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Harvard - RCH - 2007
OZONE AND ITS PRECURSORS OVER THE UNITED STATES: SOURCES, OUTFLOW, TRANSPACIFIC INFLOW, AND HEMISPHERIC INFLUENCERynda Hudman Thesis Defense April 3, 2007Intercontinental Influence of Ozone(1) primary constituent of smog in surface air [NRC, 199
Harvard - GSW - 3
Three Outcomes of Ethnic Conflict: The Cases of Bulgaria, Macedonia and Yugoslavia 1989-1999Abstract During the 1990s three different outcomes of ethnic conflict were observed in three neighboring states in the Balkans Bulgaria, Macedonia and Yugo
Harvard - OBSTETRICS - 07
Brachial Plexus Birth Palsy Early Care, Decisions: Long-term ProblemsPeter Waters MD Childrens Hospital Harvard Medical School Boston MADisclaimers I am not an Ob-Gyn MD or expert I am not an expert on shoulder dystocia before or while it is hap
Harvard - V - 26
Poor Crisis Managementby Deborah LaValley, BSN, RN, CPHQMs. LaValley is a Program Directors, Loss Prevention and Patient Safety, for CRICO/RMF.After indications of fetal distress, a child delivered via vacuum assisted delivery was diagnosed with
Harvard - EPS - 109
EPS 109: Earth Resources and the Environment _Professor: John H. Shaw Head TF: Judith Hubbard TF: Amanda Hughes shaw@eps.harvard.edu; 5-8008; Room 215 Geo Museum jhubbard@fas.harvard.edu; 5-0498; Room 209 Geo Museum ahughes@fas.harvard.edu; 5-0428;
Harvard - EPS - 171
EPS 171: Lab 1 - Exercise 1 Aname: _ Determine the strike & dip of the sandstones (shaded layers) in A & B. Strike - draw line connecting two points of equal elevation on either the top or bottom of the sandstone bed. Measure the azimuth of line t
Harvard - EPS - 171
EPS171 Spring 2008Name: _Lab 6: Analog ModelingThis session will introduce you to the analog modeling of faults and related structures in extension and contraction. Analog models are often used to investigate the initiation and evolution of fau
Harvard - EPS - 171
EPS171: Mid-term Exam (100pts. total) 1) Isostasy (20 pts.) Provide the equations of differential isostasy.name:_A series of volcanic eruptions place flood basalts on a valley floor. Using differential isostasy, calculate the change in elevation
Harvard - EPS - 171
EPS 171: Structural Geology & Tectonics Spring 2008Instructor: Prof. John H. Shaw shaw@eps.harvard.edu 5-8008/ Rm. 215 Geology Museum Judith Hubbard jhubbard@fas.harvard.edu Rm. 209 Geology Museum Tuesday & Thursday; 10:00-11:30AM - Geology Museum R
Harvard - EPS - 109
EPS 109: Earth Resources and the Environment _Professor: John H. Shaw Head TF: Judith Hubbard TF: Amanda Hughes shaw@eps.harvard.edu; 5-8008; Room 215 Geo Museum jhubbard@fas.harvard.edu; 5-0498; Room 209 Geo Museum ahughes@fas.harvard.edu; 5-0428;
Harvard - EPS - 171
EPS 171 Structural Geology and TectonicsLab 2 Cross SectionsBusk method (Busk, 1929)Similar Fold MethodCMB060404Observation: In layered rocks, axial surfaces often bisect fold angleCMB0604041Examples from Seismic Reflection DataCMB
Harvard - EPS - 109
EPS 109: Earth Resources and the Environment _Professor: John H. Shaw Head TF: Judith Hubbard TF: Amanda Hughes shaw@eps.harvard.edu; 5-8008; Room 215 Geo Museum jhubbard@fas.harvard.edu; 5-0498; Room 209 Geo Museum ahughes@fas.harvard.edu; 5-0428;
Harvard - EPS - 171
EPS 171 Lab 2 Exercise 1: Structural interpretation of a SPOT ImageTM scene from the Andean foothillsGoal: Locate the major anticlines and synclines using landforms that indicate dipping beds. Tape your map to your desk (just so it stays in place) a
