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Differential geometry: under surjective immersion, the advance of a $ k $ shape is smooth

Leave $ pi: P a M $ to be a director $ G $-make. Leave $ psi in Omega ^ k (P) $ such that $ psi_ {p cdot g} big (r_ {g *} (v_1), …, r_ {g *} (v_k) big) = psi_p (v_1, …, v_k) $ for all $ g in G $ and all $ p in P $ with any $ v_1, …, v_k in T_pP $ that is to say $ psi $ is $ G $-invariant. Here, $ r_g: P a P $ is defined by $ p mapsto p cdot g $. Furthermore, suppose that $ psi $ fades when one of its arguments is a vertical vector. I want to show, $ psi $ it is a basic form, that is $ psi in text {Im} big ( pi ^ *: Omega ^ k (M) to Omega ^ k (P) big) $.

So, define $ psi ^ flat in Omega ^ k (M) $ as follows: choose $ m in M ​​$ and $ u_1, …, u_k in T_m M $then define $ psi ^ flat_m (u_1, …, u_k): = psi_p (v_1, …, v_k) in Bbb R $, where $ pi (p) = m $ and $ pi _ {* p} (v_i) = u_i $ for all $ i $. Now we show $ psi ^ flat $ It is well defined. Choose another set $ v_1 & # 39 ;, …, v_k & # 39; $ with $ pi _ {* p} (v_i & # 39;) = u_i $ for all $ i $, so $ v_i-v_i & # 39; $ are vertical vectors for all $ i $. Thus, $ psi_p (v_1 & # 39 ;, …, v_k & # 39;) = psi_p big (v_1 + text {vertical}, …, v_k + text {vertical} big) = psi_p (v_1, …, v_k) $. Then choose $ q in pi ^ {- 1} (m) $so that $ q = p cdot g $ for some $ g in G $. So, $ pi _ {* q} big (r_ {g *} (v_i) big) = big ( pi circ r_g) _ {* p} (v_i) = pi _ {* p} (v_i ) = u_i $ for all $ i $therefore using $ G $-invariance of $ psi $ we have$ psi_q big (r_ {g *} (v_1), …, r_ {g *} (v_k) big) = psi_p (v_1, …, v_k) $. Then we are done. Too, $ pi ^ * big ( psi ^ flat big) = psi $that is to say $ psi ^ flat_m big ( pi _ {* p} (v_1), …, pi _ {* p} (v_k) big) = psi_p (v_1, …, v_k) $. So $ psi ^ flat $ It is well defined.

Now my question is how to show $ psi ^ flat $ is smooth, any vector field is given $ Z_1, …, Z_k in mathfrak X (M) $ we have to show $ M ni m mapsto psi ^ flat_m big (Z_1 (m), …, Z_k (m) big) in Bbb R $ it's soft. I know, motto of horizontal elevation, meaning given $ Z_1, …, Z_k in mathfrak X (M) $ we have horizontal vector fields $ widetilde Z_1, …, widetilde Z_k in mathfrak X (P) $ such that $ pi _ {* p} big ( widetilde Z_i (p) big) = Z_i big ( pi (p) big) $ for all $ p in P $. I guess I have to use the fact that $ pi $ It is a subjective immersion. Any help will be applied.

hacks: IPS patch for Walk Through Walls in Pokémon Emerald, played on gpSP-Nspire (Game Boy Advance emulator for TI-Nspire)

I'm looking for an IPS patch for Pokémon Emerald that allows the player to walk through the walls. I am using gpSP-Nspire (Game Boy Advance emulator for TI-Nspire). I tried to use a GameShark code that I got from this website:

https://www.pokemoncoders.com/pokemon-emerald-cheats/

I got the Pokémon Emerald ROM from here:

https://romsmania.cc/roms/gameboy-advance/pokemon-emerald-version-225038

And I called it "Emerald.gba.tns", for the sake of TI-Nspire's default file extension (.tns).

And this is what my cheat file looks like (I'll indicate where it stops and ends with braces):

{

gameshark_v3 WalkThroughWalls

7881A409 E2026E0C

8E883EFF 92E9660D

}

It's called "Emerald.cht.tns"

Should I have created this cheat file, or am I correct when looking for an IPS patch? If I should have created this cheat file, what did I do wrong or is it a problem with the emulator? If anyone knows where I can find an IPS patch to break through walls in Pokémon Emerald, please let me know.

