離散ラプラス作用素の反復力学系による蝶の翅紋様の実現とこれに基づく進化モデルの構成 (第7回生物数学の理論とその応用)

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みいかはにうだ
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$(2) (3) (2) $\ovalbox{\tt\small REJECT}$ (1) (2) (3) (3) D $N$$

1 ( ) (B ) ( ) ( ) (1) (2) (3) (1) 4 (1) (2) (3) (2) $\ovalbox{\tt\small REJECT}$ (1) (2) (3) (3) D $N$ A

$132 2 ([1]) 1 $0$ $F$ $f\in F$ $\Delta_{t\prime},f(p)=\sum_{\epsilon(\prime},(f(q)-f(p))$ $U_{\rho}$ $p\in L$ ( ) Moor Niuman Dlag$

2 132 2 ([1]) 1 $0$ $F$ $f\in F$ $\Delta_{t\prime},f(p)=\sum_{\epsilon(\prime},(f(q)-f(p))$ $U_{\rho}$ $p\in L$ ( ) Moor Niuman Dlag Neumen Hoxagonal Slofplnskl $f_{0}\in F$ $\{f,,\}$ $f_{n}(p)=\delta_{t\prime_{p}}f_{n-1}(p)$ $M$ $M$ 3 ([1]) (1) (2) $M=\iota 28$ Moore 1

$$\not\in\cdot\cdot,\triangleright,*\cdot\backslash u\infty$ 133 (3) (4) 3$

3 $\not\in\cdot\cdot,\triangleright,*\cdot\backslash u\infty$ 133 (3) (4) 3 ([2]) $)$ (Evolutionary Developmental Biology) (1) ( ) $-_{-}1\underline{l}$

$$\prime_{\backslash _{\backslash }} ( \acute{\dot{d}}_{\dot{t}^{\dot{o}^{=},}}^{\vee}\cdot\cdot\cdot\cdot$ \cdot\backslash ;$ $\ovalbox{\tt\small REJECT}_{\vee^{\vee}}^{-}\backslash$

4 $\prime_{\backslash _{\backslash }} ( \acute{\dot{d}}_{\dot{t}^{\dot{o}^{=},}}^{\vee}\cdot\cdot\cdot\cdot$ \cdot\backslash ;$ $\ovalbox{\tt\small REJECT}_{\vee^{\vee}}^{-}\backslash \wedge\cdot\cdot\sim\wedge^{-}\alpha\sim$ $\tau$ 134 (2) $\circ n$ off $*$a $*\hslash**$ / $\text{ ^{}s_{\alpha_{\backslash }\backslash -\cdot}}\cdot\cdot_{-\dot{\cdot}}$ $\Psi=,l \backslash $^{rr-c\downarrow}$ $\vee^{\ },,$ 4 ([2], [4], [8]) (1) ( ) (2) (3) 4 ( ) $**\sim u_{\backslash,u}$ Hbx ( )

5 $=\cdot\cdot\prime 9d\backslash \cdot a\}$ $\overline{a}^{\text{ _{}\backslash }\mathfrak{c}}$ $\sim$ t $_{r_{\wedge\cdot\kappa^{\backslash,;_{**\cdot r\cdot-\backslash f*\cdot}^{\backslash *}}}}\Re_{--7_{*\dot{u}\alpha s}^{-,*\cdot m_{-}\cdot,-_{-}}\prime s--\cdot\cdot w\cdot-}\cdot$ $\ovalbox{\tt\small REJECT}_{1}^{\wedge} -\ovalbox{\tt\small REJECT}_{I}$ $*\cdot $ $ $ 135 (4) ( ) $*la\phi;\nu $\mathscr{n}_{--,-}\sim\vee $ $ux^{-}$ $-\overline{r}1*$, $\sim n- $\infty_{r^{\sim}}$ $\infty\wedge^{\wedge}u_{-}-\mu^{\vee} -\cdotarrow\overline{d}^{\wedge}\mathfrak{q}^{\gamma}d+arrow\backslash --$ x\alpha\psi 1 \cdot\cdot$ $ J \neg$ - $$ r $-\ldots\cdot$ $t_{text{ }}$ u$ $-\infty_{-\dotplus}--$ y $\alpha u$ $- \oint^{r_{\ -}},$ 4;, $ -^{\backslash \cdot\prime}\backslash \wedge 42xX\cdot\cdot\wedgebackslash *_{-,,\cdot,**r^{b}}\cdot,*-\alpha\backslash \cdot u,;^{\sim*;}$, $;, \#\cdot^{\iota,,-w\wedge d\kappa\nu} \}I \ldots$ 3 (1) ( ) ( ) REJECT}$ $\lambda$ $J\cdot-$ & #F$\ovalbox{\tt\small $\hat$ (2) ( ) ( ) $ $ $D^{-}$ $[\supset$ $[2$ (3) 4