Harvard - EPS - 109
EPS 109: Earth Resources and the EnvironmentHalf course (spring term). Tu., Th., 10:00 11:30am, Labs: to be arranged; 3 hours/week (inc. local field trips) Location: Lectures in UCE seminar room (3rd Floor, 24 Oxford St.); labs in Rm. 103C (1st Flo
Harvard - EPS - 171
EPS 171: Structural Geology & Tectonics Spring 2008Instructor: Prof. John H. Shaw shaw@eps.harvard.edu 5-8008/ Rm. 215 Geology Museum Judith Hubbard jhubbard@fas.harvard.edu Rm. 209 Geology Museum Tuesday & Thursday; 10:00-11:30AM - Geology Museum R
Harvard - EPS - 109
EPS 109: Earth Resources and the Environment _Professor: John H. Shaw Head TF: Judith Hubbard TF: Amanda Hughes shaw@eps.harvard.edu; 5-8008; Room 215 Geo Museum jhubbard@fas.harvard.edu; 5-0498; Room 209 Geo Museum ahughes@fas.harvard.edu; 5-0428;
Harvard - MATH - 101
Name: _ANSWERS_ Math 101 Take Home Midterm 2 August 5th 2005Problem 1. (10 points) If A and B are subsets of some universal set X, and B' as usual means the complement of B (in X), then prove that A B ' = if and only if A B . Solution: Prove the
Harvard - TUTORIAL - 03
tH Ve d V "aafhwX$IRXTcRb S FRD r DW V b eR FHp V D r bR bR F e rp V W H D Vd ~ D rH F uPDduYgisgXwg$CgD aXR PqdqhPRgk`GDFgUfTTufPVagGDr t dssyagEyaPqGXscq QuXQgVPFIdyggUgVXuPDhuGDuPDgXQwXQfXWcRbgdwegXWugwdPRr y FH C WH Q r F V W r
Harvard - MATH - 101
Math S101, Assignment 8, July 28, 2005Emily Riehl2 We claim that for every n N, the sum 1 + 1 + + 21 is less than 2. We already showed with n 2 induction that this sum is equal to 1(1 -1 2 1 ) 2n+1= 2(1 -1 2n+1)=2-1 , 2nwhich is cl
Harvard - MATH - 101
Math S101, Assignment 2, July 7, 2005Emily Riehl1.2.1 a. For n = 1, 2, 3, 4, 5, 6, n2 n + 41 is 41, 43, 47, 53, 61, and 71, all of which are prime. b. If p, a, b Z such that p divides a and b, then p divides a + b. If we could choose n such tha
Harvard - TUTORIAL - 03
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Harvard - TUTORIAL - 03
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Harvard - TUTORIAL - 03
7!I32eD#iY9D0 2 Up $ % 9A % WA 7 %7 $X7 ` %9$p9 % $ % % 5AX E97 C W97 5) ` 7 W m @A % `) ` 7 ` Iadi&D4!7i432i3$gD&e4!FEDBAF@4!8gVY`i{DdV$gV!7 E$ c Wf @A 2 Up $ % %7 % cA2v 9 %X9 @ %AA ` 7 $ ) m k j %$ " aedY$geD7!43232gx4wDFA3W&44B132!sV5{0Q18m
Harvard - MATH - 101
Math S101, Assignment 9, August 2, 2005Emily Riehl2 Clearly for each i I, Ai i IAi . So by the lemma in Goroff, KAi K iI Ai . As this is true for each i I, K iI Ai contains the union of the KAi and iI KAi K iI Ai . Clearly for each i I, iI
Harvard - MATH - 264
Math 264 Homework #2 Due Monday, February 11, 2002 1. Just to get a feel for this sort of thing: evaluate some products (a b ) A (G(k, n) that is, pick a pair of Schubert cycles and express their product as a linear combination of Schubert cycles i
Harvard - MATH - 264
Math 264 Tentative syllabusI. Enumerative Geometry A. Basic denitions a) Basic denitions: Chow groups, intersection products, Chow ring b) comparison with other cycle theories. Our ignorance of Chow groups in general; our indierence to this fact c)
Harvard - MATH - 264
As an application of the splitting principle, and also as another illustration of how we use the theory of characteristic classes to describe solutions of systems of polynomial equations, we will consider here a very classical problem: to describe th
Harvard - MATH - 265
