lecture notes on general relativity sean m carroll

... manipulation — electromagnetism — differential forms — Hodge duality — worldlines — proper time — energy-momentum vector — energy- momentum tensor — perfect fluids — energy-momentum conservation 2. ... four-momentum p à across a surface of constant x . To make this more concrete, let’s consider the very general category of matter which may be characterized as a fluid — a continuum of matter ... system a (1, 1) tensor is simply a matrix, M i j . Its action on a pair (ω, V ) is given by usual matrix multiplication: M( ω, V ) = (ω 1 ω 2 ··· ω n )           M 1 1 M 1 2 ··· M 1 n M 2 1 M 2 2 ···...

Ngày tải lên: 17/03/2014, 14:28

... lửụùng ủũnh m ực. Điện áp định m c: U1 m, U2 m. − Dòng điện định m c: I1 m, I2 m. − Công suất định m c: S m. 1 φ : S m = U2ñmI2 m= U1ñmI1 m. 3 φ : S m = 3 U2ủmI2 m= 3 U1ủmI1 m. ã Caực ... PHA M 2max M 1max M n n 1 2 n 1 1 n 1 n 2 2p=4 2p=2 M n M c t gia m b / a/ M c / n M c M c n n 1 n t M d / n 1 e / M y Điện 14/35 KTĐ & ĐT GVC. ThS. Nguyễn Như Phong 1999 ... Doứng m ỷ maựy ủuỷ nhoỷ. ã M m y động cơ Rotor dây quấn. Gi m dần biến trở m ỷ maựy R m . ã M ỷ maựy ủoọng cụ Rotor long sóc. − M m y trực tiếp. − Gi m điện áp...

Ngày tải lên: 25/10/2013, 13:15

... 189 6.5.3 Maximal and time-symmetric data 190 6.5.4 Solution strategy for maximal data 191 6.5.5 Explicit time-symmetric data 191 6.5.6 Non-time-symmetric data 201 6.6 Problems and recent developments ... 290 10.3 Non-spherical accretion models 292 10.3.1 Keplerian flow with magnetic dynamo 293 10.3.2 Sub-Eddington two-temperature accretion (ADAFs) 299 10.4 Comment on X-ray emission from Sgr A* ... on the test mass m is equal to the eld strength ì gravitational charge (mass) or F Mm = m f , in analogy to electrodynamics. The active gravitational mass M is thought to emanate a gravitational...

Ngày tải lên: 19/01/2014, 14:03

... on Math's Olymp Courses.pmd 11/2/2009, 3:35 PM1 Lecture 6 Some Methods of Factorization Basic Methods of Factorization (I) Extract the common factors from terms: like xm + ym + zm = m( x ... of several monomials is said to be a polynomial, its each monomial is called a term, the term not containing letters is said to be the con- stant term of the polynomial. The maximum value of ... Shelton Street, Covent Garden, London WC2H 9HE Printed in Singapore. Mathematical Olympiad Series — Vol. 6 LECTURE NOTES ON MATHEMATICAL OLYMPIAD COURSES For Junior Section ZhangJi - Lec Notes on...

Ngày tải lên: 11/03/2014, 16:55

... broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. ... 2003 PrintedinGermany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from ... Lecture Notes in Mathematics 1811 Editors: J M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris

Ngày tải lên: 14/03/2014, 18:20

...

Ngày tải lên: 17/03/2014, 14:41

... Q n . Theorem 2.47 [Williams, Blum] BLUM-Williams is a collection of one-way trapdoor permutations. Proof: This follows immediately from Lemma 2.46 because each function g n ∈ J is a permutation. The trapdoor ... function at random. One must remember that the term “random function” is misleading. It might lead one to think that certain functions are “random” and others are not. (For example, maybe the constant ... logarithm assumption there exists a strong one way function; namely, exponentiation modulo a prime p. 1 We note that a weaker assumption can be made concerning the discrete logarithm problem, and by...

Ngày tải lên: 28/03/2014, 20:20

... the same recurrence relation as s(n, k)’s with the same initial conditions. Hence, they give rise to the same sequence of numbers and are commonly known as the Stirling numbers of first kind. Notes: ... strings formed using n − 1 + ’s and m 1’s. As the +’s are indistinguishable among themselves and the same holds for 1’s, we get  n − 1 + m m  =  n − 1 + m n − 1  =  m +  n − 1  m  . Remark ... now ready to prove the s trong form of the principle of mathematical induction. Theorem 1.2.5 (Prin ciple of Mathematical Induction: Strong Form). Let P(n) be a statement about a positive integer...

Ngày tải lên: 31/03/2014, 12:20

...

Ngày tải lên: 31/03/2014, 16:27

Ngày tải lên: 24/04/2014, 17:10

Ngày tải lên: 24/04/2014, 17:12

Ngày tải lên: 24/04/2014, 17:17

Ngày tải lên: 12/05/2014, 02:47

Ngày tải lên: 24/04/2014, 17:07

... (2.15) (conditionA) 2. Ther esp onse comp onen to ft he complex conjugate ro ot is smaller than theresponse componentofthe principalroot(condition B). 3. The response componentofthe complex conjugate ... of modelingcontrol system in future mechanis mmachinesisillustrated. 1.2.2Discussion on the Performance of One AxisinaMechatronic ServoSystem In ausual, mechatronic servosystem consists of multi-axis ... Tables 13 22 2M athematical Mo del Construction of aM ec hatronic Serv oS ystem control. On above way,the ratiogain K s v of PI controlinthe general motion of an actualsystem is not the velocityamplifier...

Ngày tải lên: 13/02/2014, 08:20

... in clude dyna mic measures of performance by defining kinematic functions as the configuration-dependent terms in the manipula- tor dynamic model, e.g., contact force, inertia control, etc. [64]. In ... without violating the joint limits. Thus, for realizing a task comprising motion from an initial pose to a final one, several problems may be considered, and the solutions for some of them may not be achievable ... A voidance 37 ance scheme on such an arm provides confidence that the system can be developed and applied to other more conventional (i.e., commercial) 7- DOF manipulator designs. Section 3 extends the...

Ngày tải lên: 05/03/2014, 15:20

... holonomic systems do not apply directly to nonholonomic ones. Guidelines in Nonholonomic Motion Planning for Mobile Robots 5 minimum turning radius. Simple computation shows that the dynamic ... last one addresses collision detection, a critical operation in algorithmic motion planning. Nonholonomic Systems The research devoted to nonholonomic systems is mo- tivated mainly by mobile ... This means that the admissible control domain is no longer convex. It remains symmetric; we can still apply the LARC condition to prove that this system is small-time controllable from everywhere....

Ngày tải lên: 22/03/2014, 11:20

... estimated a value of 400,000 stadia (1 stadium=157. 5m) which is about 1.6 times its actual size. 18 MMMMMMMMMMMMMMMMMMMM MMMMMMMMMMMMMMMMMMMM MMMMMMMMMMMMMMMMMMMM MMMMMMMMMMMMMMMMMMMM The Andromeda ... perfected by Ptolemy. In his treatise the Almagest (“The Great System”) Ptolemy provided a mathematical theory of the motions of the Sun, Moon, and planets. Ptolemy vision (based on previous work ... form 1600 B.C. Secondly there was a notational problem: large numbers were very cumbersome to write since only Roman numerals were known (this notation has no notion of zero and of positional...

Ngày tải lên: 24/04/2014, 16:54