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% Original author:
% Mathias Legrand (legrand.mathias@gmail.com)
% With extensive modifications by:
% Vel (vel@latextemplates.com)
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% License:
% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
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\newtheorem{summary}[theorem]{Summary}

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%	HYPERLINKS
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\usepackage{hyperref} % Required for hyperlinks
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%	ARTICLE INFORMATION
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% Definition of \maketitle
\JournalInfo{{\raisebox{-2.5ex}{\includegraphics[width=2.8cm]{logo.jpg}} }\\e-ISSN 2687-4261 \\
Vol. **, No. **, Pag-es, 20**\\
Article Type
} % Journal information
\Archive{} % Additional notes (e.g. copyright, DOI, review/research article)



\PaperTitle{Title of Paper \\ \small{\hl{The first letters must be capitalised except prepositions (e.g."Weingarten Map of the Hypersurface  in Euclidean
$4$-Space") }}} % Article title

\Authors{Name SURNAME $^1$ \orcidA , Name SURNAME  $^2$ \orcidB, Name SURNAME $^3$ \orcidC }
\affiliation{\textit{$^1$  Department of ..., Faculty of ..., ... University, Post Code, City, Country}.\\
\textit{$^2$  Department of ..., Faculty of ..., ... University, Post Code, City, Country}.\\
\textit{$^3$ Department of ..., Faculty of ..., ... University, Post Code, City, Country}.} % Author affiliation
\affiliation{$^1$ \Envelope email1@adress, $^2$ \Envelope email2@adress,  $^3$ \Envelope email3@adress}
\affiliation{\textbf{Corresponding author}: Name SURNAME}


\Keywords{Keywords: Keyword 1 --- keyword 2 --- keyword 3 {\hl{Insert (Write) a minumum of three and maximum of 6 keywords or phrases. The first letter of the first keyword capitalized and the all other letters lowercase (compulsory).}}\\
MSC: *****, *****, ***** \hl{Write three Mathematics Subject Classification (2020) codes (compulsory).}} 
\newcommand{\keywordname}{Keywords and 2020 Mathematics Subject Classification} % Defines the keywords heading name
\affiliation{\textbf{Article History:} Received Day Month Year; Accepted Day Month Year}
%----------------------------------------------------------------------------------------
%	ABSTRACT
%----------------------------------------------------------------------------------------

\Abstract{\hl{Write your abstract here.The abstract should not exceed 250 words and should be a short summary of the article.There should be no references in the abstract. Write the ORCIDs in the relevant places at the top of the tex file. ORCIDs are compulsory.} }



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\pagestyle{fancy}
\fancyhf{}

\rhead{\raisebox{-2.5ex}{\includegraphics[width=1.8cm]{logo.jpg}}}
\lfoot{ \thepage}
\cfoot{Vol.**, No. **, Pag-es, Year}



\begin{document}

\flushbottom % Makes all text pages the same height

\maketitle % Print the title and abstract box

%\tableofcontents % Print the contents section

\thispagestyle{empty} % Removes page numbering from the first page

%----------------------------------------------------------------------------------------
%	ARTICLE CONTENTS
%----------------------------------------------------------------------------------------

\section{Introduction (Compulsory)} % The \section*{} command stops section numbering

%\addcontentsline{toc}{section}% Adds this section to the table of contents
\hl{Write an introduction here. Use American English. 


The introduction should briefly but clearly describe your study and emphasise its importance. The literature review should be carefully reviewed and important publications should be cited. The main aim and results of the study should also be mentioned. The introduction should be written in a way that scientists working in all fields can understand. }\newline

\hl{Insert citations in order of appearance, not alphabetical order. } \newline

 \hl{Double dollars should not be used to write equations:}
  $$x+y=z. \,\,\, \textcolor{red}{\textit{Do not use!}}  $$
   \hl{Equations should be written as follows: }
  \begin{equation}
      x+y=z.
  \end{equation}
  and
  \begin{equation} \label{1}
	x \otimes y \otimes z = \left| {\begin{array}{*{20}{c}}
			{{e_1}}&{{e_2}}&{{e_3}}&{{e_4}}\\
			{{x_1}}&{{x_2}}&{{x_3}}&{{x_4}}\\
			{{y_1}}&{{y_2}}&{{y_3}}&{{y_4}}\\
			{{z_1}}&{{z_2}}&{{z_3}}&{{z_4}}
	\end{array}} \right|.
\end{equation}