v E 2 % cP 5)Du V V 4 UQ%t ) c) 5)c P 4 2 0` l v w 2s EP E w E w E m 2 EP w ! E %D X ~w ) c 2 )c Q ) 2 8 5) %P q%) Q c) P 1 )5m2 f 2 E g c) #us E w h E a qt2 wg Q%P 5c2 p5` 2 5c2 zzy 2 y cS2z) Q 8%3 1 d 2 ud2
Harvard - MATH - 265
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Harvard - MATH - 264
Math 264 - Homework #3 Due Wednesday, February 20, 2002 1. Find the expected number 2, 875 of lines on a general quintic 3-fold X P4 . 2. The standard dimension count leads us to expect that a general quartic threefold X P4 will contain a one-param
Harvard - MATH - 265
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Harvard - MATH - 264
Math 264 Homework #8 Due Monday, April 8, 2002All of the following problems are in the same format: we give you a variety X, and a vector bundle E on X. The bundles will be specied in our usual, informal (to be polite) style: as a collection of ve
Harvard - MATH - 264
Math 264 - Homework #4 Due Monday, February 25, 2002 1. We've seen that the lines on a cubic surface S P3 correspond to zeroes of a section of the vector bundle E on G(1, 3) with fibers E[L] = H 0 (OL (3). Find geometric conditions on a pair (S, L)
Harvard - MATH - 264
Math 264 - Homework #9 Due Monday, April 22, 2002This is an extended exercise dealing with the lines on a cubic threefold, involving many of the ideas and techniques we've introduced over the semester. To set up, let X P4 be a smooth cubic threefo
Harvard - MATH - 264
Math 264 - Homework #7 Due Monday, March 18, 20021. In class we solved the problem: Problem: Let S, T and U P3 be general surfaces of degrees d, e and f containing a line L P3 , so that the intersection ST U = L with finite and disjoint from L.
Harvard - MATH - 264
Math 264 - Homework #5 Due Monday, March 4, 20021. We've asserted in class that the Chow ring/cohomology ring of the Grassmannian G(1, 3) is generated by the Chern classes of the universal quotient bundle, with relations obtained by setting the thi
Harvard - MATH - 264
Math 264 Homework #6 Due Monday, March 11, 2002 1. Let L P3 be a line, and let S, T and U P3 be three surfaces whose (scheme-theoretic) intersection consists of L and a bunch of reduced points. a. Suppose S, T and U are all quadrics. How many isol
Harvard - MATH - 264
Math 264 Homework #10 Due Monday, May 6, 2002These are somewhat harder exercises than the typical homework problems weve done this semester, so just do two of them. 1. Let : X Y be a double cover (that is, a nite at morphism of degree 2) of vari
Harvard - MATH - 264
Math 264 - Homework #1 Due Friday, February 8, 2002 1. Let G(k, n) PN be the Grassmannian of k-planes in Pn , embedded in projective space u of dimension N = n+1 - 1 by the Plcker embedding. k+1 n a. Let , P be two k-planes, [] and [] G(k, n) PN
Harvard - MATH - 265
t q j qw s j j o sw d o q q Br)n)TI)(S(wfWnp )j 3r)%iSrq s o m q j j pI()xg y s g u o q o t o j g m w q ~ q o u g q w q SzdSSSpSrB`p(fSfSpSr`Ir%i( s qw j o u g o w q u q o j
Harvard - MATH - 265
Y 2 E|cT 2 ) T 2 D 0( %I ! ) ! ) dP 2 8U 8SPd ) }8y&Pw ) 8y c) ) P %t2 I 1 P |2 %P 2 j DIE 64 2B Ec h ByI8USIUc c2 ) c ! c j y dT h) d ! d ) c cP |c 2 j ) @E ) %H @| Q P i5VpS%zii%hG%5#zuSqSVf#g%wiViViviGrip&wg%q|z|u}|%wq S8U5yQ%yI8Uc p
Harvard - MATH - 21
2/26/2002, BASISHOMEWORK: 3.2 6,18,28,36*,38*,48 (Preview: For next Tuesday: 3.3: 22,24,32,36,40,56*, 3.4: 4,14,16,22,32*,48)Math 21b, O. KnillDEFINITION BASIS. A set of vectors v1 , . . . , vm is a basis of a subspace X of Rn if they are linear
Harvard - MATH - 21
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Harvard - MATH - 21
