|
Education
Web
Viewing 1-5 of 5 total results
 Riemannian Geometry (PDF)
embedding if and only if k = ±1. Example 3.23. Let q ∈ S3 be a quaternion of unit length and φq : S 1 → S3 be the map defined by φq : z 7→ qz. For w ∈ S1 let γw : R → S1 be the curve given by γw(t) = weit. Then γw(0) = w, &gamma...
1
0
embedding if and only if k = ±1. Example 3.23. Let q ∈ S3 be a quaternion of unit length and φq : S 1 → S3 be the map defined by φq : z 7→ qz. For w ∈ S1 let γw : R → S1 be the curve given by γw(t) = weit. Then γw(0) = w, γ̇w(0) = iw and φq(γw(t)) = qwe it. By differentiating we yield dφq(γ̇w(0)) = d dt (φq(γw(t)))|t=0 = d dt (qweit)|t=0 = qiw. Then |dφq(γ̇w(0))| = |qwi| = |q||w| = 1 6= 0 implies that the differen- tial dφq is injective. It is easily checked that the immersion φq is an embedding. In the next
32
0
http://www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=32
www.matematik.lu.se/matematiklu/personal/sigma/Riemann.pdf#page=32
embedding if and only if k = ±1. Example 3.23. Let q ∈ <span class="highlight">S3</span> be a quaternion of unit length and φq : S 1 → <span class="highlight">S3</span> be the map defined by φq : z 7→ qz. For w ∈ S1 let γw : R → S1 be the curve given by γw(t) = weit. Then γw(0) = w, γ̇w(0) = iw and φq(γw(t)) = qwe it. By differentiating we yield dφq(γ̇w(0)) = d dt (φq(γw(t)))|t=0 = d dt (qweit)|t=0 = qiw. Then |dφq(γ̇w(0))| = |qwi| = |q||w| = 1 6= 0 implies that the differen- tial dφq is injective. It is easily checked that the immersion φq is an embedding. In the next
Logic and Circuits
are TWO complete circles. S1 and S3 will light the bulb. S2 and S3 will light the bulb. Logically this circuit is You can arrange any patterns you wish your students to investigate. You can assign a logical sentence and ask the students to arrange the circuits, or you can show a...
Asteroid Heating: A Shocking View
to 10,000 times the atmospheric pressure at the surface of the Earth. Shock Stage Effects resulting from general shock pressure Effects resulting from local P-T excursions Shock Pressure (Gpa) Minimum temp. increase (oC) S1 unshockedSharp optical extinction as viewed in microscope. Small number of...
Microsoft Word - 3969.doc
represent characters in familiar stories (PK-LL-S1) (ELA-1-E4) 8. Listen to a story and state orally what the story is about (PK-LL-R1) (PK-LL-R2) (PK-LL-L1) (ELA-1-E5) 9. Answer simple questions about a story read aloud (PK-LL-S3) (PK-LL-R4) (ELA-1-E5) 10. Share related life experiences afte...
1
0
represent characters in familiar stories (PK-LL-S1) (ELA-1-E4) 8. Listen to a story and state orally what the story is about (PK-LL-R1) (PK-LL-R2) (PK-LL-L1) (ELA-1-E5) 9. Answer simple questions about a story read aloud (PK-LL-S3) (PK-LL-R4) (ELA-1-E5) 10. Share related life experiences after stories are read aloud (PK-LL-L1) (PK-LL-S1) (ELA-1-E6) 11. Orally express thoughts about characters or events in a story (PK-LL-S1) (PK-LL-S2) (PKS-LL-R2) (ELA-1-E6) Standard 7: 12. Demonstrate understanding
1
0
http://www.doe.state.la.us/lde/uploads/3906.pdf#page=1
www.doe.state.la.us/lde/uploads/3906.pdf#page=1
represent characters in familiar stories (PK-LL-S1) (ELA-1-E4) 8. Listen to a story and state orally what the story is about (PK-LL-R1) (PK-LL-R2) (PK-LL-L1) (ELA-1-E5) 9. Answer simple questions about a story read aloud (PK-LL-<span class="highlight">S3</span>) (PK-LL-R4) (ELA-1-E5) 10. Share related life experiences after stories are read aloud (PK-LL-L1) (PK-LL-S1) (ELA-1-E6) 11. Orally express thoughts about characters or events in a story (PK-LL-S1) (PK-LL-S2) (PKS-LL-R2) (ELA-1-E6) Standard 7: 12. Demonstrate understanding
2
0
http://www.doe.state.la.us/lde/uploads/3906.pdf#page=2
www.doe.state.la.us/lde/uploads/3906.pdf#page=2
E1) 22. Carry on a conversation about a topic, thought, or idea from the classroom, home, or community (PK-LL-S1) (PK-LL-<span class="highlight">S3</span>) (ELA-4-E1) 23. Repeat an instruction given orally (PK-LL-S1) (ELA-4-E2) 24. Follow one- and two-step verbal and nonverbal directions (PK-LL-L2) (ELA-4-E2) 25. Retell part of a favorite story (PK-LL-R2) (ELA-4-E3) 26. Speak about life experiences or topics of interest (PK-LL-<span class="highlight">S3</span>) (ELA-4-E4) 27. Actively participate in role-playing, creative dramatics, finger plays, nursery
null
HIGH SCHOOL MATHEMATICS CONTENT EXPECTATIONS page 3 of 19 11/07 MICHIGAN DEPARTMENT OF EDUCATION STANDARDS (and number of core expectations in each standard) A1: Expressions, Equations, and Inequalities (16) A2: Functions (16) A3: Families of Functions (27) G1: Figures and Their Properties (29) G...
1
0
HIGH SCHOOL MATHEMATICS CONTENT EXPECTATIONS page 3 of 19 11/07 MICHIGAN DEPARTMENT OF EDUCATION STANDARDS (and number of core expectations in each standard) A1: Expressions, Equations, and Inequalities (16) A2: Functions (16) A3: Families of Functions (27) G1: Figures and Their Properties (29) G2: Relationships Between Figures (10) G3: Transformations of Figures in the Plane (5) S1: Univariate Data- Examining Distributions (9) S2: Bivariate Data— Examining Relationships (6) S3: Samples
5
0
http://www.michigan.gov/documents/Math11-14-open1_142202_7.pdf#page=5
www.michigan.gov/documents/Math11-14-open1_142202_7.pdf#page=5
HIGH SCHOOL MATHEMATICS CONTENT EXPECTATIONS page 3 of 19 11/07 MICHIGAN DEPARTMENT OF EDUCATION STANDARDS (and number of core expectations in each standard) A1: Expressions, Equations, and Inequalities (16) A2: Functions (16) A3: Families of Functions (27) G1: Figures and Their Properties (29) G2: Relationships Between Figures (10) G3: Transformations of Figures in the Plane (5) S1: Univariate Data- Examining Distributions (9) S2: Bivariate Data— Examining Relationships (6) <span class="highlight">S3</span>: Samples
|
