🚀 go-pugleaf

RetroBBS NetNews Server

Inspired by RockSolid Light RIP Retro Guy

Article View: fj.sci.math
Article #92

Re: self-similar lattice

#92
From: inoue kouichi
Date: Mon, 14 Sep 1992 03:59
83 lines
4571 bytes
  $@0f>e!wBg:eI\N)9b@l$G$9!#$I$&$b$"$j$,$H$&$4$6$$$^$9!#Bg:e650iBg$N1[6M(J
$@$5$s$K$b46<U$$$?$7$^$9!#<B$O5-;v$r=q$$$?$"$H!"2H$K5"$C$F9M$($F$?$iJ,$+$C(J
$@$F$7$^$$$^$7$?!#$=$7$F!";d$N2r<a$H$A$g$C$H0c$&$J$"$H;W$C$?$b$N$G!":#2s(J
$@$O$=$l$K$D$$$F=q$-$^$9!#(J
  $@$=$l$O!"!VAj;w!W$H$O$I$&$$$&$3$H$+$H$$$&$b$N$G$9!#;d$O%Y%/%H%k$G9M$((J
$@$F$^$7$?$N$G!"!JA02s(J(a,0),(0,b)$@$H=q$$$?$N$OI.$N8m$j$G$9!#(J(1,0),(a,b)$@$G(J
$@$9$M!"$[$s$H$O!KAj;w$H$$$&;~!"N"JV$7$N$b$N$b4^$a$F9M$($F$$$^$7$?!#1J9>(J
$@$5$s$N:G=i$N5-;v$d1[6M$5$s$N5-;v$O(JC$@Fb$G9M$($F$$$k$N$G!"$=$&$8$c$"$j$^$;(J
$@$s$h$M!#!J$D$^$j!"J?LL$NAj;wJQ4972$r(JGL(1,C) = SO(2)$@!&(JR^+$@$H$9$k$+!"(J
O(2)$@!&(JR^+$@$H$9$k$+$G$9!#!K(J
  $@$G!"N"JV$7$^$GF~$l$k$H!"<!$N$h$&$JNc$,$"$j$^$9!#(J

  $@#3JU$r(J 1,2^(1/4),2^(1/2) $@$H$9$k;03Q7A$r9M$(!"$3$l$GJ?LL$r=<E6$9$k!#(J
  $@$3$3$G$O!"86E@!"(J(1,0), ((2^(1/2)-1)/2,(3/2 2^(1/2) - 3/4)^(1/2))$@$N(J
  $@#3E@$rD:E@$H9M$(!"$U$?$D$N%Y%/%H%k(J v, w $@$r$3$N86E@0J30$N#2D:E@$N0L(J
  $@CV%Y%/%H%k$H$9$k!#$3$N$H$-!"(Jw+v, w-v $@$N:n$k;03Q7A$O85$N;03Q7A$HAj;w!#(J

  $@$3$&$$$&Nc$O$$$m$$$m:n$l$k$N$G$9$,!"$3$3$G9M$($F$$$k3J;R$O$b$A$m$s#2(J
$@<!$N@0?t$N$=$l$G$O$"$j$^$;$s!#$3$&$$$&>l9g$G$b!"LL@QHf$OI,$:@0?t$K$J$j(J
$@$^$9!#$=$l$O>ZL@$G$-$^$7$?!#$^$?!"#3<!850J>e$G$b@0?t$G$9!#0J2<$O$=$N>Z(J
$@L@!#(J

  v1,...,vn $@$N%Y%/%H%k$,(Jn$@<!85$N3J;R$r7A@.$7$F$$$k!#!J$D$^$j!"=LB`$7$F$$(J
$@$J$$$H$$$&$3$H$G$9!K$3$N;~!"3J;RFb3J;R$,85$N3J;R$HAj;w$H$$$&$3$H$r!"$"(J
$@$k(JO(n)$@$N85#A$,$"$C$F!"$^$?G\N(&A$,$"$C$F!"(J

   m1iv1+m2ivi+...+mnivi = $@&A#A(Jvi

$@$H$J$k$3$H$H$9$k!#$3$3$K!"(Jmij$@$O@0?t!#$3$N>e<0$N:8JU$O!"(J(v1 v2 ...vn) $@$H!"(J
$@%Y%/%H%k$r2#$KJB$Y$?9TNs$r#X$H$9$k$H!"(J

  $@#X(Jt(m1i,m2i,...,mni)

$@$H=q$1$k!#$3$3$G!"#t$OE>CV!#$3$l$r$5$i$K#i$K$D$$$FJB$Y$k$H!"(J

  $@#X#M(J = $@&A#A#X(J

$@$H$J$k!#$3$3$K!"#M(J = (mij) $@$H$$$&9TNs!#N>JU$N9TNs<0$r$H$k$H!"(J

  det($@#X(J)det($@#M(J) = +-$@&A(J^n det($@#X(J)

