Finite models for laws in two variables

A characterization of finite soluble groups by laws in two variables∗

Define a sequence (sn) of two-variable words in variables x, y as follows: s0(x, y) = x, sn+1(x, y) = [sn(x, y)−y, sn(x, y)] for n > 0. It is shown that a finite group G is soluble if and only if sn is a law of G for all but finitely many values of n.

Strong Laws for Weighted Sums of Negative Dependent Random Variables

In this paper, we discuss strong laws for weighted sums of pairwise negatively dependent random variables. The results on i.i.d case of Soo Hak Sung [9] are generalized and extended.

ON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES

In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.

Embedding variables in finite dimensional models

Global problems associated with the transformation from the Arnowitt, Deser and Misner (ADM) to the Kuchař variables are studied. Two models are considered: The Friedmann cosmology with scalar matter and the torus sector of the 2+1 gravity. For the Friedmann model, the transformations to the Kuchař description corresponding to three different popular time coordinates are shown to exist on the w...

Finite Models and Finitely Many Variables