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my figures cut through the text, they leave spaces between each of then and text is filling this spaces. how can correct this ? figures are not in order.

\documentclass[11pt,reqno]{article}
%-------------------------------------------------------------------------%
\usepackage{amsmath,amsthm,amssymb,cite}
\usepackage{graphicx}
\usepackage{calrsfs}
\usepackage{wrapfig}
\usepackage{tikz}
\usepackage{color}
\usetikzlibrary{fit,bending}
\usetikzlibrary{calc}
%\usepackage[dvips]{graphicx}
\usepackage{epsfig}
\usetikzlibrary{arrows,chains,matrix,positioning,scopes}
\makeatletter
\tikzset{join/.code=\tikzset{after node path={%
            \ifx\tikzchainprevious\pgfutil@empty\else(\tikzchainprevious)%
            edge[every join]#1(\tikzchaincurrent)\fi}}}
\makeatother
\tikzset{>=stealth',every on chain/.append style={join},         every join/.style={->}}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{conjecture}[theorem]{Conjecture}
%\theoremstyle{definition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{Definition}[theorem]{Definition}
\newtheorem{Acknowledgments}[theorem]{Acknowledgments}
\usepackage[english, georgian]{babel}
\begin{document}


  სტანდარტული ფორქები \\

\begin{figure}[htbt]
  \centering
  \let\nobreakspace\relax
  \begin{tikzpicture}

\filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);


\filldraw [gray] (-2-4.2,0) circle (1pt); 
\filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
\filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
\filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
\filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
\filldraw [gray] (-4.2,2/3) circle (1pt);

\tikzstyle{every node}=[font=\large]
\node[above right] at (-2-4.2, 0) {$p_0$};
\node[above] at (-2/3-4.2, 2/3) {$p_1$};
\node[above] at (2/3-4.2,2/3) {$p_2$};
\node[above] at (2/3-4.2,-2/3) {$p_3$};
\node[above] at (-2/3-4.2,-2/3) {$p_4$};
\node[above] at (-4.2,2/3) {$z$};

\draw[color=black!60, thick, rounded corners=8pt] (-2-4.2, 0) -- (-4.2,0) -- (-4.2,2/3);
\draw[color=black!60, thick][->] (-2/3-4.2, 2/3) -- (2/3-4.2,2/3);



\filldraw[color=black!60, fill=white, very thick](0,0) circle (2);


\filldraw [gray] (-2,0) circle (1pt); 
\filldraw [gray] (-2/3,2/3) circle (1pt);    
\filldraw [gray] (2/3,2/3) circle (1pt);    
\filldraw [gray] (2/3,-2/3) circle (1pt);    
\filldraw [gray] (-2/3,-2/3) circle (1pt);
\filldraw [gray] (2/3,0) circle (1pt);

\tikzstyle{every node}=[font=\large]
\node[above right] at (-2, 0) {$p_0$};
\node[above] at (-2/3, 2/3) {$p_1$};
\node[above] at (2/3,2/3) {$p_2$};
\node[above] at (2/3,-2/3) {$p_3$};
\node[above] at (-2/3,-2/3) {$p_4$};
\node[right] at (2/3,0) {$z$};

\draw[color=black!60, thick] (-2, 0) -- (2/3,0);
\draw[color=black!60, thick][<-] (2/3, -2/3) -- (2/3,2/3);



\filldraw[color=black!60, fill=white, very thick](4.2,0) circle (2);


\filldraw [gray] (-2+4.2,0) circle (1pt); 
\filldraw [gray] (-2/3+4.2,2/3) circle (1pt);    
\filldraw [gray] (2/3+4.2,2/3) circle (1pt);    
\filldraw [gray] (2/3+4.2,-2/3) circle (1pt);    
\filldraw [gray] (-2/3+4.2,-2/3) circle (1pt);
\filldraw [gray] (4.2,-2/3) circle (1pt);

