|
Education
Web
Table of Moons
J. Kleyna22,707,00061,297.7 Suttungr2000Gladman et al.19,470,00071016.8 S/2004 S07 2004D. Jewitt, S. Sheppard, J. Kleyna19,800,00061,103 S/2004 S12 2004D. Jewitt, S. Sheppard, J. Kleyna19,650,00051,048 S/2004 S13 2004D. Jewitt, S. Sheppard, J. Kleyna18,450,0006906 S/2004 S17 2004D. Jewitt, S. Sheppa...
 Riemannian Geometry (PDF)
ψk : z 7→ zk. For which k ∈ N0 are φk, ψk immersions, submersions or embeddings. Exercise 3.7. Prove that the map φ : Rm → Cm given by φ : (x1, . . . , xm) 7→ (eix1 , . . . , eixm) is a parametrization of the m-dimensional torus Tm in Cm. Exercise 3.8. Find a...
1
0
ψk : z 7→ zk. For which k ∈ N0 are φk, ψk immersions, submersions or embeddings. Exercise 3.7. Prove that the map φ : Rm → Cm given by φ : (x1, . . . , xm) 7→ (eix1 , . . . , eixm) is a parametrization of the m-dimensional torus Tm in Cm. Exercise 3.8. Find a proof for Theorem 3.26. Exercise 3.9. Prove that the Hopf-map φ : S3 → S2 with φ : (x, y) 7→ (2xȳ, |x|2 − |y|2) is a submersion.
18
0
http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=18
www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=18
16 2. DIFFERENTIABLE MANIFOLDS Example 2.25. The result of Proposition 2.24 can be used to show that the following maps are all smooth. (i) φ1 : S 2 ⊂ R3 → <span class="highlight">S3</span> ⊂ R4, φ1 : (x, y, z) 7→ (x, y, z, 0), (ii) φ2 : S 3 ⊂ C2 → S2 ⊂ C×R, φ2 : (z1, z2) 7→ (2z1z̄2, |z1|2−|z2|2), (iii) φ3 : R1 → S1 ⊂ C, φ3 : t 7→ eit, (iv) φ4 : Rm+1 \ {0} → Sm, φ4 : x 7→ x/|x|, (v) φ5 : Rm+1 \ {0} → RPm, φ5 : x 7→ [x], (vi) φ6 : S m → RPm, φ6 : x 7→ [x]. In differential geometry we are especially interested in differentiable manifolds
36
0
http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=36
www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=36
ψk : z 7→ zk. For which k ∈ N0 are φk, ψk immersions, submersions or embeddings. Exercise 3.7. Prove that the map φ : Rm → Cm given by φ : (x1, . . . , xm) 7→ (eix1 , . . . , eixm) is a parametrization of the m-dimensional torus Tm in Cm. Exercise 3.8. Find a proof for Theorem 3.26. Exercise 3.9. Prove that the Hopf-map φ : <span class="highlight">S3</span> → S2 with φ : (x, y) 7→ (2xȳ, |x|2 − |y|2) is a submersion.
Stanford Encyclopedia of Philosophy: evolutionary
do well against each other. All of the other strategies involve S3, S4, R3, or R4, which results in the same act being performed no matter what the external state is. Sender Strategies: S1:Send M1 if T1; M2 if T2 S2:Send M2 if T1;M1 if T2 S3:Send M1 if T1 or T2 S4:Send M2 if T1 or T...
Differences Among Unemployment Rates
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
How Long Does It Take Monetary Policy to Have an Effect on the Economy?
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
Why Are These Rates Different?
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
The Federal Reserve and Open Market Operations?
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
EconEdLink Online Lessons
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
How Long Does Unemployment Last?
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
Why Did Individuals Become Unemployed During the Month?
Taxation Taxes Technological Changes Tools of the Federal Reserve Trade Trade-off Trade-offs among Goals Traditional Economy Tragedy of the Commons Transaction Costs Types of Unemployment Unemployment Unemployment Rate Utility Voluntary Exchange Wage Wants Standard All Standards S1 Scarcity S2 Marg...
|
