Cartesian Tensors Reference: H. Jeffreys Cartesian Tensors Cartesian tensors 1/35 1 Coordinates and Vectors z = x3 e3 y = x2 e2 e1 x = x1 Cartesian tensors 2/35 Coordinates xi x1 = x Unit vectors ei e1 = e x = i i = 1, 2, 3 e3 = ez = k (2) i = 1, 2, 3 x2 = y x3 = z (1) e2 = e y = j General vector (formal definition to follow) denoted by components e.g. u = u i Cartesian tensors 3/35 Notation The boldface notation for vectors is referred to as dyadic notation The subscript notation is tensor notation. ...

... Printed in U.S.A. THE STELLAR DISK THICKNESS OF LOW SURFACE BRIGHTNESS GALAXIES D. Bizyaev 1,2,3 and S. Kajsin 4 Received 2003 October 23; accepted 2004 June 9 ABSTRACT We present surface photometry results for a sample of 11 edge-on galaxies observed with the 6 m telescope at the Special Astrophysical Observatory, Russia. ... We find from a comparison of photometric scales that the stellar disks of LSB galaxies are thinner than those of high surface brightness ( HSB) galaxies. ... UGC 11301 .. ...