\tikzstyle{every node}=[font=\large]
\node[above right] at (-2+4.2, 0) {$p_0$};
\node[above] at (-2/3+4.2, 2/3) {$p_1$};
\node[above] at (2/3+4.2,2/3) {$p_2$};
\node[above] at (2/3+4.2,-2/3) {$p_3$};
\node[above] at (-2/3+4.2,-2/3) {$p_4$};
\node[below] at (4.2,-2/3) {$z$};

\draw[color=black!60, thick, rounded corners=8pt] (-2+4.2, 0) -- (4.2,0)-- (4.2,-2/3);

\draw[color=black!60, thick] [<-] (-2/3+4.2, -2/3) -- (2/3+4.2,-2/3);


  \end{tikzpicture}
  \caption{Standard forks:  $F_1,~~F_2,~~F_3$}
  \label{figure 3}
\end{figure}
\begin{figure}[htbt]
    \centering
    \let\nobreakspace\relax
    \resizebox{150pt}{!}{%  
        \begin{tikzpicture}

        \filldraw[color=black!60, fill=white, very thick](0,0) circle (2);


        \filldraw [gray] (-2,0) circle (1.5pt); 
        \filldraw [gray] (-2/3,2/3) circle (1pt);    
        \filldraw [gray] (2/3,2/3) circle (1pt);    
        \filldraw [gray] (2/3,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3,-2/3) circle (1pt);
        \filldraw [gray] (20/21,0) circle (1pt);

        \tikzstyle{every node}=[font=\large]
        \node[above right] at (-2, 0) {$p_0$};
        \node[below] at (-2/3, 2/3) {$p_1$};
        \node[below] at (2/3,2/3) {$p_2$};
        \node[above] at (2/3,-2/3) {$p_3$};
        \node[above] at (-2/3,-2/3) {$p_4$};
        \node[right] at (21/20,0) {z};
        \draw[color=black!60, thick] (-2,0) -- (2/3+0.3,0);
        \draw[color=black!60, thick, rounded corners=8pt, -  ] (-2/3,2/3) -- (-2/3,2/3+0.3) - - (2/3+0.3,2/3+0.3) - - (2/3+0.3,-2/3-0.3) - - (-2/3,-2/3-0.3) - - (-2/3,-2/3);
        \draw[color=black!60, thick,->] (-0.3,2/3+0.3) - - (0.3,2/3+0.3);
        \draw[color=black!60, thick,->] (2/3+0.3,0.6) - - (2/3+0.3,0.3);
        \draw[color=black!60, thick,->] (2/3+0.3,-0.3) - - (2/3+0.3,-0.6);
        \draw[color=black!60, thick,->] (0.3,-2/3-0.3) - - (-0.3,-2/3-0.3);
        \end{tikzpicture}
    }
    \label{figure 2}
\end{figure}
{\Large   $p_0$$z$ }მონაკვეთს ვუწოდებთ ფორქის სახელურს, ხოლო {\Large $p_1$$p_4$} მრუდს ფორქის კბილანებს.\\


\begin{figure}[htbt]
    \centering
    \let\nobreakspace\relax
    \begin{tikzpicture}


    \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

    %\draw[color=red!60, fill=white, thick,] (-4.2,2) arc (0:-90:2);
    \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (-4.2, 0) - - (-4.2, 2);

    \filldraw [gray] (-2-4.2,0) circle (1pt); 
    \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
    \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);

    \tikzstyle{every node}=[font=\large]
    \node[above right] at (-2-4.2, 0) {$p_0$};
    \node[above] at (-2/3-4.2, 2/3) {$p_1$};
    \node[above] at (2/3-4.2,2/3) {$p_2$};
    \node[above] at (2/3-4.2,-2/3) {$p_3$};
    \node[above] at (-2/3-4.2,-2/3) {$p_4$};





    \filldraw[color=black!60, fill=white, thick](0,0) circle (2);

    \draw[color=red!60, thick, ->] (-2,0) - - (2,0);

