@0celo7 I see you already got an answer on your normal bundle question but the answer is, again, using a fiberwise $\Bbb R^n \to \Bbb R^n$, by shrinking everything to the open unit ball, then using this to construct a global map. I agree there's a little subtlety involved in making that chart-wise right, that's why you have to arrange it to be identity near the zero section.
Once you're done, this is a bundle-morphism also a diffeo to image.
@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ Thanks! But I cannot learn new language because I have lost my memory ability (I sometimes forget my friends name). And to learn a new language you must have a great memory. BTW, thank you for your goodwill to help me! Don't care me so much. I will leave the site for a long time after I earn fanatic badge (3 days later). It was too hard for me to visit the site for 100 consecutive day and I don't want to lose it for 3 days. Thank you very much because of all your helps! Good luck!
A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1932 in which charged particles accelerate outwards from the centre along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field. Lawrence was awarded the 1939 Nobel prize in physics for this invention. Cyclotrons were the most powerful particle accelerator technology until the 1950s when they were superseded by the synchrotron, and are still used to produce particle beams in physics and nuclear medicine. The largest...
All the modern big accelerators are synchotrons (or linear), but cyclotrons are simpler to build and operate and I think they are still used where the beam energy doesn't have to be high.
@DanielSank I regularly search for my nick on the google. The chat logs are indexed there.
@DanielSank I've read. I think the main problem is that the practical usability of most new developments seems very far away.
@DanielSank And it has a collective demoralizing effect.
@DanielSank But: if we see, how are we living differently as a century before, the change is extreme. I think, the hardcore theorists moved always parallel with the practice. Einstein has got the Nobel prize for the photoelectric effect, and not for the GR.
@DanielSank I do not think ACM meant "nobody does science to apply it in the real world". Rather, I'd interpret it as "people do not care about science just for it to be applied. Aka, stuff which doesn't have any potential applications doesn't mean it's useless"
@DanielSank hm, well if you look at your chat profile you can see some information that might be useful. Rooms you own, recent messages you've posted, recent replies to you, etc. (I'm not sure how much of this stuff is visible to you and how much is mod-only.)