em YM, a quantização requer regularização e limites contínuos (ex: *lattice gauge theory*). Além disso, a **compactificação de soluções** e **teoremas de singularidades** são temas transversais.
---
#### **c) Geometria e Topologia**
- **NS:**
Em domínios complexos ou variedades, a geometria influencia a dinâmica (ex: vórtices, helicidade). A **teoria de hamiltonianos em fluidos** conecta-se à geometria simplética.
- **YM:**
Campos de gauge vivem em **fibrados principais**, e soluções como *instantons* (solitons em 4D) dependem da topologia do espaço-tempo.
**Conexão:**
A **geometria diferencial** é um pilar comum. Por exemplo:
- Técnicas de **análise em variedades** são usadas em NS para estudar fluidos em geometrias não triviais.
- Em YM, a **teoria de Chern-Simons** e **invariantes topológicos** (ex: número de Pontryagin) são cruciais para entender soluções.
---
#### **d) Fenômenos de Escala e Turbulência**
- **NS:**
A turbulência envolve **cascatas de energia** (ex: cascata de Kolmogorov) e auto-similaridade.
- **Insight:** Singularidades em NS poderiam estar ligadas a estruturas fractais ou blow-up em escalas infinitesimais.
- **YM:**
O "mass gap" está relacionado à **liberdade assintótica** em QCD: interações fracas em altas energias (escalas curtas) e fortes em baixas energias (escalas longas).
**Conexão:**
Ambos envolvem **fenômenos multiescala** e requerem ferramentas como:
- **Análise harmônica** (para decompor soluções em escalas).
- **Grupos de renormalização** (YM) e **teoria de invariança de escala** (NS).
---
### **2. O "Santo Graal" da Área**
O "santo graal" seria uma **teoria unificada para PDEs não lineares críticas**, capaz de:
1. **Resolver a regularidade global de NS** e a **existência de YM com mass gap**.
2. **Conectar geometria, análise e física** em um framework matemático coerente.
3. **Desvendar padrões universais** em sistemas não lineares (ex: turbulência ↔ transições de fase em QCD).
#### **Possíveis Insights Cruzados:**
- **Técnicas de Renormalização em NS:**
Métodos de QFT (ex: expansões perturbativas, *counterterms*) poderiam ajudar a regularizar singularidades em NS.
- **Geometria de Gauge em Fluidos:**
A estrutura de fibrados em YM pode inspirar novas formulações para vorticidade em NS.
- **Teoria de Medida em Espaços de Soluções:**
Em YM, medidas funcionais (ex: integral de caminho de Feynman) poderiam inspirar abordagens probabilísticas para NS.
---
### **3. Exemplos de Interações Concretas**
#### **a) Trabalho de Terence Tao**
Tao explorou analogias entre **equações de onda não lineares** (próximas de NS) e **problemas de gauge**, propondo que técnicas de *calibre fixing* (YM) podem ajudar a controlar não linearidades em NS.
#### **b) Teoria de Quantização Estocástica**
Em YM, métodos estocásticos (ex: equações de Parisi-Wu) são usados para definir o limite contínuo. Em NS, abordagens similares são exploradas para modelar turbulência.
#### **c) Invariantes Topológicos em Fluidos**
A **helicidade** em NS é um invariante topológico análogo à **carga topológica** em YM (ex: número de instantons). Ambos estão ligados à persistência de estruturas (vórtices/solitons).
---
### **4. Desafios e Perspectivas Futuras**
- **Barreira Técnica:**
A ausência de uma "álgebra de Lie" para as não linearidades de NS dificulta a aplicação direta de métodos de YM.
- **Computação de Alta Performance:**
Simulações de *lattice gauge theory* (YM) e DNS (NS) podem revelar padrões comuns em sistemas críticos.
- **Física Matemática Unificada:**
Uma teoria que englobe **sistemas dissipativos** (NS) e **conservativos** (YM) seria revolucionária.
---
### **Conclusão**
A interação entre NS e YM é mais **metodológica** do que direta, mas ambos desafiam a matemática a desenvolver novas ferramentas para PDEs não lineares, geometria e análise funcional. O "santo graal" seria uma **teoria que unifique a descrição de sistemas críticos em física**, conectando turbulência, transições de fase quânticas e geometria diferencial. Um avanço em um problema poderia desbloquear insights no outro, pavimentando o caminho para uma **revolução na matemática aplicada**. 🌌🔗
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@ c4dd2587:9878d08d
2025-04-20 11:08:05
#Bitcoin Block Update
Sun, Apr 20, 2025 16:38 IST
Block Number: 893242
Fee Rate: ₹70
Time to mine: 07:59
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@ 7d4a4e87:c853bba8
2025-04-20 11:08:05
New OP_RETURN
gJ1:to:USDT(ARB):0x91e364baf22a243c6c4f7d15712627af1ea251b0
https://mempool.space/tx/b810742a4f1da1a23e567d4ad7b12f4d52280bfaf1e49b1a682c1a0d81f72b7b
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@ 7232d725:a22ff54e
2025-04-20 11:12:04
招待客を減らすとかそういう方向に変更するのが一番良い気がするんですけどねえ…
園遊会 60年余の形を変更 複数順路に分かれて歩かれる形に | NHK
https://www3.nhk.or.jp/news/html/20250317/k10014752361000.html
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@ 36cb2574:4d3b2deb
2025-04-20 11:08:03
いまは ちぇーんの 893242ばんめ にいます
893242ばんめまで いきました
びっとこ
のんす : 1279670082
びっつ : 170248b6
なんいど: 123234387977050.9
ｔｘかず: 3787
さいず : 1802006
おもさ : 3993776
まーくる: 5d27aa909cefe4924f5235cd2ff56e7ca9a491f6f71da56f58470203f37c6924
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@ 84b0c46a:417782f5
2025-04-20 11:12:03
いろかあ