\hl{The following is an example of itemize within text. }

	\begin{itemize}
	\item[i.]
	You can write your equations. 	
	\item[ii.] The following is given:\begin{equation} \label{2}
	M^3=\left \{X \in E^4 | f:U\subset E^4\overset{diff.}{\rightarrow} \mathbb{R},\, f(X)=const. \,\,\, {\overrightarrow {\nabla f} \left| {_P}\neq 0, \right. P\in M^3}  \right \}.\end{equation}
		
	\item[iii.] $\left\langle {x \otimes y \otimes z,t} \right\rangle  = \det \left( {x,y,z,t} \right)$.
\end{itemize}


\hl{All abbreviations need to be defined when they are first used.}\newline


\hl{Do not number equations or mathematical expressions unless necessary.}


\section{Section 2}

\hl{The titles of the sections should be written in lower case except for the first word and for proper names (e.g. 
"The matrix of the Weingarten map of hypersurface"). }


\begin{definition}
\label{def1} Let
$x=\sum\limits_{i=1}^{4}{{{x}_{i}}{{e}_{i}}}$ and $y=\sum\limits_{i=1}^{4}{{{y}_{i}}{{e}_{i}}}$,  be two vectors in $\mathbb{R}^{4}$, equipped with the standard inner product given by 
\begin{equation*}
    \left< x,y\right>=x_1y_1+x_2y_2+x_3y_3+x_4y_4,
\end{equation*}
where $\left\{e_1, e_2, e_3, e_4\right\}$ is the standard basis of $\mathbb{R}^{4}$.
\end{definition} 

\hl{This is an example of a label of the definition} Definition \ref{def1}.


\begin{equation} \label{4}
	S = \left( {\begin{array}{*{20}{c}}
			{\frac{\varphi_{11}} {\phi _{11}}}&{\frac{\varphi_{12}} {{\sqrt {\phi _{11} \phi _{22}} }}}&{\frac{\varphi_{13}}{{\sqrt {\phi _{11} \phi _{33}} }}}\\\\
			{\frac{\varphi_{12}}{{\sqrt {\phi _{11} \phi _{22}} }}}&{\frac{\varphi_{22}}{\phi _{22}}}&{\frac{\varphi_{23}}{{\sqrt \phi _{22} \phi _{33}}}}\\\\
			{\frac{\varphi_{13}}{{\sqrt { \phi _{11} \phi _{33}} }}}&{\frac{\varphi_{23}}{{\sqrt \phi _{22} \phi _{33}}}}&{\frac{\varphi_{33}}{\phi _{33}}}
	\end{array}} \right),
\end{equation}
where
\begin{equation*}
\begin{array}{l}
\varphi_{11} =- \left\langle {{\phi _{uu}},N} \right\rangle ,\,\,\varphi_{12} =- \left\langle {{\phi _{uv}},N} \right\rangle ,\,\,\varphi_{13} =- \left\langle {{\phi _{uw}},N} \right\rangle,\\
\varphi_{22} = -\left\langle {{\phi _{vv}},N} \right\rangle ,\,\,\varphi_{23} =- \left\langle {{\phi _{vw}},N} \right\rangle ,\,\,\varphi_{33} = -\left\langle {{\phi _{ww}},N} \right\rangle .
\end{array}
\end{equation*}


\hl{This is an example of a label of the equation} (\ref{4}).