6 $\ovalbox{\tt\small REJECT}_{\wedge-w\alpha^{\backslash }}^{\ovalbox{\tt\small REJECT}^{\wedge\sim\wedge}}\kappa r!\^{-}\backslash \ovalbox{\tt\small REJECT}*_{\wedge\cdot\sim}$ $S\mathscr{J}$ $t_{*,-}$ _{b}-\nearrow\backslash$ 136 (2) seeds $Q$ $$ $v$ $\mu_{c}_{\dot{\grave{h}},}$ $V_{\backslash }^{\prime} \cdot\backslash t\backslash B\vee$ $\alpha_{\backslash \sim}\re_{\wedge} $ $Q$ $ \check{\dot{\lambda}}^{\acute{\triangleleft}}\searrow P_{\wedge}$ $\cdot\backslash 4 (1) Ne ghborhood Analysis $i$ (2) Seed Analysis (5 ) (3) Separat ion Analys is 4 (6 ) ( ) seed (1) (2) (3) (4)

$\ovalbox{\tt\small REJECT}_{{}^{t}i}^{}\wedge A;$ $J$ $s$ mmetr $\acute{l}_{i^{=}}^{/}\prime J$ $\Omega_{\backslash }$ $(_{\sim}^{\backslash })$ $\langle_{\backslash }\backslash _{\backslash }1x$

7 $\ovalbox{\tt\small REJECT}_{{}^{t}i}^{}\wedge A;$ $J$ $s$ mmetr $\acute{l}_{i^{=}}^{/}\prime J$ $\Omega_{\backslash }$ $(_{\sim}^{\backslash })$ $\langle_{\backslash }\backslash _{\backslash }1x$ ([7]) 5 $\uparrow ype$ Standard seeds $\prime f4_{li}\cdot t_{\vee}$ $Y^{\cdot}yp*\mathfrak{R}t oty\varphi t)$ Standard Type seeds (1) Stall( $lu\cdot(1$ type defol$\mathfrak{n}iiati_{c\backslash 11S}\cdot$ ic neigh as nnnetr ic neigh (3) $F\iota utliel$ iiioi $e$ $\int_{\vee}\lfloor$ $1h^{}$ detoi lliatiol

8 ([3]) ([3])

9 $\{\begin{array}{l}\frac{\partial u}{\partial t}=\delta u+f(u,v)\frac{\partial v}{\partial t}=d\delta v+g(u,v)\end{array}$ $-$ $\Psi=\frac{\partial^{2}f}{\partial x^{2}}+\frac{\partial^{2}f}{\phi^{2}}$ $\ovalbox{\tt\small REJECT}^{^{\backslash \backslash \wedge=a}}\ovalbox{\tt\small REJECT}^{1}$ 139 $\{\Delta^{n}fn=1,2,\ldots\}\Rightarrow\frac{\partial f}{\partial t}=4(,$ Gi erer $-Meinhardt$ ([3 ]) ( ) $\ovalbox{\tt\small REJECT}^{b}\mathfrak{B}\ovalbox{\tt\small REJECT}$ ( (1990) ) [1]M Aiba, $0$ K Maigaito, Suzuki, Evolution model described by iteration dynamical system of discretelaplacian on the plane lattice, (2006) [2] [3] ( ) Vol 3, (2006) [4] S Narita, $0$ M Nomura, Y Kato, Yata and D Kageyama Molecular phylogeography of two sibling species of Eurema butterflies Genetica, 131 $(2007) $ $[5]0$ Suzuki Recent developments on the iteration dynamical systems of discrete Laplacians, Proc of IKEM(2009) (Weimar) $[6]0$ Suzuki (with Y Makino, C Hadlich, G Guerlebeck, A Kimura) Iteration dynamical systems od discrete Laplacians on the planelattice (Its mathematical structure and computer simulations of designs), , [71 Suzuki (with Makoto Mori and Yasuo Watatani) Representations of Cuntz algebras on $0$ fractal sets, Kyushu J Math vol $61, (2007)$ [8]H Umada and $0$ YataComparative morphology of the genus Chilasa (Lepidoptera, Pap $i1i$ on $i$ dae) Trans lepi Soc Jspsn 57 (1) 2006, $d$

Title 改良型 S 字型風車についての数値シミュレーション ( 複雑流体の数理とシミュレーション ) Author(s) 桑名, 杏奈 ; 佐藤, 祐子 ; 河村, 哲也 Citation 数理解析研究所講究録 (2007), 1539: Issue Date URL

Title 改良型 S 字型風車についての数値シミュレーション ( 複雑流体の数理とシミュレーション ) Author(s) 桑名, 杏奈 ; 佐藤, 祐子 ; 河村, 哲也 Citation 数理解析研究所講究録 (2007), 1539 43-50 Issue Date 2007-02 URL http//hdlhandlenet/2433/59070 Right Type Departmental