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\title{{Relativization in universal standard mathematics:}}
\subtitle{a corpus-based study on newspaper physics} % Commend this line if you don't have a subtitle
\author{Sanni Hullberger}
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\makefrontpage{77}{Joensuu}{2016}
{Department of Physics and Mathematics}
{Auditorium M301 in Metria Building at the University of Eastern Finland, Joensuu,
 on November 25th, 2016, at 12 o'clock.}
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\begin{center}
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  Grano Oy\\
  Jyv\"askyl\"a, 2016\\
  Editors:  Pertti Pasanen, Pekka Toivanen,\\
  Jukka Tuomela, and Matti Vornanen\\[1cm]
  Distribution:\\
  University of Eastern Finland Library / Sales of publications\\
  \url{julkaisumyynti@uef.fi}\\
  \url{http://www.uef.fi/kirjasto}\\[1cm]
  ISBN: xxx-xxx-xx-xxxx-x (print)\\
  ISSNL: 1798-5668\\
  ISSN:  1798-5668\\
  ISBN: xxx-xxx-xx-xxxx-x (pdf)\\
  ISSNL: 1798-5668\\
  ISSN:  1798-5668
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\begin{tabular}{p{45mm}l}
  Author's address: & University of Eastern Finland\\
              & Department of XXXXXXXXXXXXXXX \\ % or Institute of Photonics
              & P.O.Box 1234 \\
              & 12345 JOENSUU/KUOPIO \\
              & FINLAND \\
              & email: firstname.lastname@uef.fi \\[2mm]
  Supervisors:& Professor Special Expert\\
              & University of Eastern Finland \\
              & Department of Environmental Sciences \\
              & P.O.Box 1627 \\
              & 70211 KUOPIO \\
              & FINLAND \\
              & email: firstname.lastname@uef.fi \\[2mm]
              & Professor Xxxxx Yyyyyyy \\
              & University of Eastern Finland \\
              & Department of Environmental Sciences \\
              & P.O.Box 1627 \\
              & 70211 KUOPIO \\
              & FINLAND \\
              & email: firstname.lastname@uef.fi \\[2mm]
  Reviewers:  & Professor Special Expert\\
              & University of Eastern Finland \\
              & Department of Environmental Sciences \\
              & P.O.Box 1627 \\
              & 70211 KUOPIO \\
              & FINLAND \\
              & email: firstname.lastname@uef.fi \\[2mm]
              & Professor Xxxxx Yyyyyyy \\
              & University of Eastern Finland \\
              & Department of Environmental Sciences \\
              & P.O.Box 1627 \\
              & 70211 KUOPIO \\
              & FINLAND \\
              & email: firstname.lastname@uef.fi \\[2mm]
  Opponent:   & Professor Special Expert\\
              & University of Eastern Finland \\
              & Department of Environmental Sciences \\
              & P.O.Box 1627 \\
              & 70211 KUOPIO \\
              & FINLAND \\
              & email: xxx@xx.yy
\end{tabular}
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\makeabstracthead{Joensuu}{2016} % place and year
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\section*{ABSTRACT} % A short 'example'
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This work contains several theoretical and numerical studies on
diffractive optics and variable coherence.  A generalized Iterative
Fourier-Transform Algorithm (IFTA) for spatially partially coherent
light is introduced. A diffractive element with a non-paraxial
line focus is designed by rigorous diffraction theory.
A novel method to control the coherence properties of an optical field
by a vibrating grating is derived theoretically. The use of Bragg
selectivity of a volume grating to extract a coherent component
from a partially coherent field is introduced.

The effect of partial spatial coherence in non-paraxial Talbot imaging
and the validity of the paraxial approximation in Lau imaging
are analyzed.  Non-paraxial Bessel beams generated by diffractive
axicons are analyzed by a new quasi-rigorous electromagnetic method.

A new method to encode the  complex amplitude of an arbitrary optical
field in a zeroth-order diffractive structure is introduced.
Waveguide discontinuities and index-modulated waveguide
structures are analyzed by applying periodic boundary conditions,
which enables the  use of rigorous grating-diffraction theories.
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\par
\vspace{5mm}
\noindent
\textit{\textbf{Universal Decimal Classification:} 53.084.85, 535.3, 535.4, 681.7.02 \\
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%\textbf{MSC 2010:} 35J20,  47G10, 30F15 \\   % see http://www.ams.org/msc/msc2010.html
%\textbf{PACS 2010:} 42.40.Eq, 42.40.Jv  \\   % see https://publishing.aip.org/publishing/pacs/pacs-2010-regular-edition
\textbf{OCIS codes:} 050.1960, 130.4815  \\   % see https://www.osapublishing.org/submit/ocis/
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\textbf{Keywords:} Diffraction gratings, optical switching devices, partial differential equations, complex analysis}
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\section*{ACKNOWLEDGEMENTS}
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\par
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\noindent
Joensuu, November 25, 2016    \\[3mm]
\indent\hspace{6mm}\textit{\theauthor}
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\section*{LIST OF PUBLICATIONS}
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This thesis consists of the present review of the author's work
in the field of optical phenomena and the following
selection of the author's publications:
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\begin{enumerate}
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\item[\myp{1}]
S. Hullberger, J. K\"aiv\"ar\"ainen, and J. Saarelainen, "Meromorphic functions in modeling of optical fields with singularities," {\em J. Math. Anal. Appl.} \textbf{424}, 1113--1121 (2015).

\item[\myp{2}]
S. Hullberger and J. K\"aiv\"ar\"ainen, "Synthesis of phase gratings for desired
coherence states," {\em Opt. Express} \textbf{24}, 1432--1439 (2016).

\item[\myp{3}]
L.-T. Koiranen, S. Hullberger, J. Saarelainen, and T. Arola, "Interpretation of polarization patterns,"
{\em Opt. Lett.} \textbf{41}, 1353--1356 (2016).

\item[\myp{4}]
S. Hullberger, J. Saarelainen, and T. Arola, "Detection of light beams with aid of golden nanorods,"
{\em Appl. Phys. Lett.} \textbf{109}, 082015 (2016).
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\end{enumerate}
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\vspace{1mm}
\noindent
Throughout the overview, these papers will be referred to by Roman numerals.
\vspace{20mm}
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\section*{AUTHOR'S CONTRIBUTION}
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The publications selected in this dissertation are original research papers on differential equations.
Here you should explain what is your contribution in each of the papers.
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