Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Mrinal Kanti Roychowdhury

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Jasang Yoon


Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals κ,where κ is the unique number given by ((1/3)(1/5)2)(κ/(2 + κ)) + ((1/3)(1/5)2) (κ/(2 + κ)) = 1, the quantization coefficient for P does not exist, and the D( P)-dimensional lower and upper quantization coefficients for P are finite and positive.


Copyright 2018 Shankar Parajulee. All Rights Reserved.

Included in

Mathematics Commons