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WRITE YOUR THESIS TITLE HERE

SMLA

Ph. D (THESIS) JANUARY 2005


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UNIVERSITY OF YANGON

DEPARTMENT OF MATHEMATICS

WRITE YOUR THESIS TITLE HERE

By

SMLA

Board of Examiners


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Chairman Dr. Daw Kyi Kyi Aung . . . . .Head & Professor

Mathematics DepartmentYangon University

External Examiner Dr. Mya Oo . . . . . . . . . . . . . . . . . .RectorUniversity of Distance EducationYangon

External Examiner Dr. Oo Mya . . . . . . . . . . . . . . . . . .Rank

Ministry NameMinistry Long Name

Supervisor Dr. Sann Myint . . . . . . . . . . . . . .Associate ProfessorMathematics DepartmentYangon University

Internal Examiner Dr. Myo Thein Gyi . . . . . . . . . .Lecturer

Mathematics DepartmentYangon University

Thesis submitted to the University of Yangon

as a requirement for the degree of Doctor of Philosophy inMathematics

Ph. D (Thesis) January 2005

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UNIVERSITY OF YANGONDEPARTMENT OF MATHEMATICS

THESIS TITLELONG THESIS TITLE

By

SMLA

Thesis submitted to the University of Yangon

as a requirement for the degree of Doctor of Philosophy in


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Mathematics

Ph. D (Thesis) January 2005

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Dedication

This thesis is dedicated to my parents, U XXX YYY and Daw YYY ZZZ,for their encouragement throughout the whole of my education.

It is also dedicated to my mother-in-law, Daw ZZZ WWW, my wife DawWWW TTT SSS, and my daughter Ma UUU VVV TTT, whose letters and

telephone calls were a constant source of encouragement and comfort, duringthe course of my study in QQQQQQQ.

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Acknowledgements

I would like to express my gratitude to Professor Daw Kyi Kyi Aung, Headof the Department of Mathematics, University of Yangon, for hers kind per-mission to write this thesisI wish to record here my deepest gratitude to my supervisor Dr. xxx yyy,

Lecturer, Department of Mathematics, University of Yangon, for introducingme to this topic and for his guidance, assistance and encouragement at alltimes we have worked together.I am deeply indebted to all my teachers for their invaluable encouragementthroughout my education career.Last, but not the least, I wish to thank all the staff from the Department ofMathematics, University of Yangon for the help they have given me through-out my studies.

January 2005 SMLA

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Abstract

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Contents

1 Weighted Spaces 11.1 Nachbin families and Np families . . . . . . . . . . . . . . . . 1

1.1.1 Function Spaces . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Definitions: . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3 Definitions: . . . . . . . . . . . . . . . . . . . . . . . . 11.1.4 Definitions: . . . . . . . . . . . . . . . . . . . . . . . . 11.1.5 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.6 Remark: . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.7 Definitions: . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Section Heading . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Subsection Heading . . . . . . . . . . . . . . . . . . . . 2


1.4 Section Heading . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4.1 Subsection Heading . . . . . . . . . . . . . . . . . . . . 31.5 Section Heading . . . . . . . . . . . . . . . . . . . . . . . . . . 4


1.6.1 Subsection Heading . . . . . . . . . . . . . . . . . . . . 4

2 Chapter Heading 52.1 Section Heading . . . . . . . . . . . . . . . . . . . . . . . . . . 5



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A Appendix Title 11

B Appendix Title 12

C Appendix Title 13

D Appendix Title 14

References 15

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Chapter 1

Weighted Spaces

Throughout this paper (except otherwise), X could denote

1.1 Nachbin families and Np families

Section starts here.

1.1.1 Function Spaces

Subsection starts here.

1.1.2 Definitions:Subsubsection starts here.

1.1.3 Definition:

Subsubsection starts here.

1.1.4 Definition:


1


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1.1.5 Examples:


1.1.6 Remark:


1.1.7 Definition:


1.1.8 Definition:


1.1.9 Proposition:


1.2 Section Heading


1.2.1 Subsection Heading


Subsubsection Heading


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1.3 Section Heading






1.4 Section Heading






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1.5 Section Heading






1.6 Section Heading






4


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Chapter 2

Chapter Heading

Chapter starts here.

2.1 Section Heading




Subsubsection HeadingSubsubsection starts here.

2.2 Section Heading




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6


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Chapter 3

Chapter Heading


3.1 Section Heading





3.2 Section Heading




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Chapter 4

Chapter Heading


4.1 Section Heading





4.2 Section Heading




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10


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Appendix A

Appendix Title

Write Appendix A here.

11


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Appendix B

Appendix Title

Write Appendix B here.

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Appendix C

Appendix Title

Write Appendix C here.

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Appendix D

Appendix Title

Write Appendix D here.

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References

[1] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions,Dover Publications, New York, 1965.

[2] P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals forEngineers and Scientists, Second Edition, Revised, Springer-Verlag,Berlin, New York, 1971.

[3] H. Hancock, Lectures on the Theory of Elliptic Functions, DoverPublications, New York, 1958.

[4] G. B. Whitham, Linear and Nonlinear Waves, John Wiley, NewYork, 1974.

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