$@=LB`$7$F$J$$$+$i(J det($@#X(J)$@$O#0$G$O$J$/!"(Jdet($@#M(J)$@$O@0?t$@$+$i!"&A(J^$@#n!"$9$J(J
$@$o$ABN@QHf$O@0?t!#$^$?!"#M$K$D$$$F$N>r7o$O!"J#;($G$9$,!"(J

  t$@#M(Jt$@#X#X#M(J = $@&A(J^2t$@#X#X(J

$@$H$J$j$^$9!#!J(Jt$@#X#X$O(Jv1,...,vn$@$N$*8_$$$NFb@Q$r@.J,$H$9$kBP>N9TNs$G$9!#!K(J
$@;d$O$3$N<0$r$3$l0J>e4JC1$K$G$-$J$+$C$?$N$G!"!V#2<!$N@0?t$NC19`%$%G%"%k!W(J
$@$H$$$&$N$KL\$+$iNZ$N;W$$$G$7$?!#$3$A$i$N%"%W%m!<%A$O!"9b<!85$G$b$$$1$^(J
$@$9$+!)(J

In article <NAGAE.92Sep14001233@ipc4.an.isl.titech.ac.jp> nagae@an.isl.titech.ac.jp writes:
>>>$@!t(J $@<+8JAj;w6u4V=<E6$NOC$,$7$?$/$F$&$:$&$:$7$F$$$k$,!$2fK}$7$F$$$k(J :P
>>>$@!t(J $@Ii<!85$NOC$b$`$7$+$($7$?$$$1$I!$4.$($F$$$k(J^^;
>>
>>  $@$J$<4.$($F$$$k!)(J
>
>-----8<-----8<-----8<-----
>$@$@$C$FB@ED$5$s$,$$$8$a$k$s$@$b$s!%(J
>-----8<-----8<-----8<-----

  $@$$$d!":#B@ED;a$O(Jfj.news.policy$@$NJ}$NHsFq$KBP=h$9$k$N$KK;$7$=$&$G$9$h!#(J
$@:#$J$iBg>fIW!#!J!0!2!0!K!J$*$*!"4V1d$S$7$?4i$@!K(J

>$@0JA0$K!$(J2$@<!85$N<+8JAj;w3J;R!$$H$$$&Bj$GO@J8$G$b=q$3$&$+$J!<$H;W$C$F$[$C(J
>$@$?$i$+$7$F$k$N$,$"$C$?$s$G$9$,(J(^^)$@!$$"!$<+8JAj;w3J;R$H$$$&$N$O!$B$8l$G!$(J
>$@C10L3J;R$NItJ,=89g$,!$C10L3J;R$KAj;w$K$J$k$d$D$J$s$G$9$,!$$=$l$K$h$k$H!$(J

  $@8@$C$A$c$&$HEpMQ$5$l$^$9$h!J$[$s$H$+!)!K!"$9$0O@J8$K$9$k$Y$-$G$7$g$&!#(J

> $@H=JL<0(J: D = (m_1 + m_4)^2 - 4(m_1m_4 - m_2m_3) < 0.   ...(6)
>
>$@$H$$$&Fs<!J}Dx<0$N7A$K$^$H$a$i$l$F!$$a$G$?$/5uFs<!BN$N@0?t$NOC$K$?$I$j(J
>$@$D$/$o$1$G$9(J($@$U!<(J)$@!%(J

  $@$J$k$[$I!<!#(J

-- 
=================================== $@0f>e9@0l!wBg:eI\N)9b@l(J=====================
                   Phone : (0720) 21-6401 ($@Fb@~(J304)  Fax : (0720) 21-0134
                   E-mail: f51323@sakura.kudpc.kyoto-u.ac.jp
==============================================$@;d$O(Jmohta$@;a$K5wN%$r$*$-$^$9!#(J====
Technical Details
Message-ID: <1992Sep14.035937.4134@kudpc.kyoto-u.ac.jp>
Path: arc1-ca.pugleaf.net!sparky!uunet!sun-barr!sh.wide!wnoc-snd-ss2!akiu!hakata!kudpc!sakura.kudpc.kyoto-u.ac.jp!f51323
References: <NAGAE.92Sep11142606@momo.an.isl.titech.ac.jp> <1992Sep12.030706.18358@kudpc.kyoto-u.ac.jp> <NAGAE.92Sep14001233@ipc4.an.isl.titech.ac.jp>

Show Full Headers
Complete Article Headers
Path: arc1-ca.pugleaf.net!sparky!uunet!sun-barr!sh.wide!wnoc-snd-ss2!akiu!hakata!kudpc!sakura.kudpc.kyoto-u.ac.jp!f51323
From: f51323@sakura.kudpc.kyoto-u.ac.jp (inoue kouichi)
Newsgroups: fj.sci.math
Subject: Re: self-similar lattice
Message-ID: <1992Sep14.035937.4134@kudpc.kyoto-u.ac.jp>
Date: 14 Sep 92 03:59:37 GMT
References: <NAGAE.92Sep11142606@momo.an.isl.titech.ac.jp> <1992Sep12.030706.18358@kudpc.kyoto-u.ac.jp> <NAGAE.92Sep14001233@ipc4.an.isl.titech.ac.jp>
Sender: news@kudpc.kyoto-u.ac.jp
Distribution: fj
Organization: Osaka Prefectural College of Technology
Lines: 83
Nntp-Posting-Host: sakura.kudpc.kyoto-u.ac.jp