Thanks in advance.

repair – Take M900 Novacam I: my film winder does not advance the film correctly

As you may have noticed, the Shot uses an electronic motor to automatically wind the film. At this point, it's a very old electronic device with an unknown history purchased from a cameraless store (the store has no incentive to repair / fix it).

It could be used beyond its primer and just wear out (likely), it could have been dropped / damaged, it could have gotten wet, any lubricant that has definitely been used is now at its best.

So the unfortunate reality is that this camera is cheaper to replace than to repair. (I found a new one in the box on eBay today for $ 25, for example.) Therefore, I would recommend simply replacing it. If you want to break it to see if you can repair it yourself, you can too. Don't break your heart if you destroy it in your attempt.

magento 2 catalog pricing rules do not apply to advance pricing tables

I set up the catalog pricing rules, it works great with one single price. However, we had advance pricing tables for simple items (buy 10 = $ 10 each, buy 20 = $ 8 each … etc), the catalog pricing rules seem to not apply to the advance pricing table Is this a mistake or did I not? set up? Please notify

How can I schedule the sending of emails more than 3 days in advance?

I want to outsource the work of scheduling emails to an email delivery service, but I have not found one that can schedule emails more than 3 days in advance.

How can I schedule email delivery more than 3 days in advance, without creating, hosting and managing this scheduling logic on my server?

ubuntu packages and Advance Package Manager

I am new to Linux but I used Windows before. I have not used the command line anymore. I googled apt and dpkg and knew they are related to something called package.
What is meant by package here? Is the executable application also called a package?

With little programming experience, I know the package is a group of some program files

What do you really mean when you say package?

for example apt (Advance Package Tool)? What is the package in the advanced package tool?

What email delivery services allow you to schedule more than 3 days in advance? [closed]

I am looking for a list of email delivery services that allow me to send scheduled emails more than 3 days in advance.

  • SparkPost is sincere about not allowing scheduling more than 72 hours in advance
  • Sendgrid does not mention this limitation, but it exists
  • Mandrill doesn't mention anything about scheduling limitations, they don't have a GitHub presence to ask (Issues in their fake BitBucket account repositories have been disabled), they have conflicting information about the cost of this feature ("An additional fee applies "vs." at no additional cost ") and it appears that they have no mechanism to receive comments or answer a question unless you purchase a paid account.

Do tickets for these Korean trains need to be reserved in advance?

I've been in Korea with some friends two years ago and we could just buy the tickets at the station. Most of the stations will understand English, and the ones you go should know. Smaller / less touristy like Mokpo station will have some problems with English but nothing too big to not be able to buy tickets.

Be aware of:

  • Typically you will get rear-facing seats
  • Forward-facing seats will cost (slightly) more
  • Family seats (2 sets of 2 seats facing each other will also cost (slightly) more

Also, if you are going from Seoul directly to Busan or from Busan directly to Seoul, try to get the "direct" KTX. That will take approximately 1 hour of your travel time compared to one that stops at more stations.

Lastly, when you leave Seoul make sure you have at least enough cash to get a return ticket and maybe some food. We made the mistake of not doing that in a couple of smaller cities where the KTX stopped and had to walk back to the station to get to an international ATM.

Character Advance: Understanding Increased Proficiency in Leveling Up for Untrained Skills

Some of that level-up text looks like a remnant of the game test when its level was always added to the competition. Instead of using that section to explain your competition bonus, check out the competition section.

Competition is a system that measures the aptitude of a character in a specific task or quality, and has five ranges: untrained, trained, expert, master, and legendary. Competition gives you a bonus that is added by determining the following modifiers and stats: AC, attack rolls, Perception, saving throws, abilities, and spell effectiveness. If you are not trained, your proficiency bonus is +0. If you are trained, expert, master, or legendary, your proficiency bonus equals your level plus 2, 4, 6, or 8, respectively.

To help understand this, we can rearrange it into a table, like so:

begin {array} {| c | c |}
hline
textbf {Proficiency} & textbf {Bonus} \ hline
text {Untrained} and text {0} \ hline
text {Trained} and text {Level + 2} \ hline
text {Expert} and text {Level + 4} \ hline
text {Master} and text {Level + 6} \ hline
text {Legendary} & text {Level + 8} \ hline
end {array}

So, to use your example, if you go from No Training to Medical Trained at level 5, you would go from having a +0 bonus to a +7 bonus. This would work similarly for other competition mods too.