sean carroll lecture notes on general relativity pdf

Lecture notes on general relativity   s  carroll

Lecture notes on general relativity s 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 ... 1997 Lecture Notes on General Relativity Sean M. Carroll Institute for Theoretical Physics University of California Santa Barbara, CA 93106 carroll@ itp.ucsb.edu December 1997 Abstract These notes ... 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 à =...

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LECTURE NOTES ON ELECTRICAL & ELECTRONIC TECHNIQUE

LECTURE NOTES ON ELECTRICAL & ELECTRONIC TECHNIQUE

... 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 ... Nguyễn Như Phong 1999 KTHTCN - ẹHBK ẹIEU CHặNH TOC ẹO ẹC. KẹB () 1 1nn s= ã Thay ủoồi vaọn toỏc ủong bộ p f n 60 1 = − Thay đổi số cực p(a/) − Thay đổi tần số f. o Giữ U1 = const (b/) ... 22 22 P 0 WRIP AII A Z U I VUUUVU jU Pp pd p p p pndpPn an =ì== == = + == ==== +== ã Máy Điện 18/35 KTĐ & ĐT GVC. ThS. Nguyễn Như Phong 1999 KTHTCN - ĐHBK MỞ MÁY ĐỘNG CƠ KHONG ẹONG BO ã Yeõu cau: Mm > Mc. − M: đủ lớn để thời gian mở máy...

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The galactic black hole lectures on general relativity and astrophysics

The galactic black hole lectures on general relativity and astrophysics

... 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 ... equation: R à 1 2 Rg à Einstein tensor G à +g à = T à . (1.44) The value := 8G/c 4 of Einsteins gravitational constant can be determined by a transition to the Newtonian limit of general relativity. ...

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Toán học quốc tế olympiad vol6 lecture notes on mathematical olympiad courses for junior section vol 1

Toán học quốc tế olympiad vol6 lecture notes on mathematical olympiad courses for junior section vol 1

... 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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Lecture Notes on Cryptography ppt

Lecture Notes on Cryptography ppt

... 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...

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Tài liệu Lecture Notes in Control and Information SciencesEditors: M. Thoma pdf

Tài liệu Lecture Notes in Control and Information SciencesEditors: M. Thoma pdf

... (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 ... be considered. When the velocityofpresentcontourcontrol is below25[m /min], the tra- jectory deviation does notoccur.Therefore, in the controlbasedonthe previ- ousposition decisioncontrol concept, ... of opportunities of discussion with Kyura,who is long-term working on theservo controller design and its application in mechatronic industry, on thecontrol of mechatronic machine during the past...

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Tài liệu Lecture Notes in Geoinformation and Cartography pdf

Tài liệu Lecture Notes in Geoinformation and Cartography pdf

... 1990; Rushton and Lolonis 1996). Again, on the left, patterns are different and depend on scale. We can conclude that patterns depend on scale and actions based on patterns should consider the ... LAN Epidemic Prevention Policy, Medicine and OA Information …. DEMΞΞ Data acquisition and Communication  GPS Data Acquisition  Field Investigation Data  Image Data Extraction …. S tatistical ... Region Segregation and Query  Real Time Alarm, Display and Process- ing Internet Information Publishing  Epidemic Information Publishing on Web  Statistical Query on Web  Decision Analysis...

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Tài liệu Lecture Notes in Economics and Mathematical Systems pdf

Tài liệu Lecture Notes in Economics and Mathematical Systems pdf

... |X n |≤YP- a.s. for all n. Condition 2. is Lebesgue’s ’dominated convergence’ condition. The relation between L 1 -convergence and convergence in probabil- ity is now given by Proposition 1.2.4. (Lebesgue) ... (1973), which leads to the solution of PDE’s under boundary conditions. 1.2 Convergence Concepts for Random Variables 9 The above example shows that an additional condition is needed which prevents ... 50 3 The Girsanov Transformation 55 3.1 HeuristicIntroduction 55 3.2 TheGeneralGirsanovTransformation 58 3.3 ApplicationtoBrownianMotion 63 4 Application to Financial Economics 67 4.1 The Market...

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Báo cáo khoa học: Identification of small scale biochemical networks based on general type system perturbations pdf

Báo cáo khoa học: Identification of small scale biochemical networks based on general type system perturbations pdf

... assumption of con- stant parameter perturbations.) Choice of sampling time and dealing with moiety conservations Biochemical networks generally contain dynamic modes with a wide range of time constants. ... expression levels of large gene sets and the concentrations of metabolites, are evolving rapidly. These data sets contain the information required to uncover the organization of biological systems on ... param- eter, not only concentrations of specific components, and that the direct effect of the perturbations does not need to be known. This is important as concentration perturbations are often difficult...

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Data Mining Classification: Alternative Techniques - Lecture Notes for Chapter 5 Introduction to Data Mining pdf

Data Mining Classification: Alternative Techniques - Lecture Notes for Chapter 5 Introduction to Data Mining pdf

... a collection of “if…then…” rules Rule: (Condition) → y where ã Condition is a conjunctions of attributes ã y is the class label – LHS: rule antecedent or condition – RHS: rule consequent – Examples ... Introduction to Data Mining 8 From Decision Trees To Rules YESYESNONO NONO NONO Yes No {Married} {Single, Divorced} < 80K > 80K Taxable Income Marital Status Refund Classification Rules (Refund=Yes) ... removing one of the conjuncts in A – Compare the pessimistic error rate for r against all r’s – Prune if one of the r’s has lower pessimistic error rate – Repeat until we can no longer improve generalization...

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