Theses and Dissertations

Date of Award

12-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Mrinal Kanti Roychowdhury

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Jasang Yoon

Abstract

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.

Comments

Copyright 2018 Shankar Parajulee. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/asymptotic-quantization-condensation-system/docview/2177355805/se-2?accountid=7119

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