\begin{theorem}
	Write your theorem here.
\end{theorem}

\begin{proof}
Write your proof here.
\begin{equation*}
    \left\{\begin{matrix}
x=\left ( {x}_{1},{x}_{2},{x}_{3}, 0 \right ), \\
y=\left ( {y}_{1},{y}_{2},{y}_{3}, 0 \right ). \\
\end{matrix}\right.
\end{equation*}
\end{proof}
\begin{example}
Write your example here.   
\begin{equation}
    \begin{split}
        \varphi_{11} =- \left\langle {{\phi _{uu}},N} \right\rangle ,\,\,\varphi_{12} =- \left\langle {{\phi _{uv}},N} \right\rangle ,\,\,\varphi_{13} =- \left\langle {{\phi _{uw}},N} \right\rangle,\\
\varphi_{22} = -\left\langle {{\phi _{vv}},N} \right\rangle ,\,\,\varphi_{23} =- \left\langle {{\phi _{vw}},N} \right\rangle ,\,\,\varphi_{33} = -\left\langle {{\phi _{ww}},N} \right\rangle .
    \end{split}
\end{equation}
\end{example}

\begin{lemma}
Let .... satisfies the following conditions:

\begin{itemize}
\item[i.]
\item[ii.] 
\item[iii.] 
\end{itemize}
for all $X,Y\in\Im^{1}_{0}(M)$.
\end{lemma}


\newpage


\begin{figure}[!htbp]
    \centering
    \includegraphics[width=1.95 in]{HSJGfigure}
    \caption{An image of galaxy \cite{Cite8}}
    \label{fig:galaxy1}
\end{figure}


\hl{The followings are the examples of inserting two or more images side by side:}

\begin{figure}[!htbp]
    \centering
\begin{tabular}{cc}	\includegraphics[width=1.95 in]{HSJGfigure} & \includegraphics[width=1.95 in]{HSJGfigure} \\ 
		(a) & (b) 
	\end{tabular}
  \caption{(a) An image of galaxy \cite{Cite8}, (b) An image of galaxy \cite{Cite8}}  \label{fig:galaxy12}
\end{figure}


\begin{figure}[!htbp]
    \centering
\begin{tabular}{ccc}	\includegraphics[width=1.95 in]{HSJGfigure} & \includegraphics[width=1.95 in]{HSJGfigure} 
& \includegraphics[width=1.95 in]{HSJGfigure} \\ 
		(a) & (b) & (c) 
	\end{tabular}
   \caption{(a) An image of galaxy \cite{Cite8}, (b) An image of galaxy \cite{Cite8}, (c) An image of galaxy \cite{Cite8}}  \label{fig:galaxy12}
\end{figure}



\hl{Tables and figures should be capitalised and referred to by the number in the text and not abbreviated (e.g. "see in Figure 1" rather than "Fig. 1" or "figure 1").}


%------------------------------------------------

\section{Section 3}

\hl{The titles of the sections should be written in lower case except for the first word and for proper names (e.g. 
"The matrix of the Weingarten map of hypersurface"). }\newpage

\subsection{Subsection}
\hl{The titles of the subsections should be written in lower case except for the first word and for proper names (e.g. 
"The matrix of the Weingarten map of hypersurface"). }


\hl{This is an example of a table:}

\begin{table}[h!]
\caption{Table caption.}
\medskip
\centering \renewcommand{\arraystretch}{1.2}\scalebox{1.1}{ %This is for scaling.
\begin{tabular}{ccccc}
\hline
\hline
  & \textbf{Title 1} &  \textbf{Title 2} & \textbf{Title 3}  &  \textbf{Title 4} \\ \hline \hline
$\varphi_{11} $ & $\frac{\varphi_{11}} {\phi _{11}} $ & $\frac{\varphi_{12}} {\phi _{12}} $ & $\frac{\varphi_{13}} {\phi _{13}}$ & $\frac{\varphi_{14}} {\phi _{14}}$   \\ \hline
Data & Entry 1 & Entry 2  &  Entry 3 &   Entry 4  \\ \hline
(...) & (...)  & (...)  & (...)  & (...)  \\ \hline \hline
\end{tabular}
\label{tab:my-table2}
}
\end{table}
\section{Conclusions (Compulsory)}
 \hl{This section is compulsory. The conclusion should contain the main take-home message to come out of your work. The conclusion should be summarizing your main finding is sufficient, with the implications for future research. The conclusion should be directly related to the main objective and endpoint of the article.}

 This section is compulsory. The conclusion should encapsulate the main take-home message derived from your work. Summarizing your primary findings is sufficient, along with discussing their implications for future research. The conclusion should be directly related to the main objectives and endpoints of the article.