    \filldraw [gray] (-2,0) circle (1pt); 
    \filldraw [gray] (-2/3,2/3) circle (1pt);    
    \filldraw [gray] (2/3,2/3) circle (1pt);    
    \filldraw [gray] (2/3,-2/3) circle (1pt);    
    \filldraw [gray] (-2/3,-2/3) circle (1pt);

    \tikzstyle{every node}=[font=\large]
    \node[above right] at (-2, 0) {$p_0$};
    \node[above] at (-2/3, 2/3) {$p_1$};
    \node[above] at (2/3,2/3) {$p_2$};
    \node[above] at (2/3,-2/3) {$p_3$};
    \node[above] at (-2/3,-2/3) {$p_4$};





    \filldraw[color=black!60, fill=white, thick](4.2,0) circle (2);


    \draw[color=red!60, thick, rounded corners=10pt, - > ] (-2+4.2,0) - - (4.2, 0) - - (4.2, -2);


    \filldraw [gray] (-2+4.2,0) circle (1pt); 
    \filldraw [gray] (-2/3+4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3+4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3+4.2,-2/3) circle (1pt);    
    \filldraw [gray] (-2/3+4.2,-2/3) circle (1pt);

    \tikzstyle{every node}=[font=\large]
    \node[above right] at (-2+4.2, 0) {$p_0$};
    \node[above] at (-2/3+4.2, 2/3) {$p_1$};
    \node[above] at (2/3+4.2,2/3) {$p_2$};
    \node[above] at (2/3+4.2,-2/3) {$p_3$};
    \node[above] at (-2/3+4.2,-2/3) {$p_4$};


    \end{tikzpicture}
    \caption{Standard noodles: $N_1,~~N_2,~~N_3$}
    \label{figure 5}
\end{figure}
 დავითვალოთ მოცემული $\sigma_1$ ბრეიდის შესაბამისი მატრიცა. გამოვიყენოთ შემდები ჩადგმა $\left\langle F_i\sigma ,N_j\right\rangle$.\\
\begin{figure}[htbp]
 \centering
 \begin{tikzpicture}[bullet/.style={circle,fill,inner sep=1pt}]
 \begin{scope}[local bounding box=stuff]
 \path foreach \Y in {1,2,3,4}
 {(225-\Y*90:1) node[bullet,label=above:$P_\Y$] (B\Y){}};
 \draw[thick,-stealth,shorten >=2pt,shorten <=2pt] 
 (B2) edge[bend right] (B1) (B1) edge[bend right] (B2); 
 \end{scope};
  \node[circle,draw,fit=(stuff)]{};
 \end{tikzpicture}
 \caption{$\sigma_1$}
 \end{figure}

პირველი სვეტის პირველი სტრიქონის დასათვლელად($i=1$,$j=1$) $\sigma$ ბრეიდზე ვიმოქმედოთ  $F_1$ ფორქით და $N_1$ ნუდლით.(სურ.5)\\
       \begin{figure}
       \centering

        \begin{tikzpicture}

    \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

    \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, 2);


    \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3-3.7, -0.1) - - (2/3-3.7, 2/3+0.2)--(2/3-4.4, 2/3+0.2)--(2/3-4.4, 2/3);
    \draw[color=black!60, thick,  -> ] (2/3-4.2,2/3) -- (-2/3-4.2, 2/3);

    \filldraw [gray] (-2-4.2,0) circle (1pt); 
    \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
    \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
    \tikzstyle{every node}=[font=\large]
    =   \node[right] at (-2-4.2, 0) {$p_0$};
    \node[above] at (-2/3-4.2, 2/3) {$p_1$};
    \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
    \node[above] at (2/3-4.2,-2/3) {$p_3$};
    \node[above] at (-2/3-4.2,-2/3) {$p_4$};
  \end{tikzpicture} 
     \caption{$F_1\sigma_1 ,N_1$}
      \end{figure}

