lecture notes on general relativity carroll

... December 1997 Lecture Notes on General Relativity Sean M. Carroll 1 Special Relativity and Flat Spacetime We will begin with a whirlwind tour of special relativity (SR) and life in ... integration 3. Curvature covariant derivatives and connections — connection coefficients — transformation properties — the Christoffel connection — structures on manifolds — parallel trans- port — the parallel ... prop- erties of tensors. First consider the operation of contraction, which turns a (k, l) tensor into a (k −1, l −1) tensor. Contraction proceeds by summing over one upper and one lower index: S µρ σ =...

Ngày tải lên: 17/03/2014, 14:28

... U m sin(ωt+θ) ωt 0 Máy Điện 28/35 KTĐ & ĐT GVC. ThS. Nguyễn Như Phong 1999 KTHTCN - ĐHBK MPMC KÍCH TỪ HỖ HP Với MP kích từ song song: I t ↑ → U t . Để khắc phục, quấn cuộn kích từ nối tiếp ... Phong 1999 KTHTCN - ĐHBK CÁC LOẠI ĐC. KĐB MỘT PHA. • Động cơ dùng dây quấn phụ mở máy. − Dùng trong: máy điều hòa, máy giặt, quạt, bơm ly tâm. − CC % CP lệch 90 0 điện trong ... nhỏ, y thấp. − Khả năng quá tải kém. − Dùng trong đồ chơi tải nhỏ. . . 1 n m M n M Máy Điện 11/35 KTĐ & ĐT GVC. ThS. Nguyễn Như Phong 1999 KTHTCN - ĐHBK MÁY BIẾN ÁP ĐẶC BIỆT • ...

Ngày tải lên: 25/10/2013, 13:15

... black hole: a general relativistic introduction [21] Will C M 2001 The confrontation between general relativity and experiment Living Rev. Relativity 4 4 [Online article]: cited on 17 Nov 2001. ... parameter 2m is an integration constant. Its interpretation can be obtained by means of a transition to Newton’s theory. It turns out that (G is Newton’s gravitational constant and M is the mass ... non-adiabatic spherical accretion 284 10.2.3 Radiation from spherical accretion 288 10.2.4 Calculation of the spectrum due to spherical accretion 290 10.3 Non-spherical accretion models 292 10.3.1 Keplerian...

Ngày tải lên: 19/01/2014, 14:03

... 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 ... − 3(x + y) + 1 = 0. Solution (I) By operations on equations to eliminate a variable. 19 Lectur e Notes on Mathematical Olympiad 17 Solution We rewrite the given equation in the form (a − 3)x = ... formulae: like those mentioned in Lecture 5. How- ever, contrary to Lecture 5, at present each formula is applied for con- verting an expression in non-product form to a new expression in product form. (III)...

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Ngày tải lên: 17/03/2014, 14:41

... collection of one way functions. For this we must show that it satisfies each of the conditions in the definition of a collection of one way functions. For condition 1, define S 1 to run as follows on ... definition of a hard-core predicate for a one way function, to a collection of hard core predicates for a collection of one-way functions. Definition 2.50 A hard-core predicate of a one-way function ... that one can consider. One, as before, is that the adversary gets an oracle for the function g being tested. However when g is a permutation one can also consider the Cryptography: Lecture Notes...

Ngày tải lên: 28/03/2014, 20:20

... 106 1.3. RELATIONS AND PARTITIONS 19 Definition 1.3.9 (Partition of a set). Let A be a non-empty set. Then a partition Π of A, into m-parts, is a collection of non-empty subsets A 1 , A 2 , . ... y) : x ∈ R}. Definition 1.3.3 (Relation). A relation R on a non-empty set A, is a subset of A × A. Example 1.3.4. 1. Le t A = {a, b, c, d}. Then, some of the re lations R on A are: (a) R = A ×A. (b) ... script A in Defin ition 1.4.9 will be removed, whenever there is n o chance of confus ion about the domain of the function. Theorem 1.4.10 (Properties of Identity Function). Fix two non-empty sets A...

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Ngày tải lên: 31/08/2014, 13:44

... Occassional Paper, No.22, 1983 McKinnon, R. The Order of Economic Liberalization: Financial Control in the Transition to a Market Economy, 2nd edition, The Johns Hopkins Studies in Economic Development, ... following criteria must be met before complete deregulation: (a) macroeconomic conditions are reasonably stable; (b) the financial conditions of banks and their borrowers is sound; (c) at least ... trade liberalization requires depreciation, while sudden capital inflows that tend to go along with liberalization cause appreciation pressures. The latter may derail the trade liberalization process. Second,...

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Ngày tải lên: 21/09/2013, 16:27

... dimension n. Lecture Notes: Introduction to Finite Element Method Chapter 1. Introduction © 1998 Yijun Liu, University of Cincinnati 12 Solution Techniques for Linear Systems of Equations • Gauss ... Lecture Notes: Introduction to Finite Element Method Chapter 1. Introduction © 1998 Yijun Liu, University of Cincinnati 7 II. Review of Matrix Algebra Linear System of Algebraic Equations a ... are nonsingular. Differentiation and Integration of a Matrix Let [ ] A( ) ( )t a t ij = then the differentiation is defined by d dt t da t dt ij A( ) ( ) =       and the integration by A(...

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