%------------------------------------------------



\section{Acknowledgements (if necessary)}
\hl{This section enable you to thank all who have helped in carrying out the paper. 
The names of the funding organisations should be spelt out completely.}





\textcolor{Acknowledgements are not mandatory. If they are included, they should be brief. Grant or contribution numbers may be acknowledged. For specific requirements, please refer to the journal-level guidelines.}



\section{About writing references}


The list of references should only include works that are cited in the text and that have been published or accepted for publication. Personal communications and unpublished works should only be mentioned in the text. Do not use footnotes or endnotes as a substitute for a reference list.  

\hl{The reference section should list all the sources you used in your article. It is your ethical and professional responsibility to reference your work adequately. Do not abbreviate last names. Use APA format. }


\begin{itemize}
    \item [i. ] \hl{Use single parentheses for citation numbers that appear together,} e.g. \cite{Cite2,Cite3}, not \cite{Cite2}, \cite{Cite3}. 
    \item [ii. ] \hl{References should be written with respect for punctuation and capitalisation.} 
 \item [iii. ]  \hl{References should be written in order of appearance, not alphabetical order. }
\end{itemize}


\hl{References should be written as follows:}

%	REFERENCE LIST
%----------------------------------------------------------------------------------------
%\phantomsection
%\bibliographystyle{unsrt}
%\bibliography{sample}

% use google scholar APA format  
\begin{thebibliography}{}
	
\bibitem{Cite1} Yüce, S. (2019). \textit{Weingarten map of the hypersurface in Euclidean 4-space and its applications}. Hagia Sophia Journal of Geometry, 1(1), 1--8. \hl{article}

\bibitem{Cite2}
Van der Waerden, B. L. (1976). \textit{Hamilton's discovery of quaternions}. Math. Mag., 49(5), 227--234. \hl{article}

\bibitem{Cite3} Ay, Ç., \& Yüce, S. (2024). \textit{
On slant submanifolds of para-quaternion Kaehler manifolds}. TWMS Journal of Pure and Applied Mathematics (accepted/in press).
\hl{accepted or in press paper}


\bibitem{Cite4} Gürses, N. B., Bektaş, Ö., \& Yüce, S. (2016). \textit{Special Smarandache curves in $\mathbb{R}^3_1$}. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(2), 143--160. \hl{article with more than one author}

\bibitem{Cite5}
Hamilton, W. R. (1853). Lectures on quaternions. Hodges and Smith, Dublin. \hl{book}


\bibitem{Cite6} Yüce, S. (2020). Linear algebra (in Turkish). 3rd Edition, Pegem Academy Publication, Ankara. \hl{non-English book}

\bibitem{Cite7} Molodtsov, D. A. (2004). Soft set theory (in Russian), URSS, Moscow. \hl{non-English book}


\bibitem{Cite8} Şentürk, G. Y., \& Yüce, S. (2017). \textit{The Spacelike ruled surfaces with Darboux frame in $\mathbb{E}^3_1$}. 15th International Geometry Symposium, Amasya, (p. 45). \hl{ conference} 



\bibitem{Cite9} Yüce, S. (1999). \textit{Homothety and connection preserving maps and their invariant in Lorentz space (in Turkish)}. Master’s Thesis, Ondokuz Mayıs University, Samsun.
\hl{master's thesis}

\bibitem{Cite10} Yüce, S. (2004). \textit{The generalization of Holditch theorem to two closed curves and an open curve (Holditch sickles) under homothetic motions (in Turkish)}. Doctoral Dissertation, Ondokuz Mayıs University, Samsun.
\hl{doctoral dissertation}


\bibitem{Cite11} Wikipedia, https://en.wikipedia.org/wiki/Deltoidal\_hexecontahedron. [Accessed 28 July 2023]. \hl{web page} 

\bibitem{Cite12} NASA, https://www.nasa.gov/image-feature/goddard/2021/hubble-images-a-galaxy-in-dazzling-detail. [Accessed 27 October 2023]. \hl{web page}


\bibitem{Cite13} Şentürk, G. Y., Gürses, N., \& Yüce, S. (2021). \textit{New insight into quaternions and their matrices}. https://www.preprints.org/manuscript/202104.0519/v1. [Accessed 27 October 2023]. \hl{misc}



 
\end{thebibliography}



\end{document}