Orthogonal Matrices 3/12/2002HOMEWORK: 5.3: 2,6,8,18*,20,44defgh*Math 21b, O. KnillDEFINITION The transpose of a matrix A is the matrix (AT )ij = Aji . If A is a n m matrix, then AT is a m n matrix. For square matrices, the transposed matrix i
Harvard - MATH - 21
Determinant Properties 3/19/2002Homework for Thursday, March 21, 6.2 Nr. 3,4,6,16*,36,40*Math 21b, O. KnillREMINDER. The determinant of a square matrix A = aij was defined as the sum over all possible products (-1) a1(1) an(n) , where (-1) is
Harvard - MATH - 21
2/14/2002, LINEAR TRANSFORMATIONS (II)HOMEWORK: 2.2: 4,8,10,32,47*,50*, 2.3: 10,20,26*,30,40,42*Math 21b, O. KnillINVERSE OF LINEAR TRANSFORMATION. If A is a n n matrix and T : x Ax has an inverse S, then S is linear and the A-1 , the matrix b
Harvard - MATH - 21
Gram-Schmidt process and QR factorization 3/8/2002Homework: Section 5.2, 2,14,16,34,40,42Math 21b, O. KnillMOTIVATION. The Gram-Schmidt process is an algorithm to build from an arbitrary basis an orthonormal basis. Why do we care to have an orth
Harvard - MATH - 21
2/21/2002, IMAGE AND KERNELHOMEWORK: 3.1 10,22,34,38*,44,48*Math 21b, O. KnillIMAGE. If T : Rn Rm is a linear transformation, then {T (x) | x Rn } is called the image of T . If T (x) = Ax, then the image of T is also called the image of A. We
Harvard - MATH - 21
Diagonalise to solve Markov process 4/4/2002Math 21b, O. KnillThe percentage of people using Apple OS X or the Gnu/Linux m . Let 2/3 operating system is represented by a vector v = l be the percentage of Mac OS X users, who switch to Linux each m
Harvard - MATH - 21
2/7/2002, MATRICES AND GAUSS-JORDANHOMEWORK: 1.2: 6,11,18,20,30,38*, 1.3:4,14,26*,34,48,50, Due: Tue 2/12/2002Math 21b, O. KnillMATRIX REFORMULATION. Consider the The system can be written as Ax = b, where A is a matrix system of linear equation
Harvard - MATH - 21
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Harvard - MATH - 21
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Harvard - MATH - 21
2/19/2002, LINEAR TRANSFORMATIONS (III)HOMEWORK: 2.4: 4,14,26*,28,40,48Math 21b, O. KnillMATRIX PRODUCT. If B is a m n matrix and A is a n p matrix, then BA is a m p matrix with entries n (BA)ij = k=1 Bik Akj . EXAMPLE. If B is a 3 4 matrix,
Harvard - MATH - 21
2/12/2002, LINEAR TRANSFORMATIONS (I)HOMEWORK: due Thursday 2.1: 10,20,26*,30,40,42* 4,8*,10,20,28,42*, (Due next Tuesday:Math 21b, O. Knill2.2: 4,8,10,32,47*,50*, 2.3:LINEAR TRANSFORMATION. A map T from Rn to Rm is called a linear transformati
Harvard - MATH - 21
Least Squares and Data fitting 3/14/2002HOMEWORK: 5.4 2,4,10,22,26,38Math 21b, O. KnillGOAL. We want to find "solutions" of a linear systems Ax = b also in the case when the system is not consistent. The best possible solution will be called the
Harvard - MATH - 21
~ { u | ~ u C) v$ "8pP E$ C) $ (bQ$hVxh| p ~ x|`Ch Ep rfu)|Q}xdrex v 8p QQ|hxh|x$ n b ~ | ~ | | ~ | u s u Ev$xxh|h(zp " qTHqt p " ~ | | v u s p r t r Q}{ u ~| | ~
Harvard - MATH - 21
f B f a @ s B q B f a @ h B y w X 3 y G x 8 3 c5neqR5i0eu5574I`cu5h f R9`eI4`eue8 f geEAtwcA5`wrtdW@ q p w Y Q a G v a S 3 H q p q q a y q f f t q u t t s f a @ s q f a @ h y @ 3 a G k X G d h @ a Y X V S Q F a 3 r G F G A`45itd`i0IWw4cu`i
Harvard - MATH - 21
FIRST MIDTERM REVIEWGENERAL TIPS. Practice midterm, practice TF questions, Make list of facts on a sheet of paper, Fresh up short-term memory before test Review homework, especially errors. Find error patterns.Math 21a Ask questions: Ask a q