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From: shull@cs.utep.edu (Srinandan)
Subject: How to prove this correlation?
Message-ID: <1994Nov24.002644.21584@cs.utep.edu>
Organization: CS Dept, University of Texas at El Paso
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Date: Thu, 24 Nov 1994 00:26:44 GMT
Lines: 34

Hi Netters, 
    I am posting this for a friend. Kindly sugget some ideas to
the problem explained below.	

	|   |<-x-->| 					  |
	|<--------d---------->|                           |
	|<----------------------------------------------->|
	|		        X			  |


Supposing we a finite line "d" and at any given time the length of this line
is <= "X", i.e., d<="X" at all times, and d>0 at all times. Now if we assuume
that for every "d" there exists an appropriate "x" i.e., as "d" increases 
or decreases (within its bounds :  d > 0 <= X ) with time, "x" follows suit (it may be seen that the value of "x" is bounded to be a small
fraction of "d").

	Intutively it may be argued that as "d" increases or decreases
"x" follows suit (in line with the above assumption). Now how do I prove
the above correlation, i.e., the correlation between "x" and "d" 
mathematically?
	The below mentioned example illustrates the concept.
Suppose "X" is the maximum possible length of a Histogram, and at a given
time "t", the histogram actually occupies only "d" levels. Then I hav e to 
prove mathematically that  "x" changes with dynamic change in "d", 
in other words prove that the below mentioned formula correlates,
"x" and "d".
	mu_d(x) = mu_x(d) * d, where "mu" is a membership for example, 
mu_d(x) means the degree of belonging of x  in d.
	Please kindly suggest some clues to prove the correlation.
          
Thanks in advance.

Srinandan. H.J