    მატრიცის პირველი წევრის ($a_{11}$) დასათვლელად ჯერ გავარკვიოთ $t$ პარამეტრის ნიშანი. ნიშანი იყოს დადებითი თუ ფორქის დადებითი მიმართულებიდან ნუდლის დადებით მიმართულებაზე გადასვლა ხდება მარცხნიდან.(უარყოფითი თუ გადასვლა ხდება მარჯვნიდან). ანუ მოძრაობას ვიწყებთ $p_0$ წერტილიდან მივუყვებით ფორქის სახელურს შემდეგ ვაგრძელებს მოძრაობას ფორქის კბილანაზე ნუდლთან მისვლამდე და თუ ნუდლზე გადასასვლელად მიწევს მარცხნივ "მოხვევა" $t$ პარამეტრის ნიშანი იქნება დადებითი.(მარჯვნივ-უარყოფითი)\\
    \begin{figure}
   \centering
    \definecolor{ffqqqq}{rgb}{1,0,0}
    \begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=0.5cm,y=0.5cm]
    \clip(-0.07329043126526,-0.796492988559363) rectangle (9.567791037095613,9.97807138066155);
    \draw [->,line width=2pt] (10,5) -- (0,5);
    \draw [->,line width=2pt] (5,0) -- (5,10);
    \draw [shift={(10-5,5.001014801310472)},line width=2pt,color=ffqqqq]  plot[domain=1.5707963267948966:2.8257080879245375,variable=\t]({1*2.4229434178792486*cos(\t r)+0*2.4229434178792486*sin(\t r)},{0*2.4229434178792486*cos(\t r)+1*2.4229434178792486*sin(\t r)});
    \draw [->,line width=2pt,color=ffqqqq] (2.696939088106593,5.7537200838434694) -- (2.544859707985099,5);
    \begin{scriptsize}
    \draw [fill=black] (10,9.833835474935935) circle (0.5pt);
    \draw[color=black] (7.00904720302078,9.489934628472703) node {\Large {$Fork$}};
    \draw [fill=black] (5.674489813878187,5) circle (0.5pt);
    \draw[color=black] (1.399712145615680487,4.03933260822143) node {\Large {$Noodle$}};
    \end{scriptsize}
    \end{tikzpicture}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=0.5cm,y=0.5cm]
\clip(-0.07329043126526,-0.796492988559363) rectangle (9.967791037095613,9.97807138066155);
\draw [->,line width=2pt] (0,5)--(10,5) ;
\draw [->,line width=2pt] (5,0) -- (5,10);
\draw [->,shift={(10-5,5)},line width=2pt,color=ffqqqq] (0,2) arc(90:00:2);
\begin{scriptsize}
\draw [fill=black] (10,9.833835474935935) circle (0.5pt);
\draw[color=black] (7.00904720302078,9.489934628472703) node {\Large {$Fork$}};
\draw [fill=black] (5.674489813878187,5) circle (0.5pt);
\draw[color=black] (7.699712145615680487,4.03933260822143) node {\Large {$Noodle$}};
\end{scriptsize}
\end{tikzpicture}
    \caption{დადებითი(მარცხნივ)  , უარყოფითი(მარჯვნივ)}

\end{figure}
  როგორც $F_1\sigma_1 ,N_1$ ნახაზზე ვხედავთ გადავსლა კბილანიდან ნუდლზე ხდება მარჯვნიდან, ანუ $t$ პარამეტრის ნიშანი იქნება უარყოფითი.\\ 
  \ $t$-ს ხარისხის დასათვლელად ვიწყებთ ისევ მოძრაობას $p_0$  წერტილიდან მივუყვებით ფორქის სახელურს მივდივართ ნუდლამდე და შემდეგ ნუდლის გასწვრივ მოძრაობით ვუბრუნდებით $p_0$ წერტილს.(სურ.5)\\ 
  \begin{figure}
       \centering
        \begin{tikzpicture}

    \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

    \draw[color=red!60, thick, rounded corners=10pt, - ] (-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, 2/3);


    \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3-3.7, -0.1) - - (2/3-3.7, 2/3+0.2)--(2/3-4.4, 2/3+0.2)--(2/3-4.4, 2/3);
    \draw[color=black!60, thick,  - ] (2/3-4.2,2/3) -- (-4.2, 2/3);

