General relativity and cosmology for undergraduates j norbury

... tunneling even if matter or radiation are present. 2.5 Summary GENERAL RELATIVITY & COSMOLOGY for Undergraduates Professor John W. Norbury Physics Department University of Wisconsin-Milwaukee P.O. ... A i ˆe i and defined the scalar product as A.B ≡ AB cos θ (3.24) where A and B are the magnitudes of the vectors A and B and θ is the angle between them. Thus A.B = A i ˆe...

Ngày tải lên: 17/03/2014, 13:34

... tunneling even if matter or radiation are present. 2.5 Summary GENERAL RELATIVITY & COSMOLOGY for Undergraduates Professor John W. Norbury Physics Department University of Wisconsin-Milwaukee P.O. ... A i ˆe i and defined the scalar product as A.B ≡ AB cos θ (3.24) where A and B are the magnitudes of the vectors A and B and θ is the angle between them. Thus A.B = A i ˆe...

Ngày tải lên: 24/04/2014, 17:07

... which use high-sounding scientific jargon; for example J. Randi 6 mentions that the NIH Office of Alternative Medicine has given credence to such claims as a cure for multiple sclerosis (despite the ... a conversa- tion about UFO’s, or astrology, or some form of mysticism, expanded consciousness, new types of awareness, ESP, and so forth. And I’ve concluded that it’s not a sci- entific w...

Ngày tải lên: 24/04/2014, 16:54

... Bardeen J M and Wagoner R V 1969 Uniformly rotating disks in general relativity Astrophys. J. 158 L65 [22] Bardeen J M and Wagoner R V 1971 Relativistic disks I. Uniform rotation Astrophys. J. 167 ... Rotating matter and black hole formation 89 Figure 3.5. Relation between M and M 2 /J for the Newtonian Maclaurin disk (broken curve), the general- relativistic dust disk...

Ngày tải lên: 19/01/2014, 14:03

... other, and with other molecules possessing dipole moments. The attractive force between two dipolar molecules, for example, CH 3 C1, methyl chloride, and CHC1 3 , chloroform, are ... aldehydes and ketones. 14.5 Oxi- dation of aldehydes and ketones. 14.6 Reduction of aldehydes and ketones. 14.7 Reaction of aldehydes and ketones with alcohol. CHAPTER 15 Carboxylic Ac...

Ngày tải lên: 06/03/2014, 07:20

... B = A i ˆe i × B j ˆe j = A i B j ˆe i × ˆe j = A i B j  ijk ˆe k Thus our general formula for the vector product is A × B =  ijk A i B j ˆe k (2.20) The advantage of this formula is that it ... (2.5) ˆe i .ˆe j = |ˆe i ||ˆe j |cos θ = cos θ = δ ij (2.8) where δ ij is defined as δ ij ≡ 1 if i = j ≡ 0 if i = j (2.9) which can also be written as a matrix [δ ij ]=  10...

Ngày tải lên: 17/03/2014, 13:45

... +2 ˆ j and  t = ˆ j − ˆ k and  f = ˆ i − ˆ j. SOLUTION r +2  t = ˆ i +2 ˆ j +2( ˆ j − ˆ k) = ˆ i +2 ˆ j +2 ˆ j − 2 ˆ k = ˆ i +4 ˆ j − 2 ˆ k (r +2  t ).  f =( ˆ i +4 ˆ j − 2 ˆ k).( ˆ i − ˆ j) = ˆ i. ˆ i ... ×v SOLUTION A) u + v = ˆ j + ˆ k + ˆ i + ˆ j = ˆ i +2 ˆ j + ˆ k B) u −v = ˆ j + ˆ k − ˆ i − ˆ j = − ˆ i + ˆ k C) u.v =( ˆ j + ˆ k).( ˆ i +...

Ngày tải lên: 17/03/2014, 14:24

... introduction to Special and General Relativity, with applications to theoretical and observational cosmology. This course is an APS minor elective, and is intended for science majors. We will delve ... he and de Sitter published a joint paper on their Einstein-de Sitter universe, an expanding universe without a cosmological constant. Chapter 2 Overview of Modern Cosmology and...

Ngày tải lên: 24/04/2014, 17:06

Ngày tải lên: 17/03/2014, 14:28