(no subject)
You're It!
Tagged by
posty54
1. Grab the nearest book
2. Open the book to page 23.
3. Find the fifth sentence.
4. Post the text of the next 3 sentences on your blog along with these instructions.
5. Don't you dare dig for that "cool" or "intellectual" book in your closet! I know you were thinking about it! Just pick up whatever is closest.
6. Tag 5 people
"We call such a one-to-one map from the region Ω_x onto the region Ω_z a transformation of Ω_x onto Ω_z, if the functions x^i(z^1, ..., z^n) and z^i(x^1, ... , x^n) satisfy the usual requirements of smoothness. The bijectivity (one-to-oneness) then entails that the matrix (dx/dz) (with inverse (dz/dx)) is non-singular at all points of Ω_z (cf. Theorem 1.2.5). If the regions Ω_x and Ω_z are one and the same, say Ω_x = Ω_z = Ω, then we speak simply of a transformation of the region Ω."
Strictly speaking that isn't an exact quote since the partial derivatives quoted are not actually definite, but I couldn't find the right symbol.
As for the 'tag' part of this...I'll leave it to whomever reads this to go ahead and do it, if the book nearest them is something they feel like quoting.
Tagged by
posty54
1. Grab the nearest book
2. Open the book to page 23.
3. Find the fifth sentence.
4. Post the text of the next 3 sentences on your blog along with these instructions.
5. Don't you dare dig for that "cool" or "intellectual" book in your closet! I know you were thinking about it! Just pick up whatever is closest.
6. Tag 5 people
"We call such a one-to-one map from the region Ω_x onto the region Ω_z a transformation of Ω_x onto Ω_z, if the functions x^i(z^1, ..., z^n) and z^i(x^1, ... , x^n) satisfy the usual requirements of smoothness. The bijectivity (one-to-oneness) then entails that the matrix (dx/dz) (with inverse (dz/dx)) is non-singular at all points of Ω_z (cf. Theorem 1.2.5). If the regions Ω_x and Ω_z are one and the same, say Ω_x = Ω_z = Ω, then we speak simply of a transformation of the region Ω."
Strictly speaking that isn't an exact quote since the partial derivatives quoted are not actually definite, but I couldn't find the right symbol.
As for the 'tag' part of this...I'll leave it to whomever reads this to go ahead and do it, if the book nearest them is something they feel like quoting.