    \filldraw [gray] (-2-4.2,0) circle (1pt); 
    \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
    \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
    \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
    \tikzstyle{every node}=[font=\large]
    =   \node[right] at (-2-4.2, 0) {$p_0$};
    \node[above] at (-2/3-4.2, 2/3) {$p_1$};
    \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
    \node[above] at (2/3-4.2,-2/3) {$p_3$};
    \node[above] at (-2/3-4.2,-2/3) {$p_4$};
    \end{tikzpicture}
    \caption{}
    \label{figure5}
  \end{figure}
   მოძრაობისას შემოვლილი წერტილებს მივანიჭოთ რიცხვითი მნიშნელობები. თუ წერტილს შემოვუვლის საათის ისრის მიმართულებით მისი შესაბამისი რიცხვითი მნიშნელობა იქნება $-1$. თუ შემოვლა ხდება საათის ისრის საწიინაღმდეგო მიმართულებით $1$. $t$-ს  $\alpha$ ხარისხი ტოლი იქნება მოძრაობისას შემოვლილი წერტილების შესაბამისი მნიშნელობების ჯამის. სურ.5-დან ჩანს რომ შემოუარეთ ერთ წერტილს საათის ისრის საწინააღმდეგო მიმართულებით ამიტომ  $\alpha=1$.\\
   ზემოთ ხსენებული განმარტებებიდან გამომდინარე $a_{11}$-ს ნიშანი იქნება უარყოფითი, ხარისხი კი 1, ამიტომ $a_{11}=-t$
     ეხლა ვნახოთ $F_1\sigma_1 ,N_2$ და $F_1\sigma_1 ,N_3$-ის ნახაზები:\\
          \begin{figure}
        \centering
        \begin{tikzpicture}

        \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ](-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, 2);


        \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3-3.7, -0.1) - - (2/3-3.7, 2/3+0.2)--(2/3-4.4, 2/3+0.2)--(2/3-4.4, 2/3);
        \draw[color=black!60, thick,  -> ] (2/3-4.2,2/3) -- (-2/3-4.2, 2/3);

        \filldraw [gray] (-2-4.2,0) circle (1pt); 
        \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
        \tikzstyle{every node}=[font=\large]
        =   \node[right] at (-2-4.2, 0) {$p_0$};
        \node[above] at (-2/3-4.2, 2/3) {$p_1$};
        \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
        \node[above] at (2/3-4.2,-2/3) {$p_3$};
        \node[above] at (-2/3-4.2,-2/3) {$p_4$};
        \end{tikzpicture} 

            \begin{tikzpicture}

        \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, -2);


        \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3-3.7, -0.1) - - (2/3-3.7, 2/3+0.2)--(2/3-4.4, 2/3+0.2)--(2/3-4.4, 2/3);
        \draw[color=black!60, thick,  -> ] (2/3-4.2,2/3) -- (-2/3-4.2, 2/3);

        \filldraw [gray] (-2-4.2,0) circle (1pt); 
        \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
        \tikzstyle{every node}=[font=\large]
        =   \node[right] at (-2-4.2, 0) {$p_0$};
        \node[above] at (-2/3-4.2, 2/3) {$p_1$};
        \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
        \node[above] at (2/3-4.2,-2/3) {$p_3$};
        \node[above] at (-2/3-4.2,-2/3) {$p_4$};
        \end{tikzpicture} 
        \caption{$F_1\sigma_1 ,N_2$, $F_1\sigma_1 ,N_3$}
     \end{figure}\\
   თუ ნუდლი არ კვეთს ფორქის კბილანებს მისი შემისაბამისი მნიშნელობა იქნება  $0$. რადგან  $F_1\sigma_1 ,N_2$ და $F_1\sigma_1 ,N_3$ ნახაზებზე ნუდლი არ კვეთს კბილანებს {\large $a_{21}$}={\large $a_{31}$}=0.\\
    ზუსტად იგივე პირციპით დავიტვალოთ მატრიცის დანარჩენი წევრებიც.

