Properties of Carry Value Transformation

The notion of Carry Value Transformation (CVT) is a model of Discrete Deterministic Dynamical System. In this paper, we have studied some interesting properties of CVT and proved that (1) the addition of any two non-negative integers is same as the sum of their CVT and XOR values. (2) While performing the repeated addition of CVT and XOR of two non-negative integers "a" and "b" (where a >= b), the number of iterations required to get either CVT=0 or XOR=0 is at most the length of "a" when both are expressed as binary strings. A similar process of addition of Modified Carry Value Transformation (MCVT) and XOR requires a maximum of two iterations for MCVT to be zero. (3) An equivalence relation is defined in the set (Z x Z) which divides the CV table into disjoint equivalence classes.Comment: 8 pages, 2 figures and 5 table

A Note on the Optimal Selection and Weighting of Comparable Properties

This paper reexamines the recommendation by Vandell (1991), Gau, Lai and Wang (1992, 1994) and Green (1994) for the use of the minimum variance and coefficient of variation criteria in the optimum selection of comparables. These authors under-emphasize the typical valuation scenario that involves extremely small samples. The analyst must rank the few available comparable properties and select the "best" to carry the most weight in the final estimate of value. Rank transformation regression is suggested as one approach that can be used to extract the buying trend. The commonly taught paired-sale analysis will remain as the industry tool until more accurate estimates of value are developed with small samples.