Erratum to: “Compression Based Homogeneity Testing” [Dokl. Math. 85, 251–254 (2012)]

Testing Homogeneity on Large Scales

We review observational tests for the homogeneity of the Universe on large scales. Redshift and peculiar velocity surveys, radio sources, the X-Ray Background, the Lyman-α forest and the Cosmic Microwave Background are used to set constraints on inhomogeneous models and in particular on fractal-like models. Assuming the Cosmological Principle and the FRW metric, we estimate cosmological paramet...

Supplemental Notes for Math 704 . Spring 2012

1.1. Normed spaces. Recall that a (real) vector space V is called a normed space if there exists a function ‖ · ‖ : V → R such that (1) ‖f‖ ≥ 0 for all f ∈ V and ‖f‖ = 0 if and only if f = 0. (2) ‖af‖ = |a| ‖f‖ for all f ∈ V and all scalars a. (3) (Triangle inequality) ‖f + g‖ ≤ ‖f ||+ ‖g‖ for all f, g ∈ V . If V is a normed space, then d(f, g) = ‖f−g‖ defines a metric on V . Convergence w.r.t ...

Math 722: Complex Analysis Spring Semester 2012

1) Complex Analysis by Lars V. Ahlfors, Third Edition, McGraw-Hill, (QA331 A45 1979) This is a standard text, written by a winner of the Fields medal. 2) Analytic Function Theory by Einar Hille, Volume I and II, Chelsea Publishing Company, (QA331 H54 1973) The second volume especially has discussions of a number of interesting topics. 3) (a) Elements of the Theory of Functions by Konrad Knopp, ...

Math 6810 ( Probability ) Fall 2012 Lecture notes

Homework for Math 6170 §1, Spring 2012