    \begin{figure}

        \centering
            \begin{tikzpicture}

        \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, 2);


        \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3+0.2-4.2, -0.1);
        \draw[color=black!60, thick,rounded corners=5pt,  -> ] (-2/3-4.2, 2/3)--(-2/3-4,2/3+0.2)--(2/3+0.2-4.2,2/3+0.2)--(2/3+0.2-4.2,-2/3+0.2)--(2/3-4.2,-2/3);

        \filldraw [gray] (-2-4.2,0) circle (1pt); 
        \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
        \tikzstyle{every node}=[font=\large]
        =   \node[right] at (-2-4.2, 0) {$p_0$};
        \node[above] at (-2/3-4.2, 2/3) {$p_1$};
        \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
        \node[above] at (2/3-4.35,-2/3) {$p_3$};
        \node[above] at (-2/3-4.2,-2/3) {$p_4$};
        \end{tikzpicture}
            \begin{tikzpicture}

        \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (2-4.2, 0) ;


        \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3+0.2-4.2, -0.1);
        \draw[color=black!60, thick,rounded corners=5pt,  -> ] (-2/3-4.2, 2/3)--(-2/3-4,2/3+0.2)--(2/3+0.2-4.2,2/3+0.2)--(2/3+0.2-4.2,-2/3+0.2)--(2/3-4.2,-2/3);

        \filldraw [gray] (-2-4.2,0) circle (1pt); 
        \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
        \tikzstyle{every node}=[font=\large]
        =   \node[right] at (-2-4.2, 0) {$p_0$};
        \node[above] at (-2/3-4.2, 2/3) {$p_1$};
        \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
        \node[above] at (2/3-4.35,-2/3) {$p_3$};
        \node[above] at (-2/3-4.2,-2/3) {$p_4$};
        \end{tikzpicture} 
            \begin{tikzpicture}

        \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, -2);


        \draw[color=blue!100, thick, rounded corners=5pt, - ]  (-2-4.2,0) - - (-2-4.2,-0.1) -- (2/3+0.2-4.2, -0.1);
        \draw[color=black!60, thick,rounded corners=5pt,  -> ] (-2/3-4.2, 2/3)--(-2/3-4,2/3+0.2)--(2/3+0.2-4.2,2/3+0.2)--(2/3+0.2-4.2,-2/3+0.2)--(2/3-4.2,-2/3);

        \filldraw [gray] (-2-4.2,0) circle (1pt); 
        \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
        \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3-4.2,-2/3) circle (1pt);
        \tikzstyle{every node}=[font=\large]
        =   \node[right] at (-2-4.2, 0) {$p_0$};
        \node[above] at (-2/3-4.2, 2/3) {$p_1$};
        \node[above] at (2/3-4.2,2/3+0.2) {$p_2$};
        \node[above] at (2/3-4.35,-2/3) {$p_3$};
        \node[above] at (-2/3-4.2,-2/3) {$p_4$};
        \end{tikzpicture} 
        \caption{$F_2\sigma_1 ,N_1$,$F_2\sigma_1 ,N_2$,$F_2\sigma_1 ,N_3$}
        \end{figure}

       $a_{12}=t$ ,$a_{22}=1$, $a_{32}=0$ \\
        \begin{figure}
            \centering
                \begin{tikzpicture}
            \filldraw[color=black!60, fill=white, very thick](-4.2,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2-4.2,0) -- (0-4.2, 0) - - (0-4.2, 2);
            \filldraw [gray] (-2-4.2,0) circle (1pt); 
            \filldraw [gray] (-2/3-4.2,2/3) circle (1pt);    
            \filldraw [gray] (2/3-4.2,2/3) circle (1pt);    
            \filldraw [gray] (2/3-4.2,-2/3) circle (1pt);    
            \filldraw [gray] (-2/3+4.2,-2/3) circle (1pt);
            \filldraw [gray] (-4.2,-2/3) circle (1pt);

            \tikzstyle{every node}=[font=\large]
            \node[above right] at (-2-4.2, 0) {$p_0$};
            \node[above] at (-2/3-4.2, 2/3) {$p_1$};
            \node[above] at (2/3-4.2,2/3) {$p_2$};
            \node[above] at (2/3-4.2,-2/3) {$p_3$};
            \node[above] at (-2/3-4.2,-2/3) {$p_4$};


            \draw[color=blue!60, thick, rounded corners=8pt] (-2-4.2, 0) --(-2-4.1, 0.2)--(-4.2, 0.2)-- (-4.2,-2/3);

            \draw[color=black!60, thick] [<-] (-2/3-4.2, -2/3) -- (2/3-4.2,-2/3);


        \filldraw[color=black!60, fill=white, very thick](0,0) circle (2);

        \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2,0) -- (2, 0);
        \filldraw [gray] (-2,0) circle (1pt); 
        \filldraw [gray] (-2/3,2/3) circle (1pt);    
        \filldraw [gray] (2/3,2/3) circle (1pt);    
        \filldraw [gray] (2/3,-2/3) circle (1pt);    
        \filldraw [gray] (-2/3,-2/3) circle (1pt);
        \filldraw [gray] (-4.2,-2/3) circle (1pt);

        \tikzstyle{every node}=[font=\large]
        \node[above right] at (-2, 0) {$p_0$};
        \node[above] at (-2/3, 2/3) {$p_1$};
        \node[above] at (2/3,2/3) {$p_2$};
        \node[above] at (2/3,-2/3) {$p_3$};
        \node[above] at (-2/3,-2/3) {$p_4$};


        \draw[color=blue!60, thick, rounded corners=8pt] (-2, 0) --(-2+0.1, 0.2)--(0, 0.2)-- (0,-2/3);

        \draw[color=black!60, thick] [<-] (-2/3, -2/3) -- (2/3,-2/3);


  \filldraw[color=black!60, fill=white, very thick](+4.2,0) circle (2);

 \draw[color=red!60, thick, rounded corners=10pt, -> ] (-2+4.2,0) -- (0+4.2, 0) - - (0+4.2, -2);
  \filldraw [gray] (-2+4.2,0) circle (1pt); 
  \filldraw [gray] (-2/3+4.2,2/3) circle (1pt);    
  \filldraw [gray] (2/3+4.2,2/3) circle (1pt);    
  \filldraw [gray] (2/3+4.2,-2/3) circle (1pt);    
  \filldraw [gray] (-2/3+4.2,-2/3) circle (1pt);
  \filldraw [gray] (+4.2,-2/3) circle (1pt);

  \tikzstyle{every node}=[font=\large]
  \node[above right] at (-2+4.2, 0) {$p_0$};
  \node[above] at (-2/3+4.2, 2/3) {$p_1$};
  \node[above] at (2/3+4.2,2/3) {$p_2$};
  \node[above] at (2/3+4.2,-2/3) {$p_3$};
  \node[above] at (-2/3+4.2,-2/3) {$p_4$};


  \draw[color=blue!60, thick, rounded corners=8pt] (-2+4.2, 0) --(-2+4.3, 0.2)--(+4.4, 0.2)-- (4.4,-2/3);

  \draw[color=black!60, thick] [<-] (-2/3+4.2, -2/3) -- (2/3+4.2,-2/3);


  \end{tikzpicture}
  \caption{$F_3\sigma_1 ,N_1$,~~$F_3\sigma_1 ,N_2$,~~$F_3\sigma_1 ,N_3$}
        \end{figure}


         $a_{13}=0$ ,$a_{23}=0$, $a_{33}=1$\\
         $\sigma_1$-ის შესაბამის მატრიცას აქვს შემდეგი სახე :

        \[\rho \left({\sigma }_1\right)=\left( \begin{array}{ccc}
         -t & t & 0 \\ 
         0 & 1 & 0 \\ 
         0 & 0 & 1 \end{array}
         \right)\\  \]
         \end{document}
Levan Davitadze
  • 